
From nobody Sat Jul  1 14:58:55 2017
Return-Path: <philipp@jovanovic.io>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 91A2E127137 for <cfrg@ietfa.amsl.com>; Sat,  1 Jul 2017 14:58:54 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.599
X-Spam-Level: 
X-Spam-Status: No, score=-2.599 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, RCVD_IN_DNSWL_LOW=-0.7, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id YUpu7bdiq2gd for <cfrg@ietfa.amsl.com>; Sat,  1 Jul 2017 14:58:52 -0700 (PDT)
Received: from perseus.uberspace.de (perseus.uberspace.de [95.143.172.134]) (using TLSv1.2 with cipher DHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id E338F126BFD for <cfrg@irtf.org>; Sat,  1 Jul 2017 14:58:51 -0700 (PDT)
Received: (qmail 25203 invoked from network); 1 Jul 2017 21:58:49 -0000
Received: from localhost (HELO ?IPv6:2a01:2a8:8106:7b01:5a5:5673:5aac:3d14?) (127.0.0.1) by perseus.uberspace.de with SMTP; 1 Jul 2017 21:58:49 -0000
From: Philipp Jovanovic <philipp@jovanovic.io>
Content-Type: multipart/signed; boundary="Apple-Mail=_483BC09B-987C-414D-A11D-28621B4A0E0F"; protocol="application/pgp-signature"; micalg=pgp-sha256
Mime-Version: 1.0 (Mac OS X Mail 10.3 \(3273\))
Message-Id: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io>
Date: Sat, 1 Jul 2017 23:58:47 +0200
To: cfrg@irtf.org
X-Mailer: Apple Mail (2.3273)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/1m05P2QAMZKdf4hQJhAJuL-5EuU>
Subject: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Sat, 01 Jul 2017 21:58:54 -0000

--Apple-Mail=_483BC09B-987C-414D-A11D-28621B4A0E0F
Content-Transfer-Encoding: quoted-printable
Content-Type: text/plain;
	charset=utf-8

Hi CFRG,

Here=E2=80=99s a first version of an Internet-Draft on =E2=80=9CCollective=
 Edwards-Curve Digital Signature Algorithms=E2=80=9D based on Ed25519 =
and Ed448: https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/

We plan to give a short presentation on that topic at the next CFRG =
meeting in Prague.

Any feedback is more than welcome. Thanks!

All the best,
Philipp

--Apple-Mail=_483BC09B-987C-414D-A11D-28621B4A0E0F
Content-Transfer-Encoding: 7bit
Content-Disposition: attachment;
	filename=signature.asc
Content-Type: application/pgp-signature;
	name=signature.asc
Content-Description: Message signed with OpenPGP

-----BEGIN PGP SIGNATURE-----
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=4CVG
-----END PGP SIGNATURE-----

--Apple-Mail=_483BC09B-987C-414D-A11D-28621B4A0E0F--


From nobody Sun Jul  2 13:47:35 2017
Return-Path: <oleganza@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 62700129ACD for <cfrg@ietfa.amsl.com>; Sun,  2 Jul 2017 13:47:34 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.7
X-Spam-Level: 
X-Spam-Status: No, score=-2.7 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id uJjCwjnRH9xY for <cfrg@ietfa.amsl.com>; Sun,  2 Jul 2017 13:47:32 -0700 (PDT)
Received: from mail-lf0-x234.google.com (mail-lf0-x234.google.com [IPv6:2a00:1450:4010:c07::234]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 23ABB129AC1 for <cfrg@irtf.org>; Sun,  2 Jul 2017 13:47:32 -0700 (PDT)
Received: by mail-lf0-x234.google.com with SMTP id b207so92765353lfg.2 for <cfrg@irtf.org>; Sun, 02 Jul 2017 13:47:32 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:subject:from:in-reply-to:date:cc :content-transfer-encoding:message-id:references:to; bh=ijySxrPCdDO1n3GyR5ToKGmd77qj3MRsX9Z9PjUPSwI=; b=Smq6UtQDAqqsIHrYxq+4SgIUOGVLS/LuYH4ONfRjBrqzCzFcWejLj3XzS4QvxAtHSA MjSBPJQEaoOSXWxD/848qjtaqiSuIrsTDfnxNpBSVqBPh/1PoJ9frraRU/yQJYzFG2cT CEMrLYE/Jknz/rcejx7LdB+A2k+BajXwPX+Q6D+bDq1ule7ilSvOIdUTD9dcy5yCmzK+ t4qLC4yZotYK9B2t4a6dZjcNl9dYhBAZDDZI//klVKxmApD85MThmXCGf91ww2z4VBc8 kB3t+R9MWfiiqULP7wHq4xENCiM2mb7DBuytg7TVADxqsv4TyIuPqbK4Zu0uBo1XZOAR mFBg==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:subject:from:in-reply-to:date:cc :content-transfer-encoding:message-id:references:to; bh=ijySxrPCdDO1n3GyR5ToKGmd77qj3MRsX9Z9PjUPSwI=; b=K1s0zUWHSREhbLbx2VmmMtBcgo50Fi0CCEt0j+au/qxMhUsBTtvLmAH8rrVGtePIG4 HyRt4lzDTverfnZ03doTCaOEv0ehAny3djINk47JTceFTEKQamJS/lvi8F4/UupoZQrL mRvOqNTrR5uoY+GA+AefiTOF3LhjcTMpcgEV35C6dU+kkLx0dlypqIACRTWvnk1jYINC Nxr1u90uShjUPo6B7Q0IwnKtVabWCUqQF0aWLnjoEGUB5LIthqQphp73k8H1jLiMNGsT +xYuxek4URiluiPNZ0UeLh4TTueWya9FnP1S3uC4n1oVJ7e6rHKEC7aJgrSfLhCrPK0I rwdw==
X-Gm-Message-State: AKS2vOyUV85LGkkf6a5suQWWjjSnNIoRPK6v1ThtC2XqXnDhEHHeLnOl dab/5v83/yg06g==
X-Received: by 10.25.89.65 with SMTP id n62mr10505398lfb.183.1499028450333; Sun, 02 Jul 2017 13:47:30 -0700 (PDT)
Received: from [192.168.0.114] ([109.167.133.56]) by smtp.gmail.com with ESMTPSA id m16sm2194568ljb.26.2017.07.02.13.47.29 (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Sun, 02 Jul 2017 13:47:29 -0700 (PDT)
Content-Type: text/plain; charset=utf-8
Mime-Version: 1.0 (Mac OS X Mail 10.3 \(3273\))
From: Oleg Andreev <oleganza@gmail.com>
In-Reply-To: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io>
Date: Sun, 2 Jul 2017 23:47:28 +0300
Cc: cfrg@irtf.org
Content-Transfer-Encoding: quoted-printable
Message-Id: <5E91769F-B102-4A49-9ED5-B789D4FED598@gmail.com>
References: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io>
To: Philipp Jovanovic <philipp@jovanovic.io>
X-Mailer: Apple Mail (2.3273)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/2QTaj7zR80ki0cNoAqng62b6roI>
Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Sun, 02 Jul 2017 20:47:34 -0000

Hi,

First of all: nice to see a simpler approach than a full SSSS-based =
threshold signing scheme!

After a quick glance at the spec, I have two security concerns:

1. It seems unsafe to add public keys directly (A =3D Sum[A_i]) without =
multiplying them by their hashes (A =3D Sum[Hash(A_i)*A_i]). Without =
that measure, it is possible to have A_j as a linear combination of =
other public keys. See this discussion for details: =
https://bitcointalk.org/index.php?topic=3D1377298.0

2. The signature does not commit to membership bitmask Z. Maybe it could =
be argued that signature is not malleable (especially with an =
improvement mentioned above), but to stay on safe side I think =
committing to the exact set of signers is a good idea.


Additionally, I'd suggest an improvement to the API. Since the scheme is =
not a SSSS scheme, verifier needs to reconstruct the exact key from the =
individual keys (4.3.5 Signature Verification). Current spec states that =
verifier should know the set of these member-keys upfront. It could be =
more practical to provide them as a part of the signature and commit =
into the aggregate public key, so the setup process looks as simple as =
non-aggregate one, or one using SSSS: just sharing a single aggregate =
public key.

This is how it could be done:

1. Organize all member keys in a merkle tree and compute it's root hash =
`h`.
2. Compute intermediate aggregate key as `A =3D Sum[Hash(A_i)*A_i]`.
3. Compute aggregate public key with commitment to the merkle tree: `P =3D=
 Hash(A || h)*A`.
4. Signature will include:
    1) necessary member keys according to bitmask Z.
    2) merkle proof (necessary intermediate hashes needed to reconstruct =
the root hash).
    3) intermediate key A.
5. Verifier would reconstruct root hash h', compute `Hash(h' || A)*A` =
and verify it matches the P. Then it will reconstruct actual =
verification key `A' =3D A-T` and proceed with Schnorr protocol.

The member keys part of the signature could be optional, so the keys =
could be cached in case many signature from the same key are =
continuously verified.

Cheers,
Oleg.

> On 2 Jul 2017, at 00:58, Philipp Jovanovic <philipp@jovanovic.io> =
wrote:
>=20
> Hi CFRG,
>=20
> Here=E2=80=99s a first version of an Internet-Draft on =E2=80=9CCollecti=
ve Edwards-Curve Digital Signature Algorithms=E2=80=9D based on Ed25519 =
and Ed448: https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/
>=20
> We plan to give a short presentation on that topic at the next CFRG =
meeting in Prague.
>=20
> Any feedback is more than welcome. Thanks!
>=20
> All the best,
> Philipp
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg


From nobody Mon Jul  3 02:19:04 2017
Return-Path: <wwhyte@onboardsecurity.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id D85DD13153C for <cfrg@ietfa.amsl.com>; Mon,  3 Jul 2017 02:19:01 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.999
X-Spam-Level: 
X-Spam-Status: No, score=-1.999 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=onboardsecurity.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id qooRR35mYQwy for <cfrg@ietfa.amsl.com>; Mon,  3 Jul 2017 02:18:59 -0700 (PDT)
Received: from mail-wr0-x22d.google.com (mail-wr0-x22d.google.com [IPv6:2a00:1450:400c:c0c::22d]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 089ED131467 for <cfrg@irtf.org>; Mon,  3 Jul 2017 02:18:59 -0700 (PDT)
Received: by mail-wr0-x22d.google.com with SMTP id c11so231108691wrc.3 for <cfrg@irtf.org>; Mon, 03 Jul 2017 02:18:58 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=onboardsecurity.com; s=google; h=mime-version:from:date:message-id:subject:to; bh=Z1gTlSynCtOcuW50Y7RjRygYEQ3AbaLcyqjUOpc/Dik=; b=g3su+1xvWftv/UJ36AbOPuqX9sqXdHyKOPCcslQrPwKWsEb6LQii5NQ4YNaahOI0Dk IdcoAIHfY2hCc+OprYlKiKZNXqEkdKSF15/SczNUibh2v2EUNOj73YYCTXgMEd79mSLY 81QHoAGAdwTqpY6LNWEr3YHaGLdWgKI+xUFi4=
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:from:date:message-id:subject:to; bh=Z1gTlSynCtOcuW50Y7RjRygYEQ3AbaLcyqjUOpc/Dik=; b=bhzutnopXxwC4MlyAHBn1SFK2FGcZmaMLLkKqowlrytALMnReBItBjKDYRjldvnufG aQ/SJlGLTQG5/+wBgwKETmYEkOeFFgXbzKoMpswL32f3f1Y9FsulPGtVnQ5/LDnuWjXn v4wHifdGfHEI1GsitCL9ApskoJ1whOmo4Q515dvsdyklYm08Opukyz4T3qwCoKXb/Do7 mC/U9W6Ddq5KUSJXbWf9hU6cW6HovWQvFm1JA7kEFxhaickFI1z7ZvPj2eG9tzG++Xoz IUHSipLRcqsvGqwXRErTq7icYqR2FHDJRZoUTMjPAYd43nKKmkpbRpd5vTPAHr3WPLtj D1Dg==
X-Gm-Message-State: AKS2vOxLqu9HNx8GtNUOS0STrNQG3apgV3q+uoSA6Fpu1b2VKhP1Emkm jbbS0K2OaMdFhSIxtu5s5SFJ/RRthCQNN1rtww==
X-Received: by 10.223.173.143 with SMTP id w15mr30116812wrc.113.1499073536839;  Mon, 03 Jul 2017 02:18:56 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.28.30.71 with HTTP; Mon, 3 Jul 2017 02:18:35 -0700 (PDT)
From: William Whyte <wwhyte@onboardsecurity.com>
Date: Mon, 3 Jul 2017 05:18:35 -0400
Message-ID: <CAND9ES2=pEvyYJOrQhO9uyGwWBMo6RtaXuRANW-hoKuH=g6GxA@mail.gmail.com>
To: CFRG <cfrg@irtf.org>
Content-Type: multipart/alternative; boundary="f403045cf65aa7eb2005536641db"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/0BV657UyF1HqlilE4MJ0Nzugi7I>
Subject: [Cfrg] Call for papers: Security Standardization Research 2017
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 03 Jul 2017 09:19:02 -0000

--f403045cf65aa7eb2005536641db
Content-Type: text/plain; charset="UTF-8"

Hi list,

Please see below the call for papers for Security Standardization Research
2017, which I'm posting with the chairs' encouragement. This conference has
proved to be a great venue for practitioners working on security for
different standards to come together and exchange knowledge, and we'd love
to get submissions from CFRG participants. Thanks!

Best,

William



                              Call for Papers

  SSR 2017: 4th International conference on Security Standardisation
Research
          18th-19th December 2017, Royal Holloway, Egham, Surrey, UK
                         http://www.ssresearch.eu/2017

SSR covers the full spectrum of research on security standardisation,
including, but not restricted to, work on cryptographic techniques
(including
ANSI, IEEE, IETF, ISO/IEC JTC 1/SC 27, ITU-T and NIST), security management,
security evaluation criteria, network security, privacy and identity
management, smart cards and RFID tags, biometrics, security modules, and
industry-specific security standards (e.g. those produced by the payments,
telecommunications and computing industries for such things as payment
protocols, mobile telephony and trusted computing).

SSR will also accept Systematization of Knowledge (SoK) papers relating to
security standardisation, which integrate experience and previous research,
drawing new comprehensive conclusions. SoK papers should evaluate,
systematize,
and contextualize existing knowledge. They should provide a new viewpoint,
offer a comprehensive taxonomy, or cast doubt on long-held beliefs, based on
compelling evidence.

A wide range of standards now cover many of aspects of cyber security. These
documents have been published by national and international formal
standardisation bodies, as well as by industry consortia. Many of these
standards have become very widely used - to take just one example, the
ISO/IEC
27000 series has become the internationally adopted basis for managing
corporate information security.

Still, new security standards are proposed very frequently, and existing
security standards need revision often. Security standards are one of the
most
active areas for many standards bodies. There is currently intense
attention on
the methods for ensuring security within standardisation.

SSR is a forum for identifying the conclusions from this process, and
proposing
improvements to achieve transparency, more unbiased results, and higher
scientific quality.

Papers offering research contributions to all aspects of security
standardisation are solicited for submission to the SSR 2017 conference.
Papers
may present theory, applications or practical experience in the field of
security standardisation, including, but not necessarily limited to:
* access control
* biometrics
* cloud computing
* critical national infrastructure (CNI) protection
* critiques of standards
* cryptanalysis
* cryptographic protocols
* cryptographic techniques
* evaluation criteria
* formal analysis of standards
* identity management
* industrial control systems security
* internet security
* intrusion detection
* key management and PKIs
* mobile security
* network security
* payment system security
* privacy
* RFID tag security
* risk analysis
* security controls
* security management
* security protocols
* security services
* security tokens
* smart cards
* telecommunications security
* trusted computing
* web security

Submissions must be original, unpublished, and not submitted to another
conference or journal for consideration for publication. Papers must be
written
in English. Each submitted paper should begin with a title, a short
abstract,
and a list of keywords. Papers should be at most 16 pages (excluding
bibliography and appendices) in the standard LNCS format (see
http://www.springer.com/computer/lncs?SGWID=0-164-0-0-0 for details).
Reviewers
are not obliged to read appendices, so the paper must be self-contained
without
them.

Papers that do not adhere to these requirements will be rejected without
consideration of their merits.

Papers must be submitted using the EasyChair conference management system
at:
  https://easychair.org/conferences/?conf=ssr2017

Accepted papers will be presented at the conference and published in the
Springer-Verlag Lecture Notes in Computer Science (LNCS) series
(www.springer.com/lncs). At least one author of each accepted paper must
register for the conference.

Instructions for the preparation of a final proceedings version will be
sent to
the authors of accepted papers.

Papers must be submitted using the EasyChair conference management system
at:
  https://easychair.org/conferences/?conf=ssr2017
Please send any enquiries to:
  webmaster@ssresearch.eu
or:
  ssr2017@easychair.org

Important dates

 Deadline for submissions: Monday, 17 July 2017 (anywhere on earth)
 Notifications to authors: Wednesday, 20 September 2017
 Camera ready due:             Monday, 9 October 2017
 Conference:               Monday/Tuesday, 18/19 December 2017


Conference organisation

General Chair

 Chris Mitchell, RHUL, UK

Programme Committee Chair

 Joshua Guttman, MITRE and WPI, USA
 William Whyte, USA


Programme Committee:

 Steve Babbage, Vodafone
 Colin Boyd, NTNU
 Dan Brown, Certicom and BlackBerry
 Scott Cadzow, OnBoard Security
 Liqun Chen, University of Surrey
 Cas Cremers, University of Oxford
 Stephen Farrell, Trinity College Dublin
 Russ Housley, Vigil Security, LLC
 Catherine Meadows, NRL
 Karen Randall, Randall Consulting
 Ben Smyth, Huawei
 Douglas Stebila, McMaster University

-- 


PLEASE UPDATE YOUR ADDRESS BOOKS WITH MY NEW ADDRESS:
wwhyte@onboardsecurity.com

--f403045cf65aa7eb2005536641db
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div>Hi list,</div><div><br></div><div>Please see below th=
e call for papers for Security Standardization Research 2017, which I&#39;m=
 posting with the chairs&#39; encouragement. This conference has proved to =
be a great venue for practitioners working on security for different standa=
rds to come together and exchange knowledge, and we&#39;d love to get submi=
ssions from CFRG participants. Thanks!</div><div><br></div><div>Best,</div>=
<div><br></div><div>William</div><div><br></div><div><br></div><div><br></d=
iv><span style=3D"font-size:12.8px">=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 Call for=
 Papers</span><br style=3D"font-size:12.8px"><br style=3D"font-size:12.8px"=
><span style=3D"font-size:12.8px">=C2=A0 SSR 2017: 4th International confer=
ence on Security Standardisation Research</span><br style=3D"font-size:12.8=
px"><span style=3D"font-size:12.8px">=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 18t=
h-</span><span class=3D"gmail-b4c-event" style=3D"font-size:12.8px"><span c=
lass=3D"gmail-boomerang-meeting-text gmail-b4c_event_id0 gmail-b4c-green">1=
9th December 2017</span></span><span style=3D"font-size:12.8px">, Royal Hol=
loway, Egham, Surrey, UK</span><br style=3D"font-size:12.8px"><span style=
=3D"font-size:12.8px">=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0</span><a href=3D"http://www.ssresear=
ch.eu/2017" rel=3D"noreferrer" target=3D"_blank" style=3D"font-size:12.8px"=
>http://www.ssresearch.eu/2017</a><br style=3D"font-size:12.8px"><br style=
=3D"font-size:12.8px"><span style=3D"font-size:12.8px">SSR covers the full =
spectrum of research on security standardisation,</span><br style=3D"font-s=
ize:12.8px"><span style=3D"font-size:12.8px">including, but not restricted =
to, work on cryptographic techniques (including</span><br style=3D"font-siz=
e:12.8px"><span style=3D"font-size:12.8px">ANSI, IEEE, IETF, ISO/IEC JTC 1/=
SC 27, ITU-T and NIST), security management,</span><br style=3D"font-size:1=
2.8px"><span style=3D"font-size:12.8px">security evaluation criteria, netwo=
rk security, privacy and identity</span><br style=3D"font-size:12.8px"><spa=
n style=3D"font-size:12.8px">management, smart cards and RFID tags, biometr=
ics, security modules, and</span><br style=3D"font-size:12.8px"><span style=
=3D"font-size:12.8px">industry-specific security standards (e.g. those prod=
uced by the payments,</span><br style=3D"font-size:12.8px"><span style=3D"f=
ont-size:12.8px">telecommunications and computing industries for such thing=
s as payment</span><br style=3D"font-size:12.8px"><span style=3D"font-size:=
12.8px">protocols, mobile telephony and trusted computing).</span><br style=
=3D"font-size:12.8px"><br style=3D"font-size:12.8px"><span style=3D"font-si=
ze:12.8px">SSR will also accept Systematization of Knowledge (SoK) papers r=
elating to</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12=
.8px">security standardisation, which integrate experience and previous res=
earch,</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px=
">drawing new comprehensive conclusions. SoK papers should evaluate, system=
atize,</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px=
">and contextualize existing knowledge. They should provide a new viewpoint=
,</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">off=
er a comprehensive taxonomy, or cast doubt on long-held beliefs, based on</=
span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">compel=
ling evidence.</span><br style=3D"font-size:12.8px"><br style=3D"font-size:=
12.8px"><span style=3D"font-size:12.8px">A wide range of standards now cove=
r many of aspects of cyber security. These</span><br style=3D"font-size:12.=
8px"><span style=3D"font-size:12.8px">documents have been published by nati=
onal and international formal</span><br style=3D"font-size:12.8px"><span st=
yle=3D"font-size:12.8px">standardisation bodies, as well as by industry con=
sortia. Many of these</span><br style=3D"font-size:12.8px"><span style=3D"f=
ont-size:12.8px">standards have become very widely used - to take just one =
example, the ISO/IEC</span><br style=3D"font-size:12.8px"><span style=3D"fo=
nt-size:12.8px">27000 series has become the internationally adopted basis f=
or managing</span><br style=3D"font-size:12.8px"><span style=3D"font-size:1=
2.8px">corporate information security.</span><br style=3D"font-size:12.8px"=
><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">Still, new=
 security standards are proposed very frequently, and existing</span><br st=
yle=3D"font-size:12.8px"><span style=3D"font-size:12.8px">security standard=
s need revision often. Security standards are one of the most</span><br sty=
le=3D"font-size:12.8px"><span style=3D"font-size:12.8px">active areas for m=
any standards bodies. There is currently intense attention on</span><br sty=
le=3D"font-size:12.8px"><span style=3D"font-size:12.8px">the methods for en=
suring security within standardisation.</span><br style=3D"font-size:12.8px=
"><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">SSR is a =
forum for identifying the conclusions from this process, and proposing</spa=
n><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">improveme=
nts to achieve transparency, more unbiased results, and higher</span><br st=
yle=3D"font-size:12.8px"><span style=3D"font-size:12.8px">scientific qualit=
y.</span><br style=3D"font-size:12.8px"><br style=3D"font-size:12.8px"><spa=
n style=3D"font-size:12.8px">Papers offering research contributions to all =
aspects of security</span><br style=3D"font-size:12.8px"><span style=3D"fon=
t-size:12.8px">standardisation are solicited for submission to the SSR 2017=
 conference. Papers</span><br style=3D"font-size:12.8px"><span style=3D"fon=
t-size:12.8px">may present theory, applications or practical experience in =
the field of</span><br style=3D"font-size:12.8px"><span style=3D"font-size:=
12.8px">security standardisation, including, but not necessarily limited to=
:</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">* a=
ccess control</span><br style=3D"font-size:12.8px"><span style=3D"font-size=
:12.8px">* biometrics</span><br style=3D"font-size:12.8px"><span style=3D"f=
ont-size:12.8px">* cloud computing</span><br style=3D"font-size:12.8px"><sp=
an style=3D"font-size:12.8px">* critical national infrastructure (CNI) prot=
ection</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px=
">* critiques of standards</span><br style=3D"font-size:12.8px"><span style=
=3D"font-size:12.8px">* cryptanalysis</span><br style=3D"font-size:12.8px">=
<span style=3D"font-size:12.8px">* cryptographic protocols</span><br style=
=3D"font-size:12.8px"><span style=3D"font-size:12.8px">* cryptographic tech=
niques</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px=
">* evaluation criteria</span><br style=3D"font-size:12.8px"><span style=3D=
"font-size:12.8px">* formal analysis of standards</span><br style=3D"font-s=
ize:12.8px"><span style=3D"font-size:12.8px">* identity management</span><b=
r style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">* industrial =
control systems security</span><br style=3D"font-size:12.8px"><span style=
=3D"font-size:12.8px">* internet security</span><br style=3D"font-size:12.8=
px"><span style=3D"font-size:12.8px">* intrusion detection</span><br style=
=3D"font-size:12.8px"><span style=3D"font-size:12.8px">* key management and=
 PKIs</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px"=
>* mobile security</span><br style=3D"font-size:12.8px"><span style=3D"font=
-size:12.8px">* network security</span><br style=3D"font-size:12.8px"><span=
 style=3D"font-size:12.8px">* payment system security</span><br style=3D"fo=
nt-size:12.8px"><span style=3D"font-size:12.8px">* privacy</span><br style=
=3D"font-size:12.8px"><span style=3D"font-size:12.8px">* RFID tag security<=
/span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">* ris=
k analysis</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12=
.8px">* security controls</span><br style=3D"font-size:12.8px"><span style=
=3D"font-size:12.8px">* security management</span><br style=3D"font-size:12=
.8px"><span style=3D"font-size:12.8px">* security protocols</span><br style=
=3D"font-size:12.8px"><span style=3D"font-size:12.8px">* security services<=
/span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">* sec=
urity tokens</span><br style=3D"font-size:12.8px"><span style=3D"font-size:=
12.8px">* smart cards</span><br style=3D"font-size:12.8px"><span style=3D"f=
ont-size:12.8px">* telecommunications security</span><br style=3D"font-size=
:12.8px"><span style=3D"font-size:12.8px">* trusted computing</span><br sty=
le=3D"font-size:12.8px"><span style=3D"font-size:12.8px">* web security</sp=
an><br style=3D"font-size:12.8px"><br style=3D"font-size:12.8px"><span styl=
e=3D"font-size:12.8px">Submissions must be original, unpublished, and not s=
ubmitted to another</span><br style=3D"font-size:12.8px"><span style=3D"fon=
t-size:12.8px">conference or journal for consideration for publication. Pap=
ers must be written</span><br style=3D"font-size:12.8px"><span style=3D"fon=
t-size:12.8px">in English. Each submitted paper should begin with a title, =
a short abstract,</span><br style=3D"font-size:12.8px"><span style=3D"font-=
size:12.8px">and a list of keywords. Papers should be at most 16 pages (exc=
luding</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px=
">bibliography and appendices) in the standard LNCS format (see</span><br s=
tyle=3D"font-size:12.8px"><a href=3D"http://www.springer.com/computer/lncs?=
SGWID=3D0-164-0-0-0" rel=3D"noreferrer" target=3D"_blank" style=3D"font-siz=
e:12.8px">http://www.springer.com/<wbr>computer/lncs?SGWID=3D0-164-0-0-<wbr=
>0</a><span style=3D"font-size:12.8px">=C2=A0for details). Reviewers</span>=
<br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">are not obl=
iged to read appendices, so the paper must be self-contained without</span>=
<br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">them.</span=
><br style=3D"font-size:12.8px"><br style=3D"font-size:12.8px"><span style=
=3D"font-size:12.8px">Papers that do not adhere to these requirements will =
be rejected without</span><br style=3D"font-size:12.8px"><span style=3D"fon=
t-size:12.8px">consideration of their merits.</span><br style=3D"font-size:=
12.8px"><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">Pap=
ers must be submitted using the EasyChair conference management system at:<=
/span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">=C2=
=A0=C2=A0</span><a href=3D"https://easychair.org/conferences/?conf=3Dssr201=
7" rel=3D"noreferrer" target=3D"_blank" style=3D"font-size:12.8px">https://=
easychair.org/<wbr>conferences/?conf=3Dssr2017</a><br style=3D"font-size:12=
.8px"><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">Accep=
ted papers will be presented at the conference and published in the</span><=
br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">Springer-Ver=
lag Lecture Notes in Computer Science (LNCS) series</span><br style=3D"font=
-size:12.8px"><span style=3D"font-size:12.8px">(</span><a href=3D"http://ww=
w.springer.com/lncs" rel=3D"noreferrer" target=3D"_blank" style=3D"font-siz=
e:12.8px">www.springer.com/lncs</a><span style=3D"font-size:12.8px">). At l=
east one author of each accepted paper must</span><br style=3D"font-size:12=
.8px"><span style=3D"font-size:12.8px">register for the conference.</span><=
br style=3D"font-size:12.8px"><br style=3D"font-size:12.8px"><span style=3D=
"font-size:12.8px">Instructions for the preparation of a final proceedings =
version will be sent to</span><br style=3D"font-size:12.8px"><span style=3D=
"font-size:12.8px">the authors of accepted papers.</span><br style=3D"font-=
size:12.8px"><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px=
">Papers must be submitted using the EasyChair conference management system=
 at:</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">=
=C2=A0=C2=A0</span><a href=3D"https://easychair.org/conferences/?conf=3Dssr=
2017" rel=3D"noreferrer" target=3D"_blank" style=3D"font-size:12.8px">https=
://easychair.org/<wbr>conferences/?conf=3Dssr2017</a><br style=3D"font-size=
:12.8px"><span style=3D"font-size:12.8px">Please send any enquiries to:</sp=
an><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">=C2=A0=
=C2=A0</span><a href=3D"mailto:webmaster@ssresearch.eu" style=3D"font-size:=
12.8px">webmaster@ssresearch.eu</a><br style=3D"font-size:12.8px"><span sty=
le=3D"font-size:12.8px">or:</span><br style=3D"font-size:12.8px"><span styl=
e=3D"font-size:12.8px">=C2=A0=C2=A0</span><a href=3D"mailto:ssr2017@easycha=
ir.org" style=3D"font-size:12.8px">ssr2017@easychair.org</a><br style=3D"fo=
nt-size:12.8px"><br style=3D"font-size:12.8px"><span style=3D"font-size:12.=
8px">Important dates</span><br style=3D"font-size:12.8px"><br style=3D"font=
-size:12.8px"><span style=3D"font-size:12.8px">=C2=A0Deadline for submissio=
ns: Monday, 17 July 2017 (anywhere on earth)</span><br style=3D"font-size:1=
2.8px"><span style=3D"font-size:12.8px">=C2=A0Notifications to authors: Wed=
nesday, 20 September 2017</span><br style=3D"font-size:12.8px"><span style=
=3D"font-size:12.8px">=C2=A0Camera ready due:=C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0Monday, 9 October 2017</span><br style=3D"font-size:12.=
8px"><span style=3D"font-size:12.8px">=C2=A0Conference:=C2=A0 =C2=A0 =C2=A0=
 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Monday/Tuesday, 18/19 December 2017</spa=
n><br style=3D"font-size:12.8px"><br style=3D"font-size:12.8px"><br style=
=3D"font-size:12.8px"><span style=3D"font-size:12.8px">Conference organisat=
ion</span><br style=3D"font-size:12.8px"><br style=3D"font-size:12.8px"><sp=
an style=3D"font-size:12.8px">General Chair</span><br style=3D"font-size:12=
.8px"><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">=C2=
=A0Chris Mitchell, RHUL, UK</span><br style=3D"font-size:12.8px"><br style=
=3D"font-size:12.8px"><span style=3D"font-size:12.8px">Programme Committee =
Chair</span><br style=3D"font-size:12.8px"><br style=3D"font-size:12.8px"><=
span style=3D"font-size:12.8px">=C2=A0Joshua Guttman, MITRE and WPI, USA</s=
pan><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">=C2=A0W=
illiam Whyte, USA</span><br style=3D"font-size:12.8px"><br style=3D"font-si=
ze:12.8px"><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">=
Programme Committee:</span><br style=3D"font-size:12.8px"><br style=3D"font=
-size:12.8px"><span style=3D"font-size:12.8px">=C2=A0Steve Babbage, Vodafon=
e</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">=C2=
=A0Colin Boyd, NTNU</span><br style=3D"font-size:12.8px"><span style=3D"fon=
t-size:12.8px">=C2=A0Dan Brown, Certicom and BlackBerry</span><br style=3D"=
font-size:12.8px"><span style=3D"font-size:12.8px">=C2=A0Scott Cadzow, OnBo=
ard Security</span><br style=3D"font-size:12.8px"><span style=3D"font-size:=
12.8px">=C2=A0Liqun Chen, University of Surrey</span><br style=3D"font-size=
:12.8px"><span style=3D"font-size:12.8px">=C2=A0Cas Cremers, University of =
Oxford</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8px=
">=C2=A0Stephen Farrell, Trinity College Dublin</span><br style=3D"font-siz=
e:12.8px"><span style=3D"font-size:12.8px">=C2=A0Russ Housley, Vigil Securi=
ty, LLC</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12.8p=
x">=C2=A0Catherine Meadows, NRL</span><br style=3D"font-size:12.8px"><span =
style=3D"font-size:12.8px">=C2=A0Karen Randall, Randall Consulting</span><b=
r style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">=C2=A0Ben Smy=
th, Huawei</span><br style=3D"font-size:12.8px"><span style=3D"font-size:12=
.8px">=C2=A0Douglas Stebila, McMaster University</span><br clear=3D"all"><d=
iv><br></div>-- <br><div class=3D"gmail_signature"><div dir=3D"ltr"><div><b=
r></div><div><br></div>PLEASE UPDATE YOUR ADDRESS BOOKS WITH MY NEW ADDRESS=
: <a href=3D"mailto:wwhyte@onboardsecurity.com" target=3D"_blank">wwhyte@on=
boardsecurity.com</a></div></div>
</div>

--f403045cf65aa7eb2005536641db--


From nobody Mon Jul  3 10:34:30 2017
Return-Path: <daniel.slamanig@tugraz.at>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id B1ADA129B77 for <cfrg@ietfa.amsl.com>; Mon,  3 Jul 2017 10:34:27 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -4.301
X-Spam-Level: 
X-Spam-Status: No, score=-4.301 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, RCVD_IN_DNSWL_MED=-2.3, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=tugraz.at
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id H50S3-dt8bKd for <cfrg@ietfa.amsl.com>; Mon,  3 Jul 2017 10:34:24 -0700 (PDT)
Received: from mailrelay.tugraz.at (mailrelay.tugraz.at [129.27.2.202]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 982AA131668 for <cfrg@irtf.org>; Mon,  3 Jul 2017 10:34:22 -0700 (PDT)
Received: from [10.27.152.210] (nat-hiding.iaik.tugraz.at [129.27.152.126]) (authenticated bits=0) by mailrelay3.tugraz.at (8.14.9/8.14.9) with ESMTP id v63HYGA9009014 (version=TLSv1/SSLv3 cipher=ECDHE-RSA-AES256-GCM-SHA384 bits=256 verify=NO); Mon, 3 Jul 2017 19:34:16 +0200
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=tugraz.at; s=mailrelay; t=1499103260; bh=NiX2sI6wEg5N4l7+0uLeinJcYc/jcKwle1CTrdRvVXw=; h=Subject:To:References:Cc:From:Date:In-Reply-To; b=FjitOLg9m9Dtrx4lbqyRPYFNPbn/WBR5mWNRG7jpv3HMGk9AB3bDHlNSX0yl+aFnn +HEL9WUEdTtp1Ei4q1sQFT7l3L29lgxaoSF4sHiaocnITzEkY6JscqeyunklqLEyq7 TEWfCcsiJ2Ik2kuBqUtoBICPCZqNyNqu03TwuAw8=
To: Philipp Jovanovic <philipp@jovanovic.io>
References: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io>
Cc: cfrg@irtf.org
From: Daniel Slamanig <daniel.slamanig@tugraz.at>
Message-ID: <11cc5d3f-ecf9-2fd0-825c-c8b441bd2813@tugraz.at>
Date: Mon, 3 Jul 2017 19:34:15 +0200
User-Agent: Mozilla/5.0 (Windows NT 6.3; WOW64; rv:52.0) Gecko/20100101 Thunderbird/52.2.1
MIME-Version: 1.0
In-Reply-To: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
X-TUG-Backscatter-control: lAa1Aa+Pa1hp/miybLoRww
X-Spam-Scanner: SpamAssassin 3.003001 
X-Spam-Score-relay: -1.7
X-Scanned-By: MIMEDefang 2.74
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/DUK4gB7HRIM8JwBEDguFgb8rukk>
Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 03 Jul 2017 17:34:28 -0000

Hi Philipp,

looks interesting!

After looking at the protocol I also have some security concerns 
(related to what has been raised by Oleg in a previous mail).

Not committing to Z as well as the actual sum of signers public keys A' 
in the computation of the hash c for the signature seems to be problematic.

It seems to me that committing Z in the signature in plain as well as A' 
does not work given the later application of the signing procedure 
(where till the end of the protocol it is not clear who actually 
participates in the signing but c must be known at the beginning).

Committing to neither of both however seems problematic as it does not 
fix the set of actual signers.

This could be circumvented by allowing an honest leader to adapt the 
commitment to the final Z (and A') after it knows the signers without 
modifying the initially computed c using a chameleon hash (trapdoor 
commitment). I use P as a generator below, omit the brackets [a]P 
notation for scalar multiplication and write it from the perspective of 
the leader, i.e., the signer that initiates the protocol.

The leader could choose chameleon hash parameters sk_ch=y for random y 
and pk_ch=(P,Y=yP) and add pk_ch and chameleon hash CH(Z'):=h(Z')P+u'Y 
for randomly chosen u' to the computation of c, i.e., set 
c=H(R||A||pk_ch||CH(Z')||S), where h() is a collision resistant hash 
function (this is just the standard way of constructing a chameleon hash 
from DL for arbitrary message spaces as propsed in [1]). If Z' is not 
yet known one simply sets Z' to some fixed string at the beginning, 
e.g., Z':=0. At the end of the protocol, when the leader knows the exact 
signers, it can update Z' to the final value Z and use sk_ch to compute 
a collision in the chameleon hash, i.e., such that CH(Z)=CH(Z') by 
solving h(Z')+u'y = h(Z)+uy for u. He then adds u and Z as well as pk_ch 
to the signature, i.e., sets it as (R,s,u,Z,pk_ch) and discards sk_ch 
and u'. If Z is known beforehand, one simply computes the chameleon hash 
once and does not need to compute a collision. Clearly, the use of a 
chameleon hash allows to simply adapt to the actual set of signers 
representing Z without modifying c (with the knowledge of sk_ch - but it 
does not work without the knowledge of sk_ch). This would resolve the 
issue with the unknown Z at the time of signing.

Also, A is committed in the signature, but not the concrete A'=\sum A_i 
of keys used for computing the signature (I guess also due to the reason 
that one does not know the correct set of signers when computing the 
hash c). That can be problematic in a rogue key scenario in the current 
protocol, i.e., when not all signers need to prove knowledge of the 
secret key when they register their public keys but their public keys 
could be functions of other public keys (guess this could be a problem 
here). For instance, a malicious A^* could just take some key from A, 
say A_j, and compute and publish A^*=a^*A_j. And then given a collective 
signature (R,s,Z) where A_j participated, the signer can update s to s^* 
= s+a^*c as well as Z^* to exclude A_j and include A^* (as Z is not 
committed in the signature generation) and the signature (R,s^*,Z^*) 
will be a valid signature that certifies that A^* participated in 
signing - although he didn't.

If Z is committed as proposed above and it is checked during the 
verification, then this should no longer work. One could also adapt the 
hash c=H(R||pk_ch||CH(Z'||A)||S) to include a chameleon hash to 
CH(Z||A'), where A' is the real set of signers that participated in the 
signature generation and is adapted before finalizing the signature when 
known as above.

I hope that what I proposed is not just complete nonsense :) Also it 
produces quite a bit of an overhead. There may also be easier ways to 
avoid the issues.

Some editorial issues: the message to be signed is sometimes called a 
satement S and later then message msg. S could be confusing as part of 
the signature is s and your semantic is that scalars are lowercase and 
points are uppercase. Also in 4.2 "Signature Generation" steps 2 and 3 
are confusing as I guess that in the protocol all the signer compute 
their own [r_i]B values and R=\sum R_i instead of R=[r]B which would 
mean that they would send their r_i's (hope they will not do so).

Also I find it somewhat confusing that the bitmask Z identifies the 
non-signers with a bit set to 1. Why not identifying the signers with a 
bit set to 1?

Cheers,
Daniel


[1] Hugo Krawczyk, Tal Rabin: Chameleon Signatures. NDSS 2000

On 01.07.2017 23:58, Philipp Jovanovic wrote:
> Hi CFRG,
> 
> Here’s a first version of an Internet-Draft on “Collective Edwards-Curve Digital Signature Algorithms” based on Ed25519 and Ed448: https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/
> 
> We plan to give a short presentation on that topic at the next CFRG meeting in Prague.
> 
> Any feedback is more than welcome. Thanks!
> 
> All the best,
> Philipp
> 
> 
> 
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
> 


--
Dr. Daniel Slamanig
Institute for Applied Information Processing and Communications
Graz University of Technology
Inffeldgasse 16a, 8010 Graz, Austria.
Phone: +43 316 873 5509
http://www.iaik.tugraz.at


From nobody Mon Jul  3 11:02:28 2017
Return-Path: <internet-drafts@ietf.org>
X-Original-To: cfrg@ietf.org
Delivered-To: cfrg@ietfa.amsl.com
Received: from ietfa.amsl.com (localhost [IPv6:::1]) by ietfa.amsl.com (Postfix) with ESMTP id 38564129503; Mon,  3 Jul 2017 11:02:27 -0700 (PDT)
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: 7bit
From: internet-drafts@ietf.org
To: <i-d-announce@ietf.org>
Cc: cfrg@ietf.org
X-Test-IDTracker: no
X-IETF-IDTracker: 6.55.2
Auto-Submitted: auto-generated
Precedence: bulk
Message-ID: <149910494717.22786.15402730565912249191@ietfa.amsl.com>
Date: Mon, 03 Jul 2017 11:02:27 -0700
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/zY2XDqLE1b7SFNT88qSX506RCno>
Subject: [Cfrg] I-D Action: draft-irtf-cfrg-re-keying-05.txt
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 03 Jul 2017 18:02:27 -0000

A New Internet-Draft is available from the on-line Internet-Drafts directories.
This draft is a work item of the Crypto Forum of the IETF.

        Title           : Re-keying Mechanisms for Symmetric Keys
        Author          : Stanislav Smyshlyaev
	Filename        : draft-irtf-cfrg-re-keying-05.txt
	Pages           : 47
	Date            : 2017-07-03

Abstract:
   A certain maximum amount of data can be safely encrypted when
   encryption is performed under a single key.  This amount is called
   "key lifetime".  This specification describes a variety of methods to
   increase the lifetime of symmetric keys.  It provides external and
   internal re-keying mechanisms based on hash functions and on block
   ciphers, that can be used with modes of operations such as CTR, GCM,
   CCM, CBC, CFB, OFB and OMAC.


The IETF datatracker status page for this draft is:
https://datatracker.ietf.org/doc/draft-irtf-cfrg-re-keying/

There are also htmlized versions available at:
https://tools.ietf.org/html/draft-irtf-cfrg-re-keying-05
https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-re-keying-05

A diff from the previous version is available at:
https://www.ietf.org/rfcdiff?url2=draft-irtf-cfrg-re-keying-05


Please note that it may take a couple of minutes from the time of submission
until the htmlized version and diff are available at tools.ietf.org.

Internet-Drafts are also available by anonymous FTP at:
ftp://ftp.ietf.org/internet-drafts/


From nobody Mon Jul  3 15:39:29 2017
Return-Path: <daniel.slamanig@tugraz.at>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 03519131696 for <cfrg@ietfa.amsl.com>; Mon,  3 Jul 2017 15:39:22 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -4.3
X-Spam-Level: 
X-Spam-Status: No, score=-4.3 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_MED=-2.3, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=tugraz.at
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id c4b5XiuPl-4C for <cfrg@ietfa.amsl.com>; Mon,  3 Jul 2017 15:39:18 -0700 (PDT)
Received: from mailrelay.tugraz.at (mailrelay.tugraz.at [129.27.2.202]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 7918D131638 for <cfrg@irtf.org>; Mon,  3 Jul 2017 15:39:18 -0700 (PDT)
Received: from exchange.tugraz.at (exchange.tugraz.at [129.27.2.220]) by mailrelay3.tugraz.at (8.14.9/8.14.9) with ESMTP id v63MdEUY008925 (version=TLSv1/SSLv3 cipher=ECDHE-RSA-AES256-SHA384 bits=256 verify=OK); Tue, 4 Jul 2017 00:39:14 +0200
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=tugraz.at; s=mailrelay; t=1499121556; bh=Q9ynHFeo9QLGUJMVTHoR2m0r7QXJPTYwdzsN1OCfQl4=; h=From:To:CC:Subject:Date; b=LZctkRqiK4AjgkgEv6eXj+Q2lmdHingvt+huyZh4FUs8vceLAWRqNCqDUEmPu7Sk4 ish0tN/NTgxZUqB3Ug2rE/1w753WjlNx9aQ1nIsvSMNJQCzOdeGgUHps2C4JUh1xXW iCTbHVnjqQbQBi2nN6ay39MowPJcZrx+nrn0wuP4=
Received: from MBX0002.tugraz.local (2002:811b:3045::811b:3045) by MBX0002.tugraz.local (2002:811b:3045::811b:3045) with Microsoft SMTP Server (TLS) id 15.0.1263.5; Tue, 4 Jul 2017 00:39:12 +0200
Received: from MBX0002.tugraz.local ([fe80::5556:4aaf:d0f8:46ec]) by MBX0002.tugraz.local ([fe80::5556:4aaf:d0f8:46ec%12]) with mapi id 15.00.1263.000; Tue, 4 Jul 2017 00:39:12 +0200
From: "Slamanig, Daniel" <daniel.slamanig@tugraz.at>
To: Philipp Jovanovic <philipp@jovanovic.io>
CC: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
Thread-Index: AQHS9E0xFuwNyQq3DkK9EtFcxMSBZg==
Date: Mon, 3 Jul 2017 22:39:12 +0000
Message-ID: <8a0d8aec-8640-4fad-a692-c405cd05973e@email.android.com>
Accept-Language: de-AT, en-US
Content-Language: de-AT
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
x-ms-exchange-transport-fromentityheader: Hosted
Content-Type: multipart/alternative; boundary="_000_8a0d8aec86404fada692c405cd05973eemailandroidcom_"
MIME-Version: 1.0
X-TUG-Backscatter-control: lAa1Aa+Pa1hp/miybLoRww
X-Spam-Scanner: SpamAssassin 3.003001 
X-Spam-Score-relay: -1.9
X-Scanned-By: MIMEDefang 2.74
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/H_Aj4LdOIIbj-gsM9QqFDA6gHlU>
Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 03 Jul 2017 22:39:22 -0000

--_000_8a0d8aec86404fada692c405cd05973eemailandroidcom_
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: base64
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--_000_8a0d8aec86404fada692c405cd05973eemailandroidcom_
Content-Type: text/html; charset="utf-8"
Content-ID: <A1BEC26ABC977D408C0644105D5E950C@tugraz.local>
Content-Transfer-Encoding: base64
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--_000_8a0d8aec86404fada692c405cd05973eemailandroidcom_--


From nobody Tue Jul  4 07:06:29 2017
Return-Path: <Kenny.Paterson@rhul.ac.uk>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 965A5129B30; Tue,  4 Jul 2017 07:06:27 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.921
X-Spam-Level: 
X-Spam-Status: No, score=-1.921 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, RCVD_IN_DNSWL_NONE=-0.0001, RCVD_IN_MSPIKE_H3=-0.01, RCVD_IN_MSPIKE_WL=-0.01, SPF_HELO_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=rhul.onmicrosoft.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id OT9sknmIc9uC; Tue,  4 Jul 2017 07:06:25 -0700 (PDT)
Received: from EUR02-AM5-obe.outbound.protection.outlook.com (mail-eopbgr00061.outbound.protection.outlook.com [40.107.0.61]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 89BCD1320B3; Tue,  4 Jul 2017 07:06:11 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=rhul.onmicrosoft.com;  s=selector1-rhul-ac-uk; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version; bh=bR+KmH9PF9Y/mKw1doRTrglrsy6S0o2b/XdKye7bfdM=; b=JRbB142rGAbmXyNLeiEmgN7THXfyWbIuwocGeOUEnUStIYAA+HMaKrXCo1oFLz8TAEMeAuXbn2eCuSWOjvQokywLNxruWJ6yGjnDCyw9FcwbeN21qC7Vx6bAVBOcr87O68c31gZf1jW76FDHdPn9boFSfo+JLjvJ3se26JFqeww=
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com (10.168.2.156) by AM4PR0301MB1907.eurprd03.prod.outlook.com (10.168.3.7) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256) id 15.1.1220.11; Tue, 4 Jul 2017 14:06:09 +0000
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a]) by AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a%14]) with mapi id 15.01.1220.018; Tue, 4 Jul 2017 14:06:08 +0000
From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: "draft-irtf-cfrg-argon2@ietf.org" <draft-irtf-cfrg-argon2@ietf.org>
CC: "cfrg@ietf.org" <cfrg@ietf.org>
Thread-Topic: [Cfrg] I-D Action: draft-irtf-cfrg-argon2-02.txt
Thread-Index: AQHSpud0G7Nvk2NWAEWKLkFqd0wSnqGoglCAgH4EpoCAHdlfgA==
Date: Tue, 4 Jul 2017 14:06:08 +0000
Message-ID: <D5815D6C.97F14%kenny.paterson@rhul.ac.uk>
References: <149061159741.30566.11599293166376872082@ietfa.amsl.com> <CALW8-7+BL5dLJiTh_yn_OD8pNNwLvEz5ZPhqK=-TfUH3xvohBg@mail.gmail.com> <D56853D6.96722%kenny.paterson@rhul.ac.uk>
In-Reply-To: <D56853D6.96722%kenny.paterson@rhul.ac.uk>
Accept-Language: en-GB, en-US
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
user-agent: Microsoft-MacOutlook/14.7.1.161129
authentication-results: ietf.org; dkim=none (message not signed) header.d=none;ietf.org; dmarc=none action=none header.from=rhul.ac.uk;
x-originating-ip: [134.219.227.30]
x-ms-publictraffictype: Email
x-microsoft-exchange-diagnostics: 1; AM4PR0301MB1907; 7: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
x-forefront-antispam-report: SFV:SKI; SCL:-1SFV:NSPM; SFS:(10009020)(6009001)(39400400002)(39850400002)(39840400002)(39450400003)(39410400002)(377424004)(24454002)(377454003)(25786009)(53546010)(4326008)(3280700002)(66066001)(86362001)(3660700001)(551544002)(2900100001)(6506006)(6486002)(5660300001)(4001350100001)(76176999)(54356999)(50986999)(413944005)(966005)(72206003)(36756003)(478600001)(2906002)(8676002)(81166006)(8936002)(189998001)(230783001)(2351001)(14454004)(7736002)(74482002)(6512007)(5250100002)(305945005)(2950100002)(42882006)(6306002)(6916009)(99286003)(53936002)(6436002)(3846002)(6116002)(102836003)(5640700003)(450100002)(2501003)(110136004)(6246003)(38730400002)(229853002); DIR:OUT; SFP:1101; SCL:1; SRVR:AM4PR0301MB1907; H:AM4PR0301MB1906.eurprd03.prod.outlook.com; FPR:; SPF:None; MLV:sfv; LANG:en; 
x-ms-office365-filtering-correlation-id: e7998bf7-19a9-458a-c5ab-08d4c2e5d1a0
x-microsoft-antispam: UriScan:; BCL:0; PCL:0; RULEID:(300000500095)(300135000095)(300000501095)(300135300095)(22001)(300000502095)(300135100095)(2017030254075)(300000503095)(300135400095)(2017052603031)(201703131423075)(201703031133081)(300000504095)(300135200095)(300000505095)(300135600095)(300000506095)(300135500095); SRVR:AM4PR0301MB1907; 
x-ms-traffictypediagnostic: AM4PR0301MB1907:
x-microsoft-antispam-prvs: <AM4PR0301MB1907F63CB37314540E88AB5DBCD70@AM4PR0301MB1907.eurprd03.prod.outlook.com>
x-exchange-antispam-report-test: UriScan:(125551606395959)(278178393323532)(158342451672863)(120809045254105)(236129657087228)(192374486261705)(48057245064654)(100405760836317)(148574349560750)(92977632026198);
x-exchange-antispam-report-cfa-test: BCL:0; PCL:0; RULEID:(100000700101)(100105000095)(100000701101)(100105300095)(100000702101)(100105100095)(6040450)(601004)(2401047)(5005006)(8121501046)(3002001)(100000703101)(100105400095)(10201501046)(93006095)(93001095)(6041248)(20161123560025)(20161123555025)(20161123558100)(20161123562025)(201703131423075)(201702281528075)(201702281529075)(201703061421075)(201703061406153)(20161123564025)(6072148)(100000704101)(100105200095)(100000705101)(100105500095); SRVR:AM4PR0301MB1907; BCL:0; PCL:0; RULEID:(100000800101)(100110000095)(100000801101)(100110300095)(100000802101)(100110100095)(100000803101)(100110400095)(100000804101)(100110200095)(100000805101)(100110500095); SRVR:AM4PR0301MB1907; 
x-forefront-prvs: 0358535363
spamdiagnosticoutput: 1:99
spamdiagnosticmetadata: NSPM
Content-Type: text/plain; charset="utf-8"
Content-ID: <B8BE7671DCCF954AA6BC9B445AE83C16@eurprd03.prod.outlook.com>
Content-Transfer-Encoding: base64
MIME-Version: 1.0
X-OriginatorOrg: rhul.ac.uk
X-MS-Exchange-CrossTenant-originalarrivaltime: 04 Jul 2017 14:06:08.5731 (UTC)
X-MS-Exchange-CrossTenant-fromentityheader: Hosted
X-MS-Exchange-CrossTenant-id: 2efd699a-1922-4e69-b601-108008d28a2e
X-MS-Exchange-Transport-CrossTenantHeadersStamped: AM4PR0301MB1907
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/TOxcs1qbgey5ie9T5ZjNKwORwNI>
Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-argon2-02.txt
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Tue, 04 Jul 2017 14:06:28 -0000
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From nobody Wed Jul  5 00:43:47 2017
Return-Path: <Kenny.Paterson@rhul.ac.uk>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 25691131AC2 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 00:43:46 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.911
X-Spam-Level: 
X-Spam-Status: No, score=-2.911 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, RCVD_IN_DNSWL_NONE=-0.0001, RCVD_IN_MSPIKE_H5=-1, RCVD_IN_MSPIKE_WL=-0.01, SPF_HELO_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=rhul.onmicrosoft.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id kd7YpMvw_Q7J for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 00:43:43 -0700 (PDT)
Received: from EUR01-HE1-obe.outbound.protection.outlook.com (mail-he1eur01on0073.outbound.protection.outlook.com [104.47.0.73]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 7A33E131AC0 for <cfrg@irtf.org>; Wed,  5 Jul 2017 00:43:42 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=rhul.onmicrosoft.com;  s=selector1-rhul-ac-uk; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version; bh=4GuChGlYQ/hR1tKLf2rRnjSyEhUMJ9xS0aSnrMtPZ7s=; b=A4U2U2HHULjIDof0/+VGbRzjvMuwCiFP7aMj6WhToWfPdFgDvoChXBa/1vCL5k1CR7Pw1pyIHTySLjx/IvrFUS0TvPzCsn5QB51CJ1kDPrPyNicaS2DnGKWVUjZir1DIgsiqYE/DlBWzlY87aJxMV/lijRjaOFKgd9/qBDOlTts=
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com (10.168.2.156) by AM4PR0301MB1906.eurprd03.prod.outlook.com (10.168.2.156) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256) id 15.1.1220.11; Wed, 5 Jul 2017 07:43:39 +0000
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a]) by AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a%14]) with mapi id 15.01.1220.018; Wed, 5 Jul 2017 07:43:38 +0000
From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: Shay Gueron <shay.gueron@gmail.com>, Adam Langley <agl@imperialviolet.org>, Yehuda Lindell <Yehuda.Lindell@biu.ac.il>
CC: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: Reviews of AES-GCM-SIV (draft-irtf-cfrg-gcmsiv-04.txt)
Thread-Index: AQHS9WJqB08RIbvyeEucDrswwscvig==
Date: Wed, 5 Jul 2017 07:43:38 +0000
Message-ID: <D5825737.9801A%kenny.paterson@rhul.ac.uk>
Accept-Language: en-GB, en-US
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
user-agent: Microsoft-MacOutlook/14.7.1.161129
authentication-results: gmail.com; dkim=none (message not signed) header.d=none;gmail.com; dmarc=none action=none header.from=rhul.ac.uk;
x-originating-ip: [134.219.227.30]
x-ms-publictraffictype: Email
x-microsoft-exchange-diagnostics: 1; AM4PR0301MB1906; 7:m8uFUq2VLrz9uY6+PeuNxoa471Hnb4JBfLaqytYjvTMCwJg00A9d8AUXlIB3dSJ/jl7FzIiRRItjqwqMXRfDcetpwCNVuPHcrU4Xoy9WR4o4gNztOizrlRWo20/r2KXmIGHsT+nq1An5vcJGCDUC/O7H6dxu72qj6nj7VaPnG7EkMx+HBQ73qBLLDGxuz/m020ws9bmijcBRWsXKJx2Ur/cLeO7OqGwjDnORRnBZ5dhS6kcy3L3yDNijua1+gZKK7AxDR6JpIvOEgLAlaymViNyYSiHxCUI+64XgoNs3DC2WlYeXpG9P7lFGz8HtwkWoHR3285dEMWbkjdCCvOGRnhLYd2np9mXZFPy8LC++Kigur2dWTfiRH5vrohSZoxOpkWXYhXGJYQbsSzKXd+Y/dRceV7ULduh0G6pdlxfhInWN9oQnRGl0P0ta4A9t8IXAgce5bS6QqvZbKKqkdOemoCHOrXzRONITVf2oUy36ez87PTJW5y3nLtbemdnFdoEPj/o6Fzsg25QM9b9ucKVPvE4072rXqpUfomZF5dVxWxFb4RAvSZTXv7Mw3VBHZmexMgGLjzP+4EMlpM1fOV9laAHg55DsmF4OQWbydmtDbUnecT5E5zWDuJld2H38xcRdsri7oyxWLeva4TgFP5J0aaUnHaEodvxdBW9xx+DOYGwsBicEAFHCgi0g88e7lcA3Zvtn8BkmqAqE3CQcQioodeP6NdqIBQLYMslcYAGGdD/Y/lzVeoUOSnsi/mSeN4TKVUTePUXaador2HB5gK5G6J7C/2242tWFPJLOPZldXac=
x-forefront-antispam-report: SFV:SKI; SCL:-1SFV:NSPM; SFS:(10009020)(6009001)(39840400002)(39410400002)(39450400003)(39850400002)(39400400002)(51694002)(54094003)(51444003)(66066001)(2906002)(99286003)(230783001)(50986999)(42882006)(54356999)(36756003)(7736002)(38730400002)(305945005)(106356001)(6512007)(81166006)(8936002)(8676002)(74482002)(53936002)(4326008)(3660700001)(6116002)(3846002)(102836003)(2900100001)(3280700002)(413944005)(6436002)(25786009)(72206003)(478600001)(14454004)(189998001)(39060400002)(83506001)(6486002)(6506006)(4001350100001)(5660300001)(5250100002)(86362001); DIR:OUT; SFP:1101; SCL:1; SRVR:AM4PR0301MB1906; H:AM4PR0301MB1906.eurprd03.prod.outlook.com; FPR:; SPF:None; MLV:ovrnspm; PTR:InfoNoRecords; LANG:en; 
x-ms-office365-filtering-correlation-id: 52276859-2461-4efe-f86b-08d4c3798ce2
x-microsoft-antispam: UriScan:; BCL:0; PCL:0; RULEID:(300000500095)(300135000095)(300000501095)(300135300095)(22001)(300000502095)(300135100095)(2017030254075)(300000503095)(300135400095)(2017052603031)(201703131423075)(201703031133081)(300000504095)(300135200095)(300000505095)(300135600095)(300000506095)(300135500095); SRVR:AM4PR0301MB1906; 
x-ms-traffictypediagnostic: AM4PR0301MB1906:
x-microsoft-antispam-prvs: <AM4PR0301MB190637E4D3C1602D3A037BDFBCD40@AM4PR0301MB1906.eurprd03.prod.outlook.com>
x-exchange-antispam-report-test: UriScan:(278178393323532)(278428928389397)(236129657087228)(192374486261705)(788757137089)(48057245064654)(148574349560750)(92977632026198)(247924648384137);
x-exchange-antispam-report-cfa-test: BCL:0; PCL:0; RULEID:(100000700101)(100105000095)(100000701101)(100105300095)(100000702101)(100105100095)(6040450)(601004)(2401047)(5005006)(8121501046)(3002001)(10201501046)(100000703101)(100105400095)(93006095)(93001095)(6041248)(20161123555025)(20161123562025)(20161123560025)(201703131423075)(201702281528075)(201702281529075)(201703061421075)(201703061406153)(20161123564025)(20161123558100)(6072148)(100000704101)(100105200095)(100000705101)(100105500095); SRVR:AM4PR0301MB1906; BCL:0; PCL:0; RULEID:(100000800101)(100110000095)(100000801101)(100110300095)(100000802101)(100110100095)(100000803101)(100110400095)(100000804101)(100110200095)(100000805101)(100110500095); SRVR:AM4PR0301MB1906; 
x-forefront-prvs: 0359162B6D
spamdiagnosticoutput: 1:99
spamdiagnosticmetadata: NSPM
Content-Type: text/plain; charset="utf-8"
Content-ID: <01693C62E3B9AF42A7D1D1ACAF3F8772@eurprd03.prod.outlook.com>
Content-Transfer-Encoding: base64
MIME-Version: 1.0
X-OriginatorOrg: rhul.ac.uk
X-MS-Exchange-CrossTenant-originalarrivaltime: 05 Jul 2017 07:43:38.7445 (UTC)
X-MS-Exchange-CrossTenant-fromentityheader: Hosted
X-MS-Exchange-CrossTenant-id: 2efd699a-1922-4e69-b601-108008d28a2e
X-MS-Exchange-Transport-CrossTenantHeadersStamped: AM4PR0301MB1906
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/Hkp2l5_x_vx7SO1HSmWV6Hvt6zM>
Subject: [Cfrg] Reviews of AES-GCM-SIV (draft-irtf-cfrg-gcmsiv-04.txt)
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 07:43:46 -0000
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From nobody Wed Jul  5 03:28:29 2017
Return-Path: <brynosaurus@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 81E431317AE for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 03:28:28 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.998
X-Spam-Level: 
X-Spam-Status: No, score=-1.998 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id jzRTfyzmh47Y for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 03:28:26 -0700 (PDT)
Received: from mail-wm0-x244.google.com (mail-wm0-x244.google.com [IPv6:2a00:1450:400c:c09::244]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 1CE81131BC1 for <cfrg@irtf.org>; Wed,  5 Jul 2017 03:28:26 -0700 (PDT)
Received: by mail-wm0-x244.google.com with SMTP id p204so31547430wmg.1 for <cfrg@irtf.org>; Wed, 05 Jul 2017 03:28:26 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=from:message-id:mime-version:subject:date:in-reply-to:cc:to :references; bh=+PyS+9lD7mtA3dW5wLXrtAWnfbx0vmPon7xe3v19PXY=; b=BRt/W1G5lwdTklTJZV9hrCnm9bakvedsJUp/Dme9mAMz3KxNiDGt2tk7CQosZwBW4q et03ODS+Kr6/QOCC+8m+J97xUuLbwetpNXR2QuPpk7HQpfaJmf76213/ZjagnK/0ROaM 6n+NgvEWPyeNUDq6YMK1UhnX7NYZ/rn9Xwkz9f3tnuV/U+RgKUWqhEcMKvb0Cm0XSslT 3lJkQdw9+wTi6V/KFyfXXm3AGiYQBuz/nFKekN3dwQQa2Rq9W0+K4Hnhr50aDf82ZWRK Qwj2fqe9oWLl73246ItSUDpnbwBO0JdsUvBW0punpGF1SQpHTk9Cohu8g9RYmPhSHCuf zC9Q==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:from:message-id:mime-version:subject:date :in-reply-to:cc:to:references; bh=+PyS+9lD7mtA3dW5wLXrtAWnfbx0vmPon7xe3v19PXY=; b=DXIXAan12HSaFlfJAUtkiLbxzhHB1Y15mB82u0kPkzriHC1Vk97Lw1Z5G0hKQgbN12 7xPYPqnCyyQ86DF03wCiwAfEVrEKZ4MtaoHqQNlfuJHTs1lUwEVqIuQxxGBtjBarg2z8 m69PWvzkXXvQ0dNAmIP39oSUeBM6vrqPnYaqthezCRvfACnhSHXN3u8Ktlp7OjYNtI7x zQZ0uoBVkm3Zk+IyM+6ftA2nn9ZPNAFqqYemexQbP4veeqVrSusGkpz2qozT1iEF9wHX DZmtZ5RRIAVf9pPD47IMpCskrnOv7sPwMbg2U8/vr6r2XQD1hkuA4FM8D8AzYpGOiXcR 4tkg==
X-Gm-Message-State: AKS2vOyS7Anu4VUu7Iz4wBpethTuKFMydBGQGi16coT3uVcZKWFaKPgG yuPar9sP15E8h9xFaHM=
X-Received: by 10.80.183.4 with SMTP id g4mr22097916ede.138.1499250504336; Wed, 05 Jul 2017 03:28:24 -0700 (PDT)
Received: from [172.20.10.3] (58.229.197.178.dynamic.wless.zhbmb00p-cgnat.res.cust.swisscom.ch. [178.197.229.58]) by smtp.gmail.com with ESMTPSA id b6sm7041155ede.23.2017.07.05.03.28.20 (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Wed, 05 Jul 2017 03:28:20 -0700 (PDT)
From: Bryan Ford <brynosaurus@gmail.com>
Message-Id: <646B4D24-AA38-4AFD-93AB-733AAFA71BFC@gmail.com>
Content-Type: multipart/signed; boundary="Apple-Mail=_6C0B81F4-96C2-4328-A3F1-B45103099FCF"; protocol="application/pgp-signature"; micalg=pgp-sha256
Mime-Version: 1.0 (Mac OS X Mail 10.3 \(3273\))
Date: Wed, 5 Jul 2017 12:28:14 +0200
In-Reply-To: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io>
Cc: Philipp Jovanovic <philipp.jovanovic@epfl.ch>, Linus Gasser <linus.gasser@epfl.ch>, Nicolas Gailly <nicolas.gailly@epfl.ch>
To: cfrg@irtf.org
References: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io>
X-Mailer: Apple Mail (2.3273)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/tip6_RCQylyiYCKNbVDpf3042oE>
Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 10:28:28 -0000

--Apple-Mail=_6C0B81F4-96C2-4328-A3F1-B45103099FCF
Content-Type: multipart/alternative;
	boundary="Apple-Mail=_909F2D55-4C58-4BA0-8585-26BB59470AE7"


--Apple-Mail=_909F2D55-4C58-4BA0-8585-26BB59470AE7
Content-Transfer-Encoding: quoted-printable
Content-Type: text/plain;
	charset=utf-8

Thanks everyone for your great comments so far on our collective signing =
draft.  More detailed responses to follow soon.

In the meantime, I just wanted to announce that we=E2=80=99ve moved the =
=E2=80=9Csource=E2=80=9D for this Internet-Draft to this public GitHub =
repo:

	https://github.com/dedis/doc/tree/master/cosi =
<https://github.com/dedis/doc/tree/master/cosi>

=E2=80=A6and we=E2=80=99re happy to take patch requests there for =
concrete textual fixes or suggestions anyone might like to propose.  =
However, let=E2=80=99s keep the main discussion here on the CFRG list.

Thanks
Bryan

> On Jul 1, 2017, at 11:58 PM, Philipp Jovanovic <philipp@jovanovic.io> =
wrote:
>=20
> Hi CFRG,
>=20
> Here=E2=80=99s a first version of an Internet-Draft on =E2=80=9CCollecti=
ve Edwards-Curve Digital Signature Algorithms=E2=80=9D based on Ed25519 =
and Ed448: https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/
>=20
> We plan to give a short presentation on that topic at the next CFRG =
meeting in Prague.
>=20
> Any feedback is more than welcome. Thanks!
>=20
> All the best,
> Philipp


--Apple-Mail=_909F2D55-4C58-4BA0-8585-26BB59470AE7
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html;
	charset=utf-8

<html><head><meta http-equiv=3D"Content-Type" content=3D"text/html =
charset=3Dutf-8"></head><body style=3D"word-wrap: break-word; =
-webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" =
class=3D""><div class=3D"">Thanks everyone for your great comments so =
far on our collective signing draft. &nbsp;More detailed responses to =
follow soon.</div><div class=3D""><br class=3D""></div><div class=3D"">In =
the meantime, I just wanted to announce that we=E2=80=99ve moved the =
=E2=80=9Csource=E2=80=9D for this Internet-Draft to this public GitHub =
repo:</div><div class=3D""><br class=3D""></div><div class=3D""><span =
class=3D"Apple-tab-span" style=3D"white-space:pre">	</span><a =
href=3D"https://github.com/dedis/doc/tree/master/cosi" =
class=3D"">https://github.com/dedis/doc/tree/master/cosi</a></div><div =
class=3D""><br class=3D""></div><div class=3D"">=E2=80=A6and we=E2=80=99re=
 happy to take patch requests there for concrete textual fixes or =
suggestions anyone might like to propose. &nbsp;However, let=E2=80=99s =
keep the main discussion here on the CFRG list.</div><div class=3D""><br =
class=3D""></div><div class=3D"">Thanks</div><div =
class=3D"">Bryan</div><br class=3D""><div><blockquote type=3D"cite" =
class=3D""><div class=3D"">On Jul 1, 2017, at 11:58 PM, Philipp =
Jovanovic &lt;<a href=3D"mailto:philipp@jovanovic.io" =
class=3D"">philipp@jovanovic.io</a>&gt; wrote:</div><br =
class=3D"Apple-interchange-newline"><div class=3D""><div class=3D"">Hi =
CFRG,<br class=3D""><br class=3D"">Here=E2=80=99s a first version of an =
Internet-Draft on =E2=80=9CCollective Edwards-Curve Digital Signature =
Algorithms=E2=80=9D based on Ed25519 and Ed448: <a =
href=3D"https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/" =
class=3D"">https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/</a><br =
class=3D""><br class=3D"">We plan to give a short presentation on that =
topic at the next CFRG meeting in Prague.<br class=3D""><br class=3D"">Any=
 feedback is more than welcome. Thanks!<br class=3D""><br class=3D"">All =
the best,<br class=3D"">Philipp<br =
class=3D""></div></div></blockquote></div><br class=3D""></body></html>=

--Apple-Mail=_909F2D55-4C58-4BA0-8585-26BB59470AE7--

--Apple-Mail=_6C0B81F4-96C2-4328-A3F1-B45103099FCF
Content-Transfer-Encoding: 7bit
Content-Disposition: attachment;
	filename=signature.asc
Content-Type: application/pgp-signature;
	name=signature.asc
Content-Description: Message signed with OpenPGP

-----BEGIN PGP SIGNATURE-----
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=FFhx
-----END PGP SIGNATURE-----

--Apple-Mail=_6C0B81F4-96C2-4328-A3F1-B45103099FCF--


From nobody Wed Jul  5 05:26:25 2017
Return-Path: <brynosaurus@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id C450113173E for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 05:26:20 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.698
X-Spam-Level: 
X-Spam-Status: No, score=-2.698 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id LBD0OJ5384x0 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 05:26:18 -0700 (PDT)
Received: from mail-wm0-x236.google.com (mail-wm0-x236.google.com [IPv6:2a00:1450:400c:c09::236]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 60C34131CC6 for <cfrg@irtf.org>; Wed,  5 Jul 2017 05:26:17 -0700 (PDT)
Received: by mail-wm0-x236.google.com with SMTP id w126so220483112wme.0 for <cfrg@irtf.org>; Wed, 05 Jul 2017 05:26:17 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=from:message-id:mime-version:subject:date:in-reply-to:cc:to :references; bh=mwnvGsPBHKiwxHkqQU9vnOJU6rT1ABBo4eRs3iflN4Y=; b=FezNIpgSwHO8zVIWCVZBEQSD639KOc1Vwv6VxUDFgqOgfMn5enTnbO64IrDoydOnRf LUAm5NxS6mYvbNCJxVtwGjQypZwEvWMJORs84yULhXK4tDkBoF+TH8rRj7fvz+2nvWmr Pzqm4P1PX0zodLxBXM1Wwx5NN4teZ6I9mheqK5IWNI8WNTwDDC9pMSbfU+NM1ZQzFmzw /vnUEWoWgZ6zrdr7t0OeJBYfZvkovaY6hcF2aD3EqkKJ2b2qK1fdNgs3KzLvAoqs/Ms2 r+Mt9gaJA10aQ7wt9ViVcKndxjtV2ZiSGQPuFGsdaUQhk3NVHvikEsn6QG5p8uxSBxUK 9olg==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:from:message-id:mime-version:subject:date :in-reply-to:cc:to:references; bh=mwnvGsPBHKiwxHkqQU9vnOJU6rT1ABBo4eRs3iflN4Y=; b=qNdc/ccIyfRKSP2/nDzln53bMM1b4Vl9zHluiwo0/roli65yayPQmlSyIp8ya5ezkp LJBrSVm91Fvrd5aBYPqGJ3DYOcNKPi81Xqq4C3bX39f274SUtvxVnEe0i5cn6Ep84o+d Efnpp3jH/ilRVjUWOozdf3iDKCCE9gAX6aWOIvwxGtl7tTxZsIvQGSZB1L+yThBY6bcx yF8FtEUIe9tzyzoOXIYtHle8vD3t8BMNIOUuM+2hevR5rdMdcJaUlwjKc1SR8V3W9KdR n4KwhG/aO7Pc1V2+o+xiguT/ISXpOManfrGFyklCSwqfGUDY9Juu+GHv7oVDtXTZURhb 3iBQ==
X-Gm-Message-State: AKS2vOyE7RLp7satfnSvJ1Fp8y3vDOSrpnb1T5JSOKMYPHY9RCPb/JK2 HqLL3pUGw8o9uvzYXRI=
X-Received: by 10.80.182.90 with SMTP id c26mr18012347ede.55.1499257575765; Wed, 05 Jul 2017 05:26:15 -0700 (PDT)
Received: from [172.20.10.3] (81.227.197.178.dynamic.wless.zhbmb00p-cgnat.res.cust.swisscom.ch. [178.197.227.81]) by smtp.gmail.com with ESMTPSA id r37sm5639975edd.19.2017.07.05.05.26.13 (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Wed, 05 Jul 2017 05:26:14 -0700 (PDT)
From: Bryan Ford <brynosaurus@gmail.com>
Message-Id: <A4104495-EE45-4CD2-B4F0-014AC6E74C34@gmail.com>
Content-Type: multipart/signed; boundary="Apple-Mail=_9B18970A-44D2-4314-BBB3-E8F2C5E69443"; protocol="application/pgp-signature"; micalg=pgp-sha256
Mime-Version: 1.0 (Mac OS X Mail 10.3 \(3273\))
Date: Wed, 5 Jul 2017 14:26:11 +0200
In-Reply-To: <5E91769F-B102-4A49-9ED5-B789D4FED598@gmail.com>
Cc: Philipp Jovanovic <philipp@jovanovic.io>, cfrg@irtf.org
To: Oleg Andreev <oleganza@gmail.com>
References: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io> <5E91769F-B102-4A49-9ED5-B789D4FED598@gmail.com>
X-Mailer: Apple Mail (2.3273)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/lcA-AZj_f7N66RFOD-Y4XrEbgH4>
Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 12:26:21 -0000

--Apple-Mail=_9B18970A-44D2-4314-BBB3-E8F2C5E69443
Content-Type: multipart/alternative;
	boundary="Apple-Mail=_18FCA772-5B90-4BA4-B589-9B20D2AD1544"


--Apple-Mail=_18FCA772-5B90-4BA4-B589-9B20D2AD1544
Content-Transfer-Encoding: quoted-printable
Content-Type: text/plain;
	charset=utf-8

Hi Oleg,

Thanks so much for your extremely constructive feedback.  Responding to =
your points inline...

> On Jul 2, 2017, at 10:47 PM, Oleg Andreev <oleganza@gmail.com> wrote:
>=20
> First of all: nice to see a simpler approach than a full SSSS-based =
threshold signing scheme!
>=20
> After a quick glance at the spec, I have two security concerns:
>=20
> 1. It seems unsafe to add public keys directly (A =3D Sum[A_i]) =
without multiplying them by their hashes (A =3D Sum[Hash(A_i)*A_i]). =
Without that measure, it is possible to have A_j as a linear combination =
of other public keys. See this discussion for details: =
https://bitcointalk.org/index.php?topic=3D1377298.0

Definitely, we=E2=80=99d like to consider incorporating delinearization =
schemes like this if/when the WG adopts collective signing in some form =
as a working group item.  We=E2=80=99ve added an Issue on the GitHub =
repo holding the internet-draft specifically for this =
(https://github.com/dedis/doc/issues/1 =
<https://github.com/dedis/doc/issues/1>).

I seem to remember that this topic was already brought up on this list =
months (years?) ago in the Ed25519/Ed448 discussion leading up to RFC =
8032, but delinearization mechanisms weren=E2=80=99t adopted at that =
point - perhaps in part simply because collective/aggregate signing =
wasn=E2=80=99t the focus of that work item.  I don=E2=80=99t remember =
all the details though - if anyone else has a clearer memory of exactly =
when that discussion occurred and can find pointers to the relevant =
parts of the CFRG mailing list archive, that would be great.

> 2. The signature does not commit to membership bitmask Z. Maybe it =
could be argued that signature is not malleable (especially with an =
improvement mentioned above), but to stay on safe side I think =
committing to the exact set of signers is a good idea.

Indeed, we=E2=80=99ve considered this question, and included it as a =
specific =E2=80=9Cpoint for discussion=E2=80=9D in section 9.2 of our =
initial Internet-Draft.  We also added an Issue to the draft=E2=80=99s =
GitHub repo to expand this list of discussion points and move it to an =
earlier, more prominent location in the draft (see =
https://github.com/dedis/doc/issues/2 =
<https://github.com/dedis/doc/issues/2>).

The clear potential benefit of including the bitmask in the hash is to =
strengthen the non-malleability of the collective signature.  Suppose, =
for example, I=E2=80=99m a member of a collective signing group and =
participated in creating a particular collective signature S, for which =
my bit in the bit mask is 1.  With the current (simple) formulation, I =
could take this signature S, and remove my =E2=80=9Cshare" of it (which =
I can do because I know both my private key and my share of the private =
Schnorr commit) to produce a new =E2=80=9Creduced=E2=80=9D signature =
S=E2=80=99 without my share and with my bit in the bit mask set to 0.  =
The resulting modified signature S=E2=80=99 will be equally valid, just =
with one fewer cosigners represented (i.e., me).

=46rom one perspective, this =E2=80=9Cattack=E2=80=9D arguably =
shouldn=E2=80=99t be a problem in most cases because the new signature =
still correctly attests that all the (remaining) signers indeed signed =
the message, and if I try to disclaim ever having signed it at all, =
anyone who knows the original full signature S can just exhibit that as =
proof.  Any signature almost by definition can=E2=80=99t be taken as a =
claim that someone else *didn=E2=80=99t* sign a message - because they =
could have signed the same message in a completely separate, unrelated =
signing process.  Both the original signature S and the reduced =
signature S=E2=80=99 will need to be checked by any verifier against =
some policy anyway (e.g., a t-of-n threshold or a more complex policy), =
so my reduction S=E2=80=99 will at best make it less likely to satisfy =
whatever verification policy might be applied to it.

Nevertheless, there have certainly been instances in which unexpected or =
poorly-understood signature malleability properties have created =
security problems in practical systems using malleable signing schemes, =
so from a purist perspective of =E2=80=9Cany malleability is probably =
bad and should be eliminated=E2=80=9D, it might be best to have the hash =
cover the bit mask purely out of an abundance of caution.

However, there=E2=80=99s another potential practical cost to enforcing =
this non-malleability: I believe it conflicts with any provisions we =
might want to make collective signing protocols =E2=80=9Crestart-proof=E2=80=
=9D and prevent DoS attacks.  This is another issue to be discussed - =
for details see https://github.com/dedis/doc/issues/2 =
<https://github.com/dedis/doc/issues/2> and section IV.D of our CoSi =
paper (http://dedis.cs.yale.edu/dissent/papers/witness-abs).

In brief, any Schnorr collective signing protocol fundamentally must =
have two phases, =E2=80=9Ccommit/challenge=E2=80=9D and =E2=80=9Cresponse=E2=
=80=9D.  If the commits and challenge depend on the exact bit mask of =
participating cosigners, then if any of those cosigners appeared to be =
online during the commit phase but then go offline (perhaps maliciously, =
deliberately at the =E2=80=9Cworst possible moment=E2=80=9D) between the =
commit/challenge and response phases, then the only way for the protocol =
to complete is to restart from scratch without the =E2=80=9Cfailed=E2=80=9D=
 cosigner.  If there are F colluding malicious cosigners in the group, =
then they can go offline one-by-one in this way, forcing up to F =
successive restarts, before the honest members of the cosigning group =
can successfully create a valid collective signature. This is of course =
a limited and potentially tolerable DoS attack, =E2=80=9Conly=E2=80=9D =
O(N) in the group size, but still a consideration.

We have considered collective signing protocol variations that would =
eliminate this DoS vulnerability, by enabling the leader to continue the =
collective-signing process without restarting, even if only a subset of =
the cosigners present in the commit phase remain participants in the =
response phase.  Again, see section IV.D of our CoSi paper for details =
(http://dedis.cs.yale.edu/dissent/papers/witness-abs).  Of course such =
provisions add complexity to the protocol, and we=E2=80=99re not at all =
certain whether they=E2=80=99re worth the trouble, or if it=E2=80=99s =
better just to require restarts and tolerate the (limited) DoS =
vulnerability that restarting on cosigner failure creates.  So this is =
one of the particular =E2=80=9Cbalance=E2=80=9D issues I=E2=80=99d like =
to see discussed further in this group.

> Additionally, I'd suggest an improvement to the API. Since the scheme =
is not a SSSS scheme, verifier needs to reconstruct the exact key from =
the individual keys (4.3.5 Signature Verification). Current spec states =
that verifier should know the set of these member-keys upfront. It could =
be more practical to provide them as a part of the signature and commit =
into the aggregate public key, so the setup process looks as simple as =
non-aggregate one, or one using SSSS: just sharing a single aggregate =
public key.
>=20
> This is how it could be done:
>=20
> 1. Organize all member keys in a merkle tree and compute it's root =
hash `h`.
> 2. Compute intermediate aggregate key as `A =3D Sum[Hash(A_i)*A_i]`.
> 3. Compute aggregate public key with commitment to the merkle tree: `P =
=3D Hash(A || h)*A`.
> 4. Signature will include:
>    1) necessary member keys according to bitmask Z.
>    2) merkle proof (necessary intermediate hashes needed to =
reconstruct the root hash).
>    3) intermediate key A.
> 5. Verifier would reconstruct root hash h', compute `Hash(h' || A)*A` =
and verify it matches the P. Then it will reconstruct actual =
verification key `A' =3D A-T` and proceed with Schnorr protocol.
>=20
> The member keys part of the signature could be optional, so the keys =
could be cached in case many signature from the same key are =
continuously verified.

Yes, I think something along these lines is a good alternative to =
consider - in fact we suggested more-or-less exactly this approach in =
Section IV.B of our CoSi paper =
(http://dedis.cs.yale.edu/dissent/papers/witness-abs).

The upside of this variation is that verifiers need to know only the =
hash of the root of the Merkle =E2=80=9Ckey tree=E2=80=9D in order to =
verify collective signatures.  The downsides are (a) more complex =
signing and verification protocols needing Merkle trees and the like, =
(b) collective signatures themselves are no longer constant-size for a =
given cosigning group size, and (c) collective signatures may have much =
larger worst-case size due to the need to include one or more Merkle =
proofs for missing or present public keys - up to N/2 Merkle proofs in =
the worst case.  Again, these are important tradeoffs to be discussed.

Backing up for the moment, I think our first step is to establish =
whether there=E2=80=99s a critical-mass of interest within CFRG to adopt =
collective signing in some form as a working group item.  We offer our =
Internet-Draft as a starting point, but only a starting point, for such =
an effort if approved, and are happy to evolve it as needed as WG =
consensus hopefully emerges eventually around the above and other =
important design issues and tradeoffs that will need to be discussed.  =
I=E2=80=99m already happy to see that there seems to be significant =
interest, at least, based on the responses so far.

Thanks
Bryan

>=20
> Cheers,
> Oleg.
>=20
>> On 2 Jul 2017, at 00:58, Philipp Jovanovic <philipp@jovanovic.io> =
wrote:
>>=20
>> Hi CFRG,
>>=20
>> Here=E2=80=99s a first version of an Internet-Draft on =E2=80=9CCollect=
ive Edwards-Curve Digital Signature Algorithms=E2=80=9D based on Ed25519 =
and Ed448: https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/
>>=20
>> We plan to give a short presentation on that topic at the next CFRG =
meeting in Prague.
>>=20
>> Any feedback is more than welcome. Thanks!
>>=20
>> All the best,
>> Philipp
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org
>> https://www.irtf.org/mailman/listinfo/cfrg
>=20
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg


--Apple-Mail=_18FCA772-5B90-4BA4-B589-9B20D2AD1544
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html;
	charset=utf-8

<html><head><meta http-equiv=3D"Content-Type" content=3D"text/html =
charset=3Dutf-8"></head><body style=3D"word-wrap: break-word; =
-webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" =
class=3D"">Hi Oleg,&nbsp;<div class=3D""><br class=3D""></div><div =
class=3D"">Thanks so much for your extremely constructive feedback. =
&nbsp;Responding to your points inline...</div><div class=3D""><br =
class=3D""></div><div class=3D""><div><blockquote type=3D"cite" =
class=3D""><div class=3D"">On Jul 2, 2017, at 10:47 PM, Oleg Andreev =
&lt;<a href=3D"mailto:oleganza@gmail.com" =
class=3D"">oleganza@gmail.com</a>&gt; wrote:</div><div class=3D""><div =
class=3D""><br class=3D"">First of all: nice to see a simpler approach =
than a full SSSS-based threshold signing scheme!<br class=3D""><br =
class=3D"">After a quick glance at the spec, I have two security =
concerns:<br class=3D""><br class=3D"">1. It seems unsafe to add public =
keys directly (A =3D Sum[A_i]) without multiplying them by their hashes =
(A =3D Sum[Hash(A_i)*A_i]). Without that measure, it is possible to have =
A_j as a linear combination of other public keys. See this discussion =
for details: <a href=3D"https://bitcointalk.org/index.php?topic=3D1377298.=
0" class=3D"">https://bitcointalk.org/index.php?topic=3D1377298.0</a><br =
class=3D""></div></div></blockquote><div><br =
class=3D""></div><div>Definitely, we=E2=80=99d like to consider =
incorporating delinearization schemes like this if/when the WG adopts =
collective signing in some form as a working group item. &nbsp;We=E2=80=99=
ve added an Issue on the GitHub repo holding the internet-draft =
specifically for this (<a href=3D"https://github.com/dedis/doc/issues/1" =
class=3D"">https://github.com/dedis/doc/issues/1</a>).</div><div><br =
class=3D""></div><div>I seem to remember that this topic was already =
brought up on this list months (years?) ago in the Ed25519/Ed448 =
discussion leading up to RFC 8032, but delinearization mechanisms =
weren=E2=80=99t adopted at that point - perhaps in part simply because =
collective/aggregate signing wasn=E2=80=99t the focus of that work item. =
&nbsp;I don=E2=80=99t remember all the details though - if anyone else =
has a clearer memory of exactly when that discussion occurred and can =
find pointers to the relevant parts of the CFRG mailing list archive, =
that would be great.</div><br class=3D""><blockquote type=3D"cite" =
class=3D""><div class=3D""><div class=3D"">2. The signature does not =
commit to membership bitmask Z. Maybe it could be argued that signature =
is not malleable (especially with an improvement mentioned above), but =
to stay on safe side I think committing to the exact set of signers is a =
good idea.<br class=3D""></div></div></blockquote><div><br =
class=3D""></div><div>Indeed, we=E2=80=99ve considered this question, =
and included it as a specific =E2=80=9Cpoint for discussion=E2=80=9D in =
section 9.2 of our initial Internet-Draft. &nbsp;We also added an Issue =
to the draft=E2=80=99s GitHub repo to expand this list of discussion =
points and move it to an earlier, more prominent location in the draft =
(see&nbsp;<a href=3D"https://github.com/dedis/doc/issues/2" =
class=3D"">https://github.com/dedis/doc/issues/2</a>).</div><div><br =
class=3D""></div><div>The clear potential benefit of including the =
bitmask in the hash is to strengthen the non-malleability of the =
collective signature. &nbsp;Suppose, for example, I=E2=80=99m a member =
of a collective signing group and participated in creating a particular =
collective signature S, for which my bit in the bit mask is 1. =
&nbsp;With the current (simple) formulation, I could take this signature =
S, and remove my =E2=80=9Cshare" of it (which I can do because I know =
both my private key and my share of the private Schnorr commit) to =
produce a new =E2=80=9Creduced=E2=80=9D signature S=E2=80=99 without my =
share and with my bit in the bit mask set to 0. &nbsp;The resulting =
modified signature S=E2=80=99 will be equally valid, just with one fewer =
cosigners represented (i.e., me).</div><div><br class=3D""></div><div>=46r=
om one perspective, this =E2=80=9Cattack=E2=80=9D arguably shouldn=E2=80=99=
t be a problem in most cases because the new signature still correctly =
attests that all the (remaining) signers indeed signed the message, and =
if I try to disclaim ever having signed it at all, anyone who knows the =
original full signature S can just exhibit that as proof. &nbsp;Any =
signature almost by definition can=E2=80=99t be taken as a claim that =
someone else *didn=E2=80=99t* sign a message - because they could have =
signed the same message in a completely separate, unrelated signing =
process. &nbsp;Both the original signature S and the reduced signature =
S=E2=80=99 will need to be checked by any verifier against some policy =
anyway (e.g., a t-of-n threshold or a more complex policy), so my =
reduction S=E2=80=99 will at best make it less likely to satisfy =
whatever verification policy might be applied to it.</div><div><br =
class=3D""></div><div>Nevertheless, there have certainly been instances =
in which unexpected or poorly-understood signature malleability =
properties have created security problems in practical systems using =
malleable signing schemes, so from a purist perspective of =E2=80=9Cany =
malleability is probably bad and should be eliminated=E2=80=9D, it might =
be best to have the hash cover the bit mask purely out of an abundance =
of caution.</div><div><br class=3D""></div><div>However, there=E2=80=99s =
another potential practical cost to enforcing this non-malleability: I =
believe it conflicts with any provisions we might want to make =
collective signing protocols =E2=80=9Crestart-proof=E2=80=9D and prevent =
DoS attacks. &nbsp;This is another issue to be discussed - for details =
see&nbsp;<a href=3D"https://github.com/dedis/doc/issues/2" =
class=3D"">https://github.com/dedis/doc/issues/2</a>&nbsp;and section =
IV.D of our CoSi paper (<a =
href=3D"http://dedis.cs.yale.edu/dissent/papers/witness-abs" =
class=3D"">http://dedis.cs.yale.edu/dissent/papers/witness-abs</a>).</div>=
<div><br class=3D""></div><div>In brief, any Schnorr collective signing =
protocol fundamentally must have two phases, =E2=80=9Ccommit/challenge=E2=80=
=9D and =E2=80=9Cresponse=E2=80=9D. &nbsp;If the commits and challenge =
depend on the exact bit mask of participating cosigners, then if any of =
those cosigners appeared to be online during the commit phase but then =
go offline (perhaps maliciously, deliberately at the =E2=80=9Cworst =
possible moment=E2=80=9D) between the commit/challenge and response =
phases, then the only way for the protocol to complete is to restart =
from scratch without the =E2=80=9Cfailed=E2=80=9D cosigner. &nbsp;If =
there are F colluding malicious cosigners in the group, then they can go =
offline one-by-one in this way, forcing up to F successive restarts, =
before the honest members of the cosigning group can successfully create =
a valid collective signature. This is of course a limited and =
potentially tolerable DoS attack, =E2=80=9Conly=E2=80=9D O(N) in the =
group size, but still a consideration.</div><div><br =
class=3D""></div><div>We have considered collective signing protocol =
variations that would eliminate this DoS vulnerability, by enabling the =
leader to continue the collective-signing process without restarting, =
even if only a subset of the cosigners present in the commit phase =
remain participants in the response phase. &nbsp;Again, see section IV.D =
of our CoSi paper for details (<a =
href=3D"http://dedis.cs.yale.edu/dissent/papers/witness-abs" =
class=3D"">http://dedis.cs.yale.edu/dissent/papers/witness-abs</a>). =
&nbsp;Of course such provisions add complexity to the protocol, and =
we=E2=80=99re not at all certain whether they=E2=80=99re worth the =
trouble, or if it=E2=80=99s better just to require restarts and tolerate =
the (limited) DoS vulnerability that restarting on cosigner failure =
creates. &nbsp;So this is one of the particular =E2=80=9Cbalance=E2=80=9D =
issues I=E2=80=99d like to see discussed further in this =
group.</div><div><br class=3D""></div><blockquote type=3D"cite" =
class=3D""><div class=3D""><div class=3D"">Additionally, I'd suggest an =
improvement to the API. Since the scheme is not a SSSS scheme, verifier =
needs to reconstruct the exact key from the individual keys (4.3.5 =
Signature Verification). Current spec states that verifier should know =
the set of these member-keys upfront. It could be more practical to =
provide them as a part of the signature and commit into the aggregate =
public key, so the setup process looks as simple as non-aggregate one, =
or one using SSSS: just sharing a single aggregate public key.<br =
class=3D""><br class=3D"">This is how it could be done:<br class=3D""><br =
class=3D"">1. Organize all member keys in a merkle tree and compute it's =
root hash `h`.<br class=3D"">2. Compute intermediate aggregate key as `A =
=3D Sum[Hash(A_i)*A_i]`.<br class=3D"">3. Compute aggregate public key =
with commitment to the merkle tree: `P =3D Hash(A || h)*A`.<br =
class=3D"">4. Signature will include:<br class=3D""> =
&nbsp;&nbsp;&nbsp;1) necessary member keys according to bitmask Z.<br =
class=3D""> &nbsp;&nbsp;&nbsp;2) merkle proof (necessary intermediate =
hashes needed to reconstruct the root hash).<br class=3D""> =
&nbsp;&nbsp;&nbsp;3) intermediate key A.<br class=3D"">5. Verifier would =
reconstruct root hash h', compute `Hash(h' || A)*A` and verify it =
matches the P. Then it will reconstruct actual verification key `A' =3D =
A-T` and proceed with Schnorr protocol.<br class=3D""><br class=3D"">The =
member keys part of the signature could be optional, so the keys could =
be cached in case many signature from the same key are continuously =
verified.<br class=3D""></div></div></blockquote><div><br =
class=3D""></div><div>Yes, I think something along these lines is a good =
alternative to consider - in fact we suggested more-or-less exactly this =
approach in Section IV.B of our CoSi paper (<a =
href=3D"http://dedis.cs.yale.edu/dissent/papers/witness-abs" =
class=3D"">http://dedis.cs.yale.edu/dissent/papers/witness-abs</a>). =
&nbsp;</div><div><br class=3D""></div><div>The upside of this variation =
is that verifiers need to know only the hash of the root of the Merkle =
=E2=80=9Ckey tree=E2=80=9D in order to verify collective signatures. =
&nbsp;The downsides are (a) more complex signing and verification =
protocols needing Merkle trees and the like, (b) collective signatures =
themselves are no longer constant-size for a given cosigning group size, =
and (c) collective signatures may have much larger worst-case size due =
to the need to include one or more Merkle proofs for missing or present =
public keys - up to N/2 Merkle proofs in the worst case. &nbsp;Again, =
these are important tradeoffs to be discussed.</div><div><br =
class=3D""></div><div>Backing up for the moment, I think our first step =
is to establish whether there=E2=80=99s a critical-mass of interest =
within CFRG to adopt collective signing in some form as a working group =
item. &nbsp;We offer our Internet-Draft as a starting point, but only a =
starting point, for such an effort if approved, and are happy to evolve =
it as needed as WG consensus hopefully emerges eventually around the =
above and other important design issues and tradeoffs that will need to =
be discussed. &nbsp;I=E2=80=99m already happy to see that there seems to =
be significant interest, at least, based on the responses so =
far.</div><div><br class=3D""></div><div>Thanks</div><div>Bryan</div><br =
class=3D""><blockquote type=3D"cite" class=3D""><div class=3D""><div =
class=3D""><br class=3D"">Cheers,<br class=3D"">Oleg.<br class=3D""><br =
class=3D""><blockquote type=3D"cite" class=3D"">On 2 Jul 2017, at 00:58, =
Philipp Jovanovic &lt;<a href=3D"mailto:philipp@jovanovic.io" =
class=3D"">philipp@jovanovic.io</a>&gt; wrote:<br class=3D""><br =
class=3D"">Hi CFRG,<br class=3D""><br class=3D"">Here=E2=80=99s a first =
version of an Internet-Draft on =E2=80=9CCollective Edwards-Curve =
Digital Signature Algorithms=E2=80=9D based on Ed25519 and Ed448: <a =
href=3D"https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/" =
class=3D"">https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/</a><br =
class=3D""><br class=3D"">We plan to give a short presentation on that =
topic at the next CFRG meeting in Prague.<br class=3D""><br class=3D"">Any=
 feedback is more than welcome. Thanks!<br class=3D""><br class=3D"">All =
the best,<br class=3D"">Philipp<br =
class=3D"">_______________________________________________<br =
class=3D"">Cfrg mailing list<br class=3D""><a =
href=3D"mailto:Cfrg@irtf.org" class=3D"">Cfrg@irtf.org</a><br =
class=3D"">https://www.irtf.org/mailman/listinfo/cfrg<br =
class=3D""></blockquote><br =
class=3D"">_______________________________________________<br =
class=3D"">Cfrg mailing list<br class=3D""><a =
href=3D"mailto:Cfrg@irtf.org" class=3D"">Cfrg@irtf.org</a><br =
class=3D"">https://www.irtf.org/mailman/listinfo/cfrg<br =
class=3D""></div></div></blockquote></div><br =
class=3D""></div></body></html>=

--Apple-Mail=_18FCA772-5B90-4BA4-B589-9B20D2AD1544--

--Apple-Mail=_9B18970A-44D2-4314-BBB3-E8F2C5E69443
Content-Transfer-Encoding: 7bit
Content-Disposition: attachment;
	filename=signature.asc
Content-Type: application/pgp-signature;
	name=signature.asc
Content-Description: Message signed with OpenPGP

-----BEGIN PGP SIGNATURE-----
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=lFNj
-----END PGP SIGNATURE-----

--Apple-Mail=_9B18970A-44D2-4314-BBB3-E8F2C5E69443--


From nobody Wed Jul  5 06:11:54 2017
Return-Path: <brynosaurus@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id BBB45131CF4 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 06:11:52 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.698
X-Spam-Level: 
X-Spam-Status: No, score=-2.698 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 8RKBwTBpRecD for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 06:11:50 -0700 (PDT)
Received: from mail-wm0-x22e.google.com (mail-wm0-x22e.google.com [IPv6:2a00:1450:400c:c09::22e]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 74CDE131CB0 for <cfrg@irtf.org>; Wed,  5 Jul 2017 06:11:49 -0700 (PDT)
Received: by mail-wm0-x22e.google.com with SMTP id 62so222356035wmw.1 for <cfrg@irtf.org>; Wed, 05 Jul 2017 06:11:49 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=from:message-id:mime-version:subject:date:in-reply-to:cc:to :references; bh=GHNZ95akZo7drPIYCl5zaY+mVkexX42Xl8N+xGmLNQA=; b=X2rCZjOXqc3Jwi0eUpMwngbNYDy6t+uNf0FWCDcXaAQSBlk87i1tWO6lvf5eKpiMnJ A2ZAlrZCh0oVvKN7HRYn5xXpN/FmxTxFnM+rb/NpXx4TwNA9i2c2B0HpPEbIO0oNzZVJ ZXjggHnWOGeMOPjoqgLrnJq4TxVh1siGItY8KnhFPobznOFqUWNYViCsyw/D4Hf5F0PK vF7EeFwy58znSG1W5au3qUpDnfqqEBsgCtnVKIUOQ6Ar4AXBYBkMgBZJpsIHwdf1zrzV wfVsj8NcF/52DK9QPbRWE3k5fxxCo6KuwNGs/s64xjXSDxuTqL2/1GPd3bFa7biTAKlc OZgw==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:from:message-id:mime-version:subject:date :in-reply-to:cc:to:references; bh=GHNZ95akZo7drPIYCl5zaY+mVkexX42Xl8N+xGmLNQA=; b=s0ZYyVaMGUwv+MMb0n9rGt/HuNcTyUjIFpPyufc4k++kiw1+FN7ejm9usDuPTcp+yU BZjHXHI6uEa4aMVCDRIQ1bwbaxfr9WwMa/Bmv/drR5tpD4qb7wv2tRVoXMbkidw2zbi1 iKHF8S3GWyMxNWYIw5WKhwz50GyWMmlMTq+WT8zGPG2nlKL8uDkgSSr8RrDrgsoDaxe6 nBL0uEXa+OXCMunIuhfiBErCFwO5vflNwoKMNxD2EQvdyZjfD+Rap/jz3jJEL4QhsOcx 5Dw6b50Q2kYzP0ctXF/WX7Bm7xTQLZClZJZl89h5CVNt2Pkfp/JxemcGi53tz1H/FBZc uGOA==
X-Gm-Message-State: AKS2vOykEIWrX9hQ0J6/cEXPoB9P7K9tcu/AWmm1sapp21kxiooSjeQm 7YugUTqsDbzHaI9eJIw=
X-Received: by 10.28.238.219 with SMTP id j88mr19891818wmi.33.1499260307905; Wed, 05 Jul 2017 06:11:47 -0700 (PDT)
Received: from [192.168.1.28] (83-103-13-156.ip.fastwebnet.it. [83.103.13.156]) by smtp.gmail.com with ESMTPSA id h10sm11431707wme.30.2017.07.05.06.11.41 (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Wed, 05 Jul 2017 06:11:46 -0700 (PDT)
From: Bryan Ford <brynosaurus@gmail.com>
Message-Id: <A423CB6E-D649-4320-BB76-2E3783D6AFE0@gmail.com>
Content-Type: multipart/signed; boundary="Apple-Mail=_C4E4CACE-761E-4B3F-B41D-B27E8D7044A1"; protocol="application/pgp-signature"; micalg=pgp-sha256
Mime-Version: 1.0 (Mac OS X Mail 10.3 \(3273\))
Date: Wed, 5 Jul 2017 15:11:36 +0200
In-Reply-To: <11cc5d3f-ecf9-2fd0-825c-c8b441bd2813@tugraz.at>
Cc: Philipp Jovanovic <philipp@jovanovic.io>, cfrg@irtf.org
To: Daniel Slamanig <daniel.slamanig@tugraz.at>
References: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io> <11cc5d3f-ecf9-2fd0-825c-c8b441bd2813@tugraz.at>
X-Mailer: Apple Mail (2.3273)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/EDzfdgrHSKDjDgKlLCZjIgBDDbc>
Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 13:11:53 -0000

--Apple-Mail=_C4E4CACE-761E-4B3F-B41D-B27E8D7044A1
Content-Type: multipart/alternative;
	boundary="Apple-Mail=_B5FF9FDC-9ED8-4DFA-971D-BAEB3D9B51E0"


--Apple-Mail=_B5FF9FDC-9ED8-4DFA-971D-BAEB3D9B51E0
Content-Transfer-Encoding: quoted-printable
Content-Type: text/plain;
	charset=utf-8

Hi Daniel, thanks for your thoughts on the commitment-to-the-bitmask =
issue.

Your proposal of using a chameleon hash, to allow the leader to =
=E2=80=9Cadjust=E2=80=9D the bit mask after the commit c has been =
established, is an interesting idea. However, if I understand it =
correctly, if the leader holds the trapdoor key for the chameleon hash, =
wouldn=E2=80=99t that still make the final collective signature =
malleable for the leader (or for anyone the leader=E2=80=99s trapdoor =
key might leak to)?  The CoSi protocol as currently defined is intended =
to ensure that the leader has no special privilege or trust with respect =
to other cosigners: i.e., the leader is merely an ordinary participant, =
but is simply the one who for whatever reason decides to initiate the =
cosigning operation.  Giving the leader special powers - e.g., making =
the signature malleable to the leader but not to others - would break =
this principle and need to be extremely carefully considered I think.

To follow up on my last message to Oleg, again I suggest reading section =
IV of our CoSi paper from IEEE S&P last year =
(http://dedis.cs.yale.edu/dissent/papers/witness-abs =
<http://dedis.cs.yale.edu/dissent/papers/witness-abs>), as it discusses =
several related issues, especially the potential desire to allow the =
leader to complete a collective signing procedure even with only a =
subset of =E2=80=9Ccommitted=E2=80=9D participants remaining present in =
the =E2=80=9Cresponse=E2=80=9D phase.  In particular, the leader can =
form all the individual Schnorr commits into a Merkle tree, and make the =
real commit c be the root of that Merkle tree.  In this way, the leader =
is committing not so much to a particular collective Schnorr commit but =
rather to *all possible* Schnorr commits that can be composed from any =
subset of the individual Schnorr commits within that Merkle tree.  This =
way, if some of the participants whose commits are present in that =
Merkle tree remain available during the response phase but others drop =
out, the leader can still use the commit c and form a correct and =
verifiable collective signature against the particular subset of Schnorr =
commits from nodes that remained available throughout the process, =
without restarting.

I guess this approach does, in a slightly different way, make the =
resulting collective signatures slightly malleable to the leader: from a =
given set of commit-time and response-time information, the leader could =
put together distinct collective signatures representing different =
subsets of response-time participants.  Some form of =
=E2=80=9Cleader-malleability=E2=80=9D of this kind seems unavoidably =
essential to enabling the leader to complete a collective signing round =
in the presence of partial failures without restarting.  Perhaps the =
same limited leader-malleability is more-or-less the same property your =
suggestion of using chameleon hashes has, although I haven=E2=80=99t had =
a chance to compare them deeply yet.

But at any rate, the higher-level tradeoff here to consider is whether =
it=E2=80=99s better to (a) enforce strict non-malleability of collective =
signatures (by anyone, leader included), at the cost of O(N)-round DoS =
attack vulnerability during signing due to the need to restart partially =
failed rounds, or (b) provide some limited form of limited =
leader-malleability in order to support restart-free operation and avoid =
DoS attacks during signing, at the cost of a more complex protocol (and =
perhaps slightly more =E2=80=9Cspecial=E2=80=9D trust in the leader than =
we might like).

Again, further thoughts on this and other topics are most welcome.

Thanks
Bryan

> On Jul 3, 2017, at 7:34 PM, Daniel Slamanig =
<daniel.slamanig@tugraz.at> wrote:
>=20
> Hi Philipp,
>=20
> looks interesting!
>=20
> After looking at the protocol I also have some security concerns =
(related to what has been raised by Oleg in a previous mail).
>=20
> Not committing to Z as well as the actual sum of signers public keys =
A' in the computation of the hash c for the signature seems to be =
problematic.
>=20
> It seems to me that committing Z in the signature in plain as well as =
A' does not work given the later application of the signing procedure =
(where till the end of the protocol it is not clear who actually =
participates in the signing but c must be known at the beginning).
>=20
> Committing to neither of both however seems problematic as it does not =
fix the set of actual signers.
>=20
> This could be circumvented by allowing an honest leader to adapt the =
commitment to the final Z (and A') after it knows the signers without =
modifying the initially computed c using a chameleon hash (trapdoor =
commitment). I use P as a generator below, omit the brackets [a]P =
notation for scalar multiplication and write it from the perspective of =
the leader, i.e., the signer that initiates the protocol.
>=20
> The leader could choose chameleon hash parameters sk_ch=3Dy for random =
y and pk_ch=3D(P,Y=3DyP) and add pk_ch and chameleon hash =
CH(Z'):=3Dh(Z')P+u'Y for randomly chosen u' to the computation of c, =
i.e., set c=3DH(R||A||pk_ch||CH(Z')||S), where h() is a collision =
resistant hash function (this is just the standard way of constructing a =
chameleon hash from DL for arbitrary message spaces as propsed in [1]). =
If Z' is not yet known one simply sets Z' to some fixed string at the =
beginning, e.g., Z':=3D0. At the end of the protocol, when the leader =
knows the exact signers, it can update Z' to the final value Z and use =
sk_ch to compute a collision in the chameleon hash, i.e., such that =
CH(Z)=3DCH(Z') by solving h(Z')+u'y =3D h(Z)+uy for u. He then adds u =
and Z as well as pk_ch to the signature, i.e., sets it as =
(R,s,u,Z,pk_ch) and discards sk_ch and u'. If Z is known beforehand, one =
simply computes the chameleon hash once and does not need to compute a =
collision. Clearly, the use of a chameleon hash allows to simply adapt =
to the actual set of signers representing Z without modifying c (with =
the knowledge of sk_ch - but it does not work without the knowledge of =
sk_ch). This would resolve the issue with the unknown Z at the time of =
signing.
>=20
> Also, A is committed in the signature, but not the concrete A'=3D\sum =
A_i of keys used for computing the signature (I guess also due to the =
reason that one does not know the correct set of signers when computing =
the hash c). That can be problematic in a rogue key scenario in the =
current protocol, i.e., when not all signers need to prove knowledge of =
the secret key when they register their public keys but their public =
keys could be functions of other public keys (guess this could be a =
problem here). For instance, a malicious A^* could just take some key =
from A, say A_j, and compute and publish A^*=3Da^*A_j. And then given a =
collective signature (R,s,Z) where A_j participated, the signer can =
update s to s^* =3D s+a^*c as well as Z^* to exclude A_j and include A^* =
(as Z is not committed in the signature generation) and the signature =
(R,s^*,Z^*) will be a valid signature that certifies that A^* =
participated in signing - although he didn't.
>=20
> If Z is committed as proposed above and it is checked during the =
verification, then this should no longer work. One could also adapt the =
hash c=3DH(R||pk_ch||CH(Z'||A)||S) to include a chameleon hash to =
CH(Z||A'), where A' is the real set of signers that participated in the =
signature generation and is adapted before finalizing the signature when =
known as above.
>=20
> I hope that what I proposed is not just complete nonsense :) Also it =
produces quite a bit of an overhead. There may also be easier ways to =
avoid the issues.
>=20
> Some editorial issues: the message to be signed is sometimes called a =
satement S and later then message msg. S could be confusing as part of =
the signature is s and your semantic is that scalars are lowercase and =
points are uppercase. Also in 4.2 "Signature Generation" steps 2 and 3 =
are confusing as I guess that in the protocol all the signer compute =
their own [r_i]B values and R=3D\sum R_i instead of R=3D[r]B which would =
mean that they would send their r_i's (hope they will not do so).
>=20
> Also I find it somewhat confusing that the bitmask Z identifies the =
non-signers with a bit set to 1. Why not identifying the signers with a =
bit set to 1?
>=20
> Cheers,
> Daniel
>=20
>=20
> [1] Hugo Krawczyk, Tal Rabin: Chameleon Signatures. NDSS 2000
>=20
> On 01.07.2017 23:58, Philipp Jovanovic wrote:
>> Hi CFRG,
>> Here=E2=80=99s a first version of an Internet-Draft on =E2=80=9CCollect=
ive Edwards-Curve Digital Signature Algorithms=E2=80=9D based on Ed25519 =
and Ed448: https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/
>> We plan to give a short presentation on that topic at the next CFRG =
meeting in Prague.
>> Any feedback is more than welcome. Thanks!
>> All the best,
>> Philipp
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org
>> https://www.irtf.org/mailman/listinfo/cfrg
>=20
>=20
> --
> Dr. Daniel Slamanig
> Institute for Applied Information Processing and Communications
> Graz University of Technology
> Inffeldgasse 16a, 8010 Graz, Austria.
> Phone: +43 316 873 5509
> http://www.iaik.tugraz.at
>=20
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg


--Apple-Mail=_B5FF9FDC-9ED8-4DFA-971D-BAEB3D9B51E0
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html;
	charset=utf-8

<html><head><meta http-equiv=3D"Content-Type" content=3D"text/html =
charset=3Dutf-8"></head><body style=3D"word-wrap: break-word; =
-webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" =
class=3D"">Hi Daniel, thanks for your thoughts on the =
commitment-to-the-bitmask issue.<div class=3D""><br class=3D""></div><div =
class=3D"">Your proposal of using a chameleon hash, to allow the leader =
to =E2=80=9Cadjust=E2=80=9D the bit mask after the commit c has been =
established, is an interesting idea. However, if I understand it =
correctly, if the leader holds the trapdoor key for the chameleon hash, =
wouldn=E2=80=99t that still make the final collective signature =
malleable for the leader (or for anyone the leader=E2=80=99s trapdoor =
key might leak to)? &nbsp;The CoSi protocol as currently defined is =
intended to ensure that the leader has no special privilege or trust =
with respect to other cosigners: i.e., the leader is merely an ordinary =
participant, but is simply the one who for whatever reason decides to =
initiate the cosigning operation. &nbsp;Giving the leader special powers =
- e.g., making the signature malleable to the leader but not to others - =
would break this principle and need to be extremely carefully considered =
I think.</div><div class=3D""><br class=3D""></div><div class=3D"">To =
follow up on my last message to Oleg, again I suggest reading section IV =
of our CoSi paper from IEEE S&amp;P last year (<a =
href=3D"http://dedis.cs.yale.edu/dissent/papers/witness-abs" =
class=3D"">http://dedis.cs.yale.edu/dissent/papers/witness-abs</a>), as =
it discusses several related issues, especially the potential desire to =
allow the leader to complete a collective signing procedure even with =
only a subset of =E2=80=9Ccommitted=E2=80=9D participants remaining =
present in the =E2=80=9Cresponse=E2=80=9D phase. &nbsp;In particular, =
the leader can form all the individual Schnorr commits into a Merkle =
tree, and make the real commit c be the root of that Merkle tree. =
&nbsp;In this way, the leader is committing not so much to a particular =
collective Schnorr commit but rather to *all possible* Schnorr commits =
that can be composed from any subset of the individual Schnorr commits =
within that Merkle tree. &nbsp;This way, if some of the participants =
whose commits are present in that Merkle tree remain available during =
the response phase but others drop out, the leader can still use the =
commit c and form a correct and verifiable collective signature against =
the particular subset of Schnorr commits from nodes that remained =
available throughout the process, without restarting.</div><div =
class=3D""><br class=3D""></div><div class=3D"">I guess this approach =
does, in a slightly different way, make the resulting collective =
signatures slightly malleable to the leader: from a given set of =
commit-time and response-time information, the leader could put together =
distinct collective signatures representing different subsets of =
response-time participants. &nbsp;Some form of =E2=80=9Cleader-malleabilit=
y=E2=80=9D of this kind seems unavoidably essential to enabling the =
leader to complete a collective signing round in the presence of partial =
failures without restarting. &nbsp;Perhaps the same limited =
leader-malleability is more-or-less the same property your suggestion of =
using chameleon hashes has, although I haven=E2=80=99t had a chance to =
compare them deeply yet. &nbsp;</div><div class=3D""><br =
class=3D""></div><div class=3D"">But at any rate, the higher-level =
tradeoff here to consider is whether it=E2=80=99s better to (a) enforce =
strict non-malleability of collective signatures (by anyone, leader =
included), at the cost of O(N)-round DoS attack vulnerability during =
signing due to the need to restart partially failed rounds, or (b) =
provide some limited form of limited leader-malleability in order to =
support restart-free operation and avoid DoS attacks during signing, at =
the cost of a more complex protocol (and perhaps slightly more =
=E2=80=9Cspecial=E2=80=9D trust in the leader than we might =
like).</div><div class=3D""><br class=3D""></div><div class=3D"">Again, =
further thoughts on this and other topics are most welcome.</div><div =
class=3D""><br class=3D""></div><div class=3D"">Thanks</div><div =
class=3D"">Bryan</div><div class=3D""><br class=3D""><div><blockquote =
type=3D"cite" class=3D""><div class=3D"">On Jul 3, 2017, at 7:34 PM, =
Daniel Slamanig &lt;<a href=3D"mailto:daniel.slamanig@tugraz.at" =
class=3D"">daniel.slamanig@tugraz.at</a>&gt; wrote:</div><br =
class=3D"Apple-interchange-newline"><div class=3D""><div class=3D"">Hi =
Philipp,<br class=3D""><br class=3D"">looks interesting!<br class=3D""><br=
 class=3D"">After looking at the protocol I also have some security =
concerns (related to what has been raised by Oleg in a previous =
mail).<br class=3D""><br class=3D"">Not committing to Z as well as the =
actual sum of signers public keys A' in the computation of the hash c =
for the signature seems to be problematic.<br class=3D""><br class=3D"">It=
 seems to me that committing Z in the signature in plain as well as A' =
does not work given the later application of the signing procedure =
(where till the end of the protocol it is not clear who actually =
participates in the signing but c must be known at the beginning).<br =
class=3D""><br class=3D"">Committing to neither of both however seems =
problematic as it does not fix the set of actual signers.<br =
class=3D""><br class=3D"">This could be circumvented by allowing an =
honest leader to adapt the commitment to the final Z (and A') after it =
knows the signers without modifying the initially computed c using a =
chameleon hash (trapdoor commitment). I use P as a generator below, omit =
the brackets [a]P notation for scalar multiplication and write it from =
the perspective of the leader, i.e., the signer that initiates the =
protocol.<br class=3D""><br class=3D"">The leader could choose chameleon =
hash parameters sk_ch=3Dy for random y and pk_ch=3D(P,Y=3DyP) and add =
pk_ch and chameleon hash CH(Z'):=3Dh(Z')P+u'Y for randomly chosen u' to =
the computation of c, i.e., set c=3DH(R||A||pk_ch||CH(Z')||S), where h() =
is a collision resistant hash function (this is just the standard way of =
constructing a chameleon hash from DL for arbitrary message spaces as =
propsed in [1]). If Z' is not yet known one simply sets Z' to some fixed =
string at the beginning, e.g., Z':=3D0. At the end of the protocol, when =
the leader knows the exact signers, it can update Z' to the final value =
Z and use sk_ch to compute a collision in the chameleon hash, i.e., such =
that CH(Z)=3DCH(Z') by solving h(Z')+u'y =3D h(Z)+uy for u. He then adds =
u and Z as well as pk_ch to the signature, i.e., sets it as =
(R,s,u,Z,pk_ch) and discards sk_ch and u'. If Z is known beforehand, one =
simply computes the chameleon hash once and does not need to compute a =
collision. Clearly, the use of a chameleon hash allows to simply adapt =
to the actual set of signers representing Z without modifying c (with =
the knowledge of sk_ch - but it does not work without the knowledge of =
sk_ch). This would resolve the issue with the unknown Z at the time of =
signing.<br class=3D""><br class=3D"">Also, A is committed in the =
signature, but not the concrete A'=3D\sum A_i of keys used for computing =
the signature (I guess also due to the reason that one does not know the =
correct set of signers when computing the hash c). That can be =
problematic in a rogue key scenario in the current protocol, i.e., when =
not all signers need to prove knowledge of the secret key when they =
register their public keys but their public keys could be functions of =
other public keys (guess this could be a problem here). For instance, a =
malicious A^* could just take some key from A, say A_j, and compute and =
publish A^*=3Da^*A_j. And then given a collective signature (R,s,Z) =
where A_j participated, the signer can update s to s^* =3D s+a^*c as =
well as Z^* to exclude A_j and include A^* (as Z is not committed in the =
signature generation) and the signature (R,s^*,Z^*) will be a valid =
signature that certifies that A^* participated in signing - although he =
didn't.<br class=3D""><br class=3D"">If Z is committed as proposed above =
and it is checked during the verification, then this should no longer =
work. One could also adapt the hash c=3DH(R||pk_ch||CH(Z'||A)||S) to =
include a chameleon hash to CH(Z||A'), where A' is the real set of =
signers that participated in the signature generation and is adapted =
before finalizing the signature when known as above.<br class=3D""><br =
class=3D"">I hope that what I proposed is not just complete nonsense :) =
Also it produces quite a bit of an overhead. There may also be easier =
ways to avoid the issues.<br class=3D""><br class=3D"">Some editorial =
issues: the message to be signed is sometimes called a satement S and =
later then message msg. S could be confusing as part of the signature is =
s and your semantic is that scalars are lowercase and points are =
uppercase. Also in 4.2 "Signature Generation" steps 2 and 3 are =
confusing as I guess that in the protocol all the signer compute their =
own [r_i]B values and R=3D\sum R_i instead of R=3D[r]B which would mean =
that they would send their r_i's (hope they will not do so).<br =
class=3D""><br class=3D"">Also I find it somewhat confusing that the =
bitmask Z identifies the non-signers with a bit set to 1. Why not =
identifying the signers with a bit set to 1?<br class=3D""><br =
class=3D"">Cheers,<br class=3D"">Daniel<br class=3D""><br class=3D""><br =
class=3D"">[1] Hugo Krawczyk, Tal Rabin: Chameleon Signatures. NDSS =
2000<br class=3D""><br class=3D"">On 01.07.2017 23:58, Philipp Jovanovic =
wrote:<br class=3D""><blockquote type=3D"cite" class=3D"">Hi CFRG,<br =
class=3D"">Here=E2=80=99s a first version of an Internet-Draft on =
=E2=80=9CCollective Edwards-Curve Digital Signature Algorithms=E2=80=9D =
based on Ed25519 and Ed448: <a =
href=3D"https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/" =
class=3D"">https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/</a><br =
class=3D"">We plan to give a short presentation on that topic at the =
next CFRG meeting in Prague.<br class=3D"">Any feedback is more than =
welcome. Thanks!<br class=3D"">All the best,<br class=3D"">Philipp<br =
class=3D"">_______________________________________________<br =
class=3D"">Cfrg mailing list<br class=3D""><a =
href=3D"mailto:Cfrg@irtf.org" class=3D"">Cfrg@irtf.org</a><br =
class=3D"">https://www.irtf.org/mailman/listinfo/cfrg<br =
class=3D""></blockquote><br class=3D""><br class=3D"">--<br class=3D"">Dr.=
 Daniel Slamanig<br class=3D"">Institute for Applied Information =
Processing and Communications<br class=3D"">Graz University of =
Technology<br class=3D"">Inffeldgasse 16a, 8010 Graz, Austria.<br =
class=3D"">Phone: +43 316 873 5509<br class=3D""><a =
href=3D"http://www.iaik.tugraz.at" =
class=3D"">http://www.iaik.tugraz.at</a><br class=3D""><br =
class=3D"">_______________________________________________<br =
class=3D"">Cfrg mailing list<br class=3D"">Cfrg@irtf.org<br =
class=3D"">https://www.irtf.org/mailman/listinfo/cfrg<br =
class=3D""></div></div></blockquote></div><br =
class=3D""></div></body></html>=

--Apple-Mail=_B5FF9FDC-9ED8-4DFA-971D-BAEB3D9B51E0--

--Apple-Mail=_C4E4CACE-761E-4B3F-B41D-B27E8D7044A1
Content-Transfer-Encoding: 7bit
Content-Disposition: attachment;
	filename=signature.asc
Content-Type: application/pgp-signature;
	name=signature.asc
Content-Description: Message signed with OpenPGP

-----BEGIN PGP SIGNATURE-----
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=pPJq
-----END PGP SIGNATURE-----

--Apple-Mail=_C4E4CACE-761E-4B3F-B41D-B27E8D7044A1--


From nobody Wed Jul  5 06:27:08 2017
Return-Path: <tgarcia.3141@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 90F53132A19 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 06:27:07 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.448
X-Spam-Level: 
X-Spam-Status: No, score=-2.448 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_ENVFROM_END_DIGIT=0.25, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id X1arLZakUaiv for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 06:27:03 -0700 (PDT)
Received: from mail-lf0-x229.google.com (mail-lf0-x229.google.com [IPv6:2a00:1450:4010:c07::229]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 3B2E6132A13 for <cfrg@irtf.org>; Wed,  5 Jul 2017 06:27:03 -0700 (PDT)
Received: by mail-lf0-x229.google.com with SMTP id t72so24793950lff.1 for <cfrg@irtf.org>; Wed, 05 Jul 2017 06:27:03 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=UKfnMuwHUZ/RgEvUOOGlINc1+jwLRDMAn5UQdl/D17s=; b=RQrqZDZipeNNA421oDvOPmrkuimuILR8SqbMcxEt+Wrp45xev9oiv0TbsC8AHJ2MUR Ys6zVKdJS7jCikBG6dyzp4RBl0RtTw3MJhGx/mYqfsw4A+LDJYAt3KjNfJ9cfZ31ssmx iSiy0LT0+DTw47mnbF8vK+XQ8ZU/2wRJ9V6iLUo5yqsFrr+a7YZePYxRpEuPzGR0ioXG kmffynVavkmAn2rdfJmoN5p5hO6zfzZ9ajThz/tVWRmLgWKPkGuOKxbbP4XJTk+WZzON 9RFp9RXEJ3tNm/lthZpXBKwMIbd+oGKLze/NuB45Ny61TQOCpA4sBCvzrR2ddSdva+2g 3iIg==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=UKfnMuwHUZ/RgEvUOOGlINc1+jwLRDMAn5UQdl/D17s=; b=GVq+boCzeQlVy/cnIdFMOIia2waEuchfUa8m5fVceoXDi5VMHMWnK5QUcMKJN7DM/k Q6juWLdjG8u1l32B0MtZf9adQNoo1uchGC8lR6wKaVW7asStCC9vlMD0abfYhojCx7oL oWVgBAT9JHzikewCAtNMr48yhiZ45OPRtP1tw2GKMvMrzUpOhZTRrW1DX+whCg7lVGCZ bU3oBZJf0SYv0QO65dgKkOIPEhtYVNLRq6IVMGEDeYiJGWWlwXvSYbEUXIdNPQSjKWW9 JhU6HhjZCxR6CDwWFN1I4UA3c1fEU6363cq+AJWdQWcnNyqwCwU2ajh1fMoZeEXjkb0G eAQA==
X-Gm-Message-State: AKS2vOzyv7Fjfn6081YP8uRg5n6FDcikuzstv4c/ecA3blIfkhuxIGgE Qi7HA3JLhQlhOppP/z4MP6Cc0w7YWA==
X-Received: by 10.46.71.72 with SMTP id u69mr13290752lja.16.1499261221388; Wed, 05 Jul 2017 06:27:01 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.25.22.211 with HTTP; Wed, 5 Jul 2017 06:27:00 -0700 (PDT)
In-Reply-To: <A423CB6E-D649-4320-BB76-2E3783D6AFE0@gmail.com>
References: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io> <11cc5d3f-ecf9-2fd0-825c-c8b441bd2813@tugraz.at> <A423CB6E-D649-4320-BB76-2E3783D6AFE0@gmail.com>
From: Thomas Garcia <tgarcia.3141@gmail.com>
Date: Wed, 5 Jul 2017 14:27:00 +0100
Message-ID: <CAFTSWve-J9pKVAaCJ=F==ZP_6=f2QMR2chD+J0T7vF6SNb95Ow@mail.gmail.com>
To: Bryan Ford <brynosaurus@gmail.com>
Cc: Daniel Slamanig <daniel.slamanig@tugraz.at>, cfrg@irtf.org
Content-Type: multipart/alternative; boundary="001a11411b8486ca1c055391f431"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/QTz9IEbcKURvqQoxI7hrfCaz3Rk>
Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 13:27:07 -0000

--001a11411b8486ca1c055391f431
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Hello,
I have a number of comments regarding the draft.
1. In the described protocol the leader, after receiving commitments from
the participants and calculating the challenge c, sends that challenge to
the participants. The participants then do not verify that c was indeed
calculated using the message that they intended to sign, allowing the
leader to procure signatures for arbitrary messages. A stage of
verification of c should be added to the protocol.
2. EdDSA is designed to withstand collision attacks against the hash
function used in the signature. On the other hand, the protocol suggested
is susceptible to such attacks. A hostile leader and participant, together,
could wait for all other participants to select their commitments. They
could then choose a commitment such that
SHA512(R||A||msg)=3DSHA512(R'||A||msg'), providing them with a signature of
msg'. This would of course have to be done in real-time, and given the
strength of SHA512 is in no way practical. This kind of attack would be
difficult to avoid without substantial modifications to the scheme, but
this does not seem to be a significant threat.

Thomas G.

On Wed, Jul 5, 2017 at 2:11 PM, Bryan Ford <brynosaurus@gmail.com> wrote:

> Hi Daniel, thanks for your thoughts on the commitment-to-the-bitmask issu=
e.
>
> Your proposal of using a chameleon hash, to allow the leader to =E2=80=9C=
adjust=E2=80=9D
> the bit mask after the commit c has been established, is an interesting
> idea. However, if I understand it correctly, if the leader holds the
> trapdoor key for the chameleon hash, wouldn=E2=80=99t that still make the=
 final
> collective signature malleable for the leader (or for anyone the leader=
=E2=80=99s
> trapdoor key might leak to)?  The CoSi protocol as currently defined is
> intended to ensure that the leader has no special privilege or trust with
> respect to other cosigners: i.e., the leader is merely an ordinary
> participant, but is simply the one who for whatever reason decides to
> initiate the cosigning operation.  Giving the leader special powers - e.g=
.,
> making the signature malleable to the leader but not to others - would
> break this principle and need to be extremely carefully considered I thin=
k.
>
> To follow up on my last message to Oleg, again I suggest reading section
> IV of our CoSi paper from IEEE S&P last year (http://dedis.cs.yale.edu/
> dissent/papers/witness-abs), as it discusses several related issues,
> especially the potential desire to allow the leader to complete a
> collective signing procedure even with only a subset of =E2=80=9Ccommitte=
d=E2=80=9D
> participants remaining present in the =E2=80=9Cresponse=E2=80=9D phase.  =
In particular, the
> leader can form all the individual Schnorr commits into a Merkle tree, an=
d
> make the real commit c be the root of that Merkle tree.  In this way, the
> leader is committing not so much to a particular collective Schnorr commi=
t
> but rather to *all possible* Schnorr commits that can be composed from an=
y
> subset of the individual Schnorr commits within that Merkle tree.  This
> way, if some of the participants whose commits are present in that Merkle
> tree remain available during the response phase but others drop out, the
> leader can still use the commit c and form a correct and verifiable
> collective signature against the particular subset of Schnorr commits fro=
m
> nodes that remained available throughout the process, without restarting.
>
> I guess this approach does, in a slightly different way, make the
> resulting collective signatures slightly malleable to the leader: from a
> given set of commit-time and response-time information, the leader could
> put together distinct collective signatures representing different subset=
s
> of response-time participants.  Some form of =E2=80=9Cleader-malleability=
=E2=80=9D of this
> kind seems unavoidably essential to enabling the leader to complete a
> collective signing round in the presence of partial failures without
> restarting.  Perhaps the same limited leader-malleability is more-or-less
> the same property your suggestion of using chameleon hashes has, although=
 I
> haven=E2=80=99t had a chance to compare them deeply yet.
>
> But at any rate, the higher-level tradeoff here to consider is whether
> it=E2=80=99s better to (a) enforce strict non-malleability of collective =
signatures
> (by anyone, leader included), at the cost of O(N)-round DoS attack
> vulnerability during signing due to the need to restart partially failed
> rounds, or (b) provide some limited form of limited leader-malleability i=
n
> order to support restart-free operation and avoid DoS attacks during
> signing, at the cost of a more complex protocol (and perhaps slightly mor=
e
> =E2=80=9Cspecial=E2=80=9D trust in the leader than we might like).
>
> Again, further thoughts on this and other topics are most welcome.
>
> Thanks
> Bryan
>
> On Jul 3, 2017, at 7:34 PM, Daniel Slamanig <daniel.slamanig@tugraz.at>
> wrote:
>
> Hi Philipp,
>
> looks interesting!
>
> After looking at the protocol I also have some security concerns (related
> to what has been raised by Oleg in a previous mail).
>
> Not committing to Z as well as the actual sum of signers public keys A' i=
n
> the computation of the hash c for the signature seems to be problematic.
>
> It seems to me that committing Z in the signature in plain as well as A'
> does not work given the later application of the signing procedure (where
> till the end of the protocol it is not clear who actually participates in
> the signing but c must be known at the beginning).
>
> Committing to neither of both however seems problematic as it does not fi=
x
> the set of actual signers.
>
> This could be circumvented by allowing an honest leader to adapt the
> commitment to the final Z (and A') after it knows the signers without
> modifying the initially computed c using a chameleon hash (trapdoor
> commitment). I use P as a generator below, omit the brackets [a]P notatio=
n
> for scalar multiplication and write it from the perspective of the leader=
,
> i.e., the signer that initiates the protocol.
>
> The leader could choose chameleon hash parameters sk_ch=3Dy for random y =
and
> pk_ch=3D(P,Y=3DyP) and add pk_ch and chameleon hash CH(Z'):=3Dh(Z')P+u'Y =
for
> randomly chosen u' to the computation of c, i.e., set
> c=3DH(R||A||pk_ch||CH(Z')||S), where h() is a collision resistant hash
> function (this is just the standard way of constructing a chameleon hash
> from DL for arbitrary message spaces as propsed in [1]). If Z' is not yet
> known one simply sets Z' to some fixed string at the beginning, e.g.,
> Z':=3D0. At the end of the protocol, when the leader knows the exact sign=
ers,
> it can update Z' to the final value Z and use sk_ch to compute a collisio=
n
> in the chameleon hash, i.e., such that CH(Z)=3DCH(Z') by solving h(Z')+u'=
y =3D
> h(Z)+uy for u. He then adds u and Z as well as pk_ch to the signature,
> i.e., sets it as (R,s,u,Z,pk_ch) and discards sk_ch and u'. If Z is known
> beforehand, one simply computes the chameleon hash once and does not need
> to compute a collision. Clearly, the use of a chameleon hash allows to
> simply adapt to the actual set of signers representing Z without modifyin=
g
> c (with the knowledge of sk_ch - but it does not work without the knowled=
ge
> of sk_ch). This would resolve the issue with the unknown Z at the time of
> signing.
>
> Also, A is committed in the signature, but not the concrete A'=3D\sum A_i=
 of
> keys used for computing the signature (I guess also due to the reason tha=
t
> one does not know the correct set of signers when computing the hash c).
> That can be problematic in a rogue key scenario in the current protocol,
> i.e., when not all signers need to prove knowledge of the secret key when
> they register their public keys but their public keys could be functions =
of
> other public keys (guess this could be a problem here). For instance, a
> malicious A^* could just take some key from A, say A_j, and compute and
> publish A^*=3Da^*A_j. And then given a collective signature (R,s,Z) where=
 A_j
> participated, the signer can update s to s^* =3D s+a^*c as well as Z^* to
> exclude A_j and include A^* (as Z is not committed in the signature
> generation) and the signature (R,s^*,Z^*) will be a valid signature that
> certifies that A^* participated in signing - although he didn't.
>
> If Z is committed as proposed above and it is checked during the
> verification, then this should no longer work. One could also adapt the
> hash c=3DH(R||pk_ch||CH(Z'||A)||S) to include a chameleon hash to CH(Z||A=
'),
> where A' is the real set of signers that participated in the signature
> generation and is adapted before finalizing the signature when known as
> above.
>
> I hope that what I proposed is not just complete nonsense :) Also it
> produces quite a bit of an overhead. There may also be easier ways to avo=
id
> the issues.
>
> Some editorial issues: the message to be signed is sometimes called a
> satement S and later then message msg. S could be confusing as part of th=
e
> signature is s and your semantic is that scalars are lowercase and points
> are uppercase. Also in 4.2 "Signature Generation" steps 2 and 3 are
> confusing as I guess that in the protocol all the signer compute their ow=
n
> [r_i]B values and R=3D\sum R_i instead of R=3D[r]B which would mean that =
they
> would send their r_i's (hope they will not do so).
>
> Also I find it somewhat confusing that the bitmask Z identifies the
> non-signers with a bit set to 1. Why not identifying the signers with a b=
it
> set to 1?
>
> Cheers,
> Daniel
>
>
> [1] Hugo Krawczyk, Tal Rabin: Chameleon Signatures. NDSS 2000
>
> On 01.07.2017 23:58, Philipp Jovanovic wrote:
>
> Hi CFRG,
> Here=E2=80=99s a first version of an Internet-Draft on =E2=80=9CCollectiv=
e Edwards-Curve
> Digital Signature Algorithms=E2=80=9D based on Ed25519 and Ed448:
> https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/
> We plan to give a short presentation on that topic at the next CFRG
> meeting in Prague.
> Any feedback is more than welcome. Thanks!
> All the best,
> Philipp
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>
>
>
> --
> Dr. Daniel Slamanig
> Institute for Applied Information Processing and Communications
> Graz University of Technology
> Inffeldgasse 16a, 8010 Graz, Austria.
> Phone: +43 316 873 5509 <+43%20316%208735509>
> http://www.iaik.tugraz.at
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>
>
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>
>

--001a11411b8486ca1c055391f431
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Hello,<div>I have a number of comments regarding the draft=
.</div><div>1. In the described protocol the leader, after receiving commit=
ments from the participants and calculating the challenge c, sends that cha=
llenge to the participants. The participants then do not verify that c was =
indeed calculated using the message that they intended to sign, allowing th=
e leader to procure signatures for arbitrary messages. A stage of verificat=
ion of c should be added to the protocol.</div><div>2. EdDSA is designed to=
 withstand collision attacks against the hash function used in the signatur=
e. On the other hand, the protocol suggested is susceptible to such attacks=
. A hostile leader and participant, together, could wait for all other part=
icipants to select their commitments. They could then choose a commitment s=
uch that SHA512(R||A||msg)=3DSHA512(R&#39;||A||msg&#39;), providing them wi=
th a signature of msg&#39;. This would of course have to be done in real-ti=
me, and given the strength of SHA512 is in no way practical. This kind of a=
ttack would be difficult to avoid without substantial modifications to the =
scheme, but this does not seem to be a significant threat.</div><div><br></=
div><div>Thomas G.</div></div><div class=3D"gmail_extra"><br><div class=3D"=
gmail_quote">On Wed, Jul 5, 2017 at 2:11 PM, Bryan Ford <span dir=3D"ltr">&=
lt;<a href=3D"mailto:brynosaurus@gmail.com" target=3D"_blank">brynosaurus@g=
mail.com</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=
=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div sty=
le=3D"word-wrap:break-word">Hi Daniel, thanks for your thoughts on the comm=
itment-to-the-bitmask issue.<div><br></div><div>Your proposal of using a ch=
ameleon hash, to allow the leader to =E2=80=9Cadjust=E2=80=9D the bit mask =
after the commit c has been established, is an interesting idea. However, i=
f I understand it correctly, if the leader holds the trapdoor key for the c=
hameleon hash, wouldn=E2=80=99t that still make the final collective signat=
ure malleable for the leader (or for anyone the leader=E2=80=99s trapdoor k=
ey might leak to)?=C2=A0 The CoSi protocol as currently defined is intended=
 to ensure that the leader has no special privilege or trust with respect t=
o other cosigners: i.e., the leader is merely an ordinary participant, but =
is simply the one who for whatever reason decides to initiate the cosigning=
 operation.=C2=A0 Giving the leader special powers - e.g., making the signa=
ture malleable to the leader but not to others - would break this principle=
 and need to be extremely carefully considered I think.</div><div><br></div=
><div>To follow up on my last message to Oleg, again I suggest reading sect=
ion IV of our CoSi paper from IEEE S&amp;P last year (<a href=3D"http://ded=
is.cs.yale.edu/dissent/papers/witness-abs" target=3D"_blank">http://dedis.c=
s.yale.edu/<wbr>dissent/papers/witness-abs</a>), as it discusses several re=
lated issues, especially the potential desire to allow the leader to comple=
te a collective signing procedure even with only a subset of =E2=80=9Ccommi=
tted=E2=80=9D participants remaining present in the =E2=80=9Cresponse=E2=80=
=9D phase.=C2=A0 In particular, the leader can form all the individual Schn=
orr commits into a Merkle tree, and make the real commit c be the root of t=
hat Merkle tree.=C2=A0 In this way, the leader is committing not so much to=
 a particular collective Schnorr commit but rather to *all possible* Schnor=
r commits that can be composed from any subset of the individual Schnorr co=
mmits within that Merkle tree.=C2=A0 This way, if some of the participants =
whose commits are present in that Merkle tree remain available during the r=
esponse phase but others drop out, the leader can still use the commit c an=
d form a correct and verifiable collective signature against the particular=
 subset of Schnorr commits from nodes that remained available throughout th=
e process, without restarting.</div><div><br></div><div>I guess this approa=
ch does, in a slightly different way, make the resulting collective signatu=
res slightly malleable to the leader: from a given set of commit-time and r=
esponse-time information, the leader could put together distinct collective=
 signatures representing different subsets of response-time participants.=
=C2=A0 Some form of =E2=80=9Cleader-malleability=E2=80=9D of this kind seem=
s unavoidably essential to enabling the leader to complete a collective sig=
ning round in the presence of partial failures without restarting.=C2=A0 Pe=
rhaps the same limited leader-malleability is more-or-less the same propert=
y your suggestion of using chameleon hashes has, although I haven=E2=80=99t=
 had a chance to compare them deeply yet. =C2=A0</div><div><br></div><div>B=
ut at any rate, the higher-level tradeoff here to consider is whether it=E2=
=80=99s better to (a) enforce strict non-malleability of collective signatu=
res (by anyone, leader included), at the cost of O(N)-round DoS attack vuln=
erability during signing due to the need to restart partially failed rounds=
, or (b) provide some limited form of limited leader-malleability in order =
to support restart-free operation and avoid DoS attacks during signing, at =
the cost of a more complex protocol (and perhaps slightly more =E2=80=9Cspe=
cial=E2=80=9D trust in the leader than we might like).</div><div><br></div>=
<div>Again, further thoughts on this and other topics are most welcome.</di=
v><div><br></div><div>Thanks</div><div>Bryan</div><div><br><div><blockquote=
 type=3D"cite"><div>On Jul 3, 2017, at 7:34 PM, Daniel Slamanig &lt;<a href=
=3D"mailto:daniel.slamanig@tugraz.at" target=3D"_blank">daniel.slamanig@tug=
raz.at</a>&gt; wrote:</div><br class=3D"m_3610228578482648793Apple-intercha=
nge-newline"><div><div>Hi Philipp,<br><br>looks interesting!<br><br>After l=
ooking at the protocol I also have some security concerns (related to what =
has been raised by Oleg in a previous mail).<br><br>Not committing to Z as =
well as the actual sum of signers public keys A&#39; in the computation of =
the hash c for the signature seems to be problematic.<br><br>It seems to me=
 that committing Z in the signature in plain as well as A&#39; does not wor=
k given the later application of the signing procedure (where till the end =
of the protocol it is not clear who actually participates in the signing bu=
t c must be known at the beginning).<br><br>Committing to neither of both h=
owever seems problematic as it does not fix the set of actual signers.<br><=
br>This could be circumvented by allowing an honest leader to adapt the com=
mitment to the final Z (and A&#39;) after it knows the signers without modi=
fying the initially computed c using a chameleon hash (trapdoor commitment)=
. I use P as a generator below, omit the brackets [a]P notation for scalar =
multiplication and write it from the perspective of the leader, i.e., the s=
igner that initiates the protocol.<br><br>The leader could choose chameleon=
 hash parameters sk_ch=3Dy for random y and pk_ch=3D(P,Y=3DyP) and add pk_c=
h and chameleon hash CH(Z&#39;):=3Dh(Z&#39;)P+u&#39;Y for randomly chosen u=
&#39; to the computation of c, i.e., set c=3DH(R||A||pk_ch||CH(Z&#39;)||S),=
 where h() is a collision resistant hash function (this is just the standar=
d way of constructing a chameleon hash from DL for arbitrary message spaces=
 as propsed in [1]). If Z&#39; is not yet known one simply sets Z&#39; to s=
ome fixed string at the beginning, e.g., Z&#39;:=3D0. At the end of the pro=
tocol, when the leader knows the exact signers, it can update Z&#39; to the=
 final value Z and use sk_ch to compute a collision in the chameleon hash, =
i.e., such that CH(Z)=3DCH(Z&#39;) by solving h(Z&#39;)+u&#39;y =3D h(Z)+uy=
 for u. He then adds u and Z as well as pk_ch to the signature, i.e., sets =
it as (R,s,u,Z,pk_ch) and discards sk_ch and u&#39;. If Z is known beforeha=
nd, one simply computes the chameleon hash once and does not need to comput=
e a collision. Clearly, the use of a chameleon hash allows to simply adapt =
to the actual set of signers representing Z without modifying c (with the k=
nowledge of sk_ch - but it does not work without the knowledge of sk_ch). T=
his would resolve the issue with the unknown Z at the time of signing.<br><=
br>Also, A is committed in the signature, but not the concrete A&#39;=3D\su=
m A_i of keys used for computing the signature (I guess also due to the rea=
son that one does not know the correct set of signers when computing the ha=
sh c). That can be problematic in a rogue key scenario in the current proto=
col, i.e., when not all signers need to prove knowledge of the secret key w=
hen they register their public keys but their public keys could be function=
s of other public keys (guess this could be a problem here). For instance, =
a malicious A^* could just take some key from A, say A_j, and compute and p=
ublish A^*=3Da^*A_j. And then given a collective signature (R,s,Z) where A_=
j participated, the signer can update s to s^* =3D s+a^*c as well as Z^* to=
 exclude A_j and include A^* (as Z is not committed in the signature genera=
tion) and the signature (R,s^*,Z^*) will be a valid signature that certifie=
s that A^* participated in signing - although he didn&#39;t.<br><br>If Z is=
 committed as proposed above and it is checked during the verification, the=
n this should no longer work. One could also adapt the hash c=3DH(R||pk_ch|=
|CH(Z&#39;||A)||S) to include a chameleon hash to CH(Z||A&#39;), where A&#3=
9; is the real set of signers that participated in the signature generation=
 and is adapted before finalizing the signature when known as above.<br><br=
>I hope that what I proposed is not just complete nonsense :) Also it produ=
ces quite a bit of an overhead. There may also be easier ways to avoid the =
issues.<br><br>Some editorial issues: the message to be signed is sometimes=
 called a satement S and later then message msg. S could be confusing as pa=
rt of the signature is s and your semantic is that scalars are lowercase an=
d points are uppercase. Also in 4.2 &quot;Signature Generation&quot; steps =
2 and 3 are confusing as I guess that in the protocol all the signer comput=
e their own [r_i]B values and R=3D\sum R_i instead of R=3D[r]B which would =
mean that they would send their r_i&#39;s (hope they will not do so).<br><b=
r>Also I find it somewhat confusing that the bitmask Z identifies the non-s=
igners with a bit set to 1. Why not identifying the signers with a bit set =
to 1?<br><br>Cheers,<br>Daniel<br><br><br>[1] Hugo Krawczyk, Tal Rabin: Cha=
meleon Signatures. NDSS 2000<span class=3D""><br><br>On 01.07.2017 23:58, P=
hilipp Jovanovic wrote:<br><blockquote type=3D"cite">Hi CFRG,<br>Here=E2=80=
=99s a first version of an Internet-Draft on =E2=80=9CCollective Edwards-Cu=
rve Digital Signature Algorithms=E2=80=9D based on Ed25519 and Ed448: <a hr=
ef=3D"https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/" target=3D"_bl=
ank">https://datatracker.ietf.org/<wbr>doc/draft-ford-cfrg-cosi/</a><br>We =
plan to give a short presentation on that topic at the next CFRG meeting in=
 Prague.<br>Any feedback is more than welcome. Thanks!<br>All the best,<br>=
Philipp<br>______________________________<wbr>_________________<br>Cfrg mai=
ling list<br><a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank">Cfrg@irtf.o=
rg</a><br><a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" target=3D"=
_blank">https://www.irtf.org/mailman/<wbr>listinfo/cfrg</a><br></blockquote=
><br><br></span><span class=3D"HOEnZb"><font color=3D"#888888">--<br>Dr. Da=
niel Slamanig<br>Institute for Applied Information Processing and Communica=
tions<br>Graz University of Technology<br>Inffeldgasse 16a, 8010 Graz, Aust=
ria.<br>Phone: <a href=3D"tel:+43%20316%208735509" value=3D"+433168735509" =
target=3D"_blank">+43 316 873 5509</a><br><a href=3D"http://www.iaik.tugraz=
.at" target=3D"_blank">http://www.iaik.tugraz.at</a></font></span><span cla=
ss=3D""><br><br>______________________________<wbr>_________________<br>Cfr=
g mailing list<br><a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank">Cfrg@i=
rtf.org</a><br><a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" targe=
t=3D"_blank">https://www.irtf.org/mailman/<wbr>listinfo/cfrg</a><br></span>=
</div></div></blockquote></div><br></div></div><br>________________________=
______<wbr>_________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/<wbr>listinfo/cfrg</a><br>
<br></blockquote></div><br></div>

--001a11411b8486ca1c055391f431--


From nobody Wed Jul  5 09:29:40 2017
Return-Path: <brynosaurus@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id A22FF131D71 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 09:29:38 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.998
X-Spam-Level: 
X-Spam-Status: No, score=-1.998 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id lf5tjaHn0m-U for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 09:29:35 -0700 (PDT)
Received: from mail-wr0-x235.google.com (mail-wr0-x235.google.com [IPv6:2a00:1450:400c:c0c::235]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id DB28E131D4E for <cfrg@irtf.org>; Wed,  5 Jul 2017 09:29:34 -0700 (PDT)
Received: by mail-wr0-x235.google.com with SMTP id k67so265319095wrc.2 for <cfrg@irtf.org>; Wed, 05 Jul 2017 09:29:34 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=from:message-id:mime-version:subject:date:in-reply-to:cc:to :references; bh=0nF05oLs9wB2XszEY29JO2CHdwTe/2lz56sZecOQ0Uc=; b=U9/piQ9M11GLE8bJhll7AhSpRQOZOQwK0gLp526EthlOGAoEApftJ2YHvbwgy6ZKe+ Ww5SeCiRLqu3mf55ut44JckE/2iywlbE3rPBw6qp0F76oCJpYxddBS7sRBOCe4yd+K/Q YoKOtFdkkv+63AfjTFBJHW4Qz+gP6U4+4xal6ri3he/5N8rwN7TMEKjXnQhmCtzBsMCg SGftIUGpDIOT/H0gdVqprS6GLhzHo3qhUqBtKhPHPkTJJqLZ0nRcbZB5bwbzA8U5FBNq a6aW0Xbi7wRPO0uef4VWPfInzN3ymPJhj0BbncEUlVIkkchyLu/q63RIyyWKf0t0WoTq ShLg==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:from:message-id:mime-version:subject:date :in-reply-to:cc:to:references; bh=0nF05oLs9wB2XszEY29JO2CHdwTe/2lz56sZecOQ0Uc=; b=UV7RCYfb4dOzYl6u//97RGahBpz8gVgha//AwYkNKrcvOmm/Sgm2ofDK3armEwqZiM +jWHKfqnHUq+BdJRI/Pr4K0HccRuD6tWbfK1u09Wpk19i/cJvZ9VnAKgv9oOho0PoMym yb3o6A5PZbvF+GVpM54NmFjdnrFe+R7mzhlZ1rR+zd9anlfgXuvVIHZzypvRbWR/CESX UEeEiq6JzUywqRAmgHvS/t81NQfmqJ/PzaQYPurAuxWsZsYK9b3ZYQoCZkEqYQvfphu0 dafkdIbcd3N9Bdo4CUtOij3VdZ3TMDHAqba64k7v9kxIsf+AZ2T4U4OhDd3oWq8c5hpC uSNQ==
X-Gm-Message-State: AKS2vOxNMv8dGs+KoSjwgxXwfOoMFT8fWMVvGN4vtRwORVPG8aDRL+Hz ecAHaDnZTjEb/g==
X-Received: by 10.223.145.227 with SMTP id 90mr39896772wri.171.1499272173395;  Wed, 05 Jul 2017 09:29:33 -0700 (PDT)
Received: from [192.168.1.28] (83-103-13-156.ip.fastwebnet.it. [83.103.13.156]) by smtp.gmail.com with ESMTPSA id 79sm12600055wrc.34.2017.07.05.09.29.25 (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Wed, 05 Jul 2017 09:29:26 -0700 (PDT)
From: Bryan Ford <brynosaurus@gmail.com>
Message-Id: <ED2ACB88-4354-410F-A4B1-090ECE814BA7@gmail.com>
Content-Type: multipart/signed; boundary="Apple-Mail=_821CAADD-B3B5-40A3-BF93-B12AD20EDA74"; protocol="application/pgp-signature"; micalg=pgp-sha256
Mime-Version: 1.0 (Mac OS X Mail 10.3 \(3273\))
Date: Wed, 5 Jul 2017 18:29:23 +0200
In-Reply-To: <CAFTSWve-J9pKVAaCJ=F==ZP_6=f2QMR2chD+J0T7vF6SNb95Ow@mail.gmail.com>
Cc: Daniel Slamanig <daniel.slamanig@tugraz.at>, cfrg@irtf.org
To: Thomas Garcia <tgarcia.3141@gmail.com>
References: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io> <11cc5d3f-ecf9-2fd0-825c-c8b441bd2813@tugraz.at> <A423CB6E-D649-4320-BB76-2E3783D6AFE0@gmail.com> <CAFTSWve-J9pKVAaCJ=F==ZP_6=f2QMR2chD+J0T7vF6SNb95Ow@mail.gmail.com>
X-Mailer: Apple Mail (2.3273)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/yIFdMZAePPiWITqXMBOKlWCtGrM>
Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 16:29:39 -0000

--Apple-Mail=_821CAADD-B3B5-40A3-BF93-B12AD20EDA74
Content-Type: multipart/alternative;
	boundary="Apple-Mail=_B73CB522-DE56-4B30-967E-A4ECA65EE493"


--Apple-Mail=_B73CB522-DE56-4B30-967E-A4ECA65EE493
Content-Transfer-Encoding: quoted-printable
Content-Type: text/plain;
	charset=utf-8

Hi Thomas,

> On Jul 5, 2017, at 3:27 PM, Thomas Garcia <tgarcia.3141@gmail.com> =
wrote:
>=20
> Hello,
> I have a number of comments regarding the draft.
> 1. In the described protocol the leader, after receiving commitments =
from the participants and calculating the challenge c, sends that =
challenge to the participants. The participants then do not verify that =
c was indeed calculated using the message that they intended to sign, =
allowing the leader to procure signatures for arbitrary messages. A =
stage of verification of c should be added to the protocol.

Oops, looks like that was an unfortunate omission that snuck into the =
first draft somehow.  Indeed, the cosigners definitely must not simply =
trust the leader to compute c correctly.  What section 5.1.3 should say =
is that the leader sends out the aggregate commitment R, which all =
participants use to compute c =3D SHA512(R || A || M) independently =
based on that R, ensuring that the responses they produced are only good =
for a particular message M they=E2=80=99ve seen and approved.  (And the =
hash might of course be further extended to cover additional =
information, such as the bit mask, depending on the outcome of other =
orthogonal discussions raised by others.)  We=E2=80=99ll make sure that =
fix gets into the next version of the spec - thanks for pointing out the =
bug.

> 2. EdDSA is designed to withstand collision attacks against the hash =
function used in the signature. On the other hand, the protocol =
suggested is susceptible to such attacks. A hostile leader and =
participant, together, could wait for all other participants to select =
their commitments. They could then choose a commitment such that =
SHA512(R||A||msg)=3DSHA512(R'||A||msg'), providing them with a signature =
of msg'. This would of course have to be done in real-time, and given =
the strength of SHA512 is in no way practical. This kind of attack would =
be difficult to avoid without substantial modifications to the scheme, =
but this does not seem to be a significant threat.

Nice observation, thanks.  Agreed, it=E2=80=99s not clear that there=E2=80=
=99s a straightforward way to protect against such attacks in the event =
the hash function has collision weaknesses - but hopefully SHA512 will =
be strong enough for long enough that this shouldn=E2=80=99t be an issue =
in practice.

Cheers
Bryan

> Thomas G.
>=20
> On Wed, Jul 5, 2017 at 2:11 PM, Bryan Ford <brynosaurus@gmail.com =
<mailto:brynosaurus@gmail.com>> wrote:
> Hi Daniel, thanks for your thoughts on the commitment-to-the-bitmask =
issue.
>=20
> Your proposal of using a chameleon hash, to allow the leader to =
=E2=80=9Cadjust=E2=80=9D the bit mask after the commit c has been =
established, is an interesting idea. However, if I understand it =
correctly, if the leader holds the trapdoor key for the chameleon hash, =
wouldn=E2=80=99t that still make the final collective signature =
malleable for the leader (or for anyone the leader=E2=80=99s trapdoor =
key might leak to)?  The CoSi protocol as currently defined is intended =
to ensure that the leader has no special privilege or trust with respect =
to other cosigners: i.e., the leader is merely an ordinary participant, =
but is simply the one who for whatever reason decides to initiate the =
cosigning operation.  Giving the leader special powers - e.g., making =
the signature malleable to the leader but not to others - would break =
this principle and need to be extremely carefully considered I think.
>=20
> To follow up on my last message to Oleg, again I suggest reading =
section IV of our CoSi paper from IEEE S&P last year =
(http://dedis.cs.yale.edu/dissent/papers/witness-abs =
<http://dedis.cs.yale.edu/dissent/papers/witness-abs>), as it discusses =
several related issues, especially the potential desire to allow the =
leader to complete a collective signing procedure even with only a =
subset of =E2=80=9Ccommitted=E2=80=9D participants remaining present in =
the =E2=80=9Cresponse=E2=80=9D phase.  In particular, the leader can =
form all the individual Schnorr commits into a Merkle tree, and make the =
real commit c be the root of that Merkle tree.  In this way, the leader =
is committing not so much to a particular collective Schnorr commit but =
rather to *all possible* Schnorr commits that can be composed from any =
subset of the individual Schnorr commits within that Merkle tree.  This =
way, if some of the participants whose commits are present in that =
Merkle tree remain available during the response phase but others drop =
out, the leader can still use the commit c and form a correct and =
verifiable collective signature against the particular subset of Schnorr =
commits from nodes that remained available throughout the process, =
without restarting.
>=20
> I guess this approach does, in a slightly different way, make the =
resulting collective signatures slightly malleable to the leader: from a =
given set of commit-time and response-time information, the leader could =
put together distinct collective signatures representing different =
subsets of response-time participants.  Some form of =
=E2=80=9Cleader-malleability=E2=80=9D of this kind seems unavoidably =
essential to enabling the leader to complete a collective signing round =
in the presence of partial failures without restarting.  Perhaps the =
same limited leader-malleability is more-or-less the same property your =
suggestion of using chameleon hashes has, although I haven=E2=80=99t had =
a chance to compare them deeply yet.
>=20
> But at any rate, the higher-level tradeoff here to consider is whether =
it=E2=80=99s better to (a) enforce strict non-malleability of collective =
signatures (by anyone, leader included), at the cost of O(N)-round DoS =
attack vulnerability during signing due to the need to restart partially =
failed rounds, or (b) provide some limited form of limited =
leader-malleability in order to support restart-free operation and avoid =
DoS attacks during signing, at the cost of a more complex protocol (and =
perhaps slightly more =E2=80=9Cspecial=E2=80=9D trust in the leader than =
we might like).
>=20
> Again, further thoughts on this and other topics are most welcome.
>=20
> Thanks
> Bryan
>=20
>> On Jul 3, 2017, at 7:34 PM, Daniel Slamanig =
<daniel.slamanig@tugraz.at <mailto:daniel.slamanig@tugraz.at>> wrote:
>>=20
>> Hi Philipp,
>>=20
>> looks interesting!
>>=20
>> After looking at the protocol I also have some security concerns =
(related to what has been raised by Oleg in a previous mail).
>>=20
>> Not committing to Z as well as the actual sum of signers public keys =
A' in the computation of the hash c for the signature seems to be =
problematic.
>>=20
>> It seems to me that committing Z in the signature in plain as well as =
A' does not work given the later application of the signing procedure =
(where till the end of the protocol it is not clear who actually =
participates in the signing but c must be known at the beginning).
>>=20
>> Committing to neither of both however seems problematic as it does =
not fix the set of actual signers.
>>=20
>> This could be circumvented by allowing an honest leader to adapt the =
commitment to the final Z (and A') after it knows the signers without =
modifying the initially computed c using a chameleon hash (trapdoor =
commitment). I use P as a generator below, omit the brackets [a]P =
notation for scalar multiplication and write it from the perspective of =
the leader, i.e., the signer that initiates the protocol.
>>=20
>> The leader could choose chameleon hash parameters sk_ch=3Dy for =
random y and pk_ch=3D(P,Y=3DyP) and add pk_ch and chameleon hash =
CH(Z'):=3Dh(Z')P+u'Y for randomly chosen u' to the computation of c, =
i.e., set c=3DH(R||A||pk_ch||CH(Z')||S), where h() is a collision =
resistant hash function (this is just the standard way of constructing a =
chameleon hash from DL for arbitrary message spaces as propsed in [1]). =
If Z' is not yet known one simply sets Z' to some fixed string at the =
beginning, e.g., Z':=3D0. At the end of the protocol, when the leader =
knows the exact signers, it can update Z' to the final value Z and use =
sk_ch to compute a collision in the chameleon hash, i.e., such that =
CH(Z)=3DCH(Z') by solving h(Z')+u'y =3D h(Z)+uy for u. He then adds u =
and Z as well as pk_ch to the signature, i.e., sets it as =
(R,s,u,Z,pk_ch) and discards sk_ch and u'. If Z is known beforehand, one =
simply computes the chameleon hash once and does not need to compute a =
collision. Clearly, the use of a chameleon hash allows to simply adapt =
to the actual set of signers representing Z without modifying c (with =
the knowledge of sk_ch - but it does not work without the knowledge of =
sk_ch). This would resolve the issue with the unknown Z at the time of =
signing.
>>=20
>> Also, A is committed in the signature, but not the concrete A'=3D\sum =
A_i of keys used for computing the signature (I guess also due to the =
reason that one does not know the correct set of signers when computing =
the hash c). That can be problematic in a rogue key scenario in the =
current protocol, i.e., when not all signers need to prove knowledge of =
the secret key when they register their public keys but their public =
keys could be functions of other public keys (guess this could be a =
problem here). For instance, a malicious A^* could just take some key =
from A, say A_j, and compute and publish A^*=3Da^*A_j. And then given a =
collective signature (R,s,Z) where A_j participated, the signer can =
update s to s^* =3D s+a^*c as well as Z^* to exclude A_j and include A^* =
(as Z is not committed in the signature generation) and the signature =
(R,s^*,Z^*) will be a valid signature that certifies that A^* =
participated in signing - although he didn't.
>>=20
>> If Z is committed as proposed above and it is checked during the =
verification, then this should no longer work. One could also adapt the =
hash c=3DH(R||pk_ch||CH(Z'||A)||S) to include a chameleon hash to =
CH(Z||A'), where A' is the real set of signers that participated in the =
signature generation and is adapted before finalizing the signature when =
known as above.
>>=20
>> I hope that what I proposed is not just complete nonsense :) Also it =
produces quite a bit of an overhead. There may also be easier ways to =
avoid the issues.
>>=20
>> Some editorial issues: the message to be signed is sometimes called a =
satement S and later then message msg. S could be confusing as part of =
the signature is s and your semantic is that scalars are lowercase and =
points are uppercase. Also in 4.2 "Signature Generation" steps 2 and 3 =
are confusing as I guess that in the protocol all the signer compute =
their own [r_i]B values and R=3D\sum R_i instead of R=3D[r]B which would =
mean that they would send their r_i's (hope they will not do so).
>>=20
>> Also I find it somewhat confusing that the bitmask Z identifies the =
non-signers with a bit set to 1. Why not identifying the signers with a =
bit set to 1?
>>=20
>> Cheers,
>> Daniel
>>=20
>>=20
>> [1] Hugo Krawczyk, Tal Rabin: Chameleon Signatures. NDSS 2000
>>=20
>> On 01.07.2017 23:58, Philipp Jovanovic wrote:
>>> Hi CFRG,
>>> Here=E2=80=99s a first version of an Internet-Draft on =E2=80=9CCollec=
tive Edwards-Curve Digital Signature Algorithms=E2=80=9D based on =
Ed25519 and Ed448: =
https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/ =
<https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/>
>>> We plan to give a short presentation on that topic at the next CFRG =
meeting in Prague.
>>> Any feedback is more than welcome. Thanks!
>>> All the best,
>>> Philipp
>>> _______________________________________________
>>> Cfrg mailing list
>>> Cfrg@irtf.org <mailto:Cfrg@irtf.org>
>>> https://www.irtf.org/mailman/listinfo/cfrg =
<https://www.irtf.org/mailman/listinfo/cfrg>
>>=20
>>=20
>> --
>> Dr. Daniel Slamanig
>> Institute for Applied Information Processing and Communications
>> Graz University of Technology
>> Inffeldgasse 16a, 8010 Graz, Austria.
>> Phone: +43 316 873 5509 <tel:+43%20316%208735509>
>> http://www.iaik.tugraz.at <http://www.iaik.tugraz.at/>
>>=20
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org <mailto:Cfrg@irtf.org>
>> https://www.irtf.org/mailman/listinfo/cfrg =
<https://www.irtf.org/mailman/listinfo/cfrg>
>=20
>=20
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org <mailto:Cfrg@irtf.org>
> https://www.irtf.org/mailman/listinfo/cfrg =
<https://www.irtf.org/mailman/listinfo/cfrg>
>=20
>=20


--Apple-Mail=_B73CB522-DE56-4B30-967E-A4ECA65EE493
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html;
	charset=utf-8

<html><head><meta http-equiv=3D"Content-Type" content=3D"text/html =
charset=3Dutf-8"></head><body style=3D"word-wrap: break-word; =
-webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" =
class=3D"">Hi Thomas,<div class=3D""><br class=3D""><div><blockquote =
type=3D"cite" class=3D""><div class=3D"">On Jul 5, 2017, at 3:27 PM, =
Thomas Garcia &lt;<a href=3D"mailto:tgarcia.3141@gmail.com" =
class=3D"">tgarcia.3141@gmail.com</a>&gt; wrote:</div><br =
class=3D"Apple-interchange-newline"><div class=3D""><div dir=3D"ltr" =
class=3D"">Hello,<div class=3D"">I have a number of comments regarding =
the draft.</div><div class=3D"">1. In the described protocol the leader, =
after receiving commitments from the participants and calculating the =
challenge c, sends that challenge to the participants. The participants =
then do not verify that c was indeed calculated using the message that =
they intended to sign, allowing the leader to procure signatures for =
arbitrary messages. A stage of verification of c should be added to the =
protocol.</div></div></div></blockquote><div><br =
class=3D""></div><div>Oops, looks like that was an unfortunate omission =
that snuck into the first draft somehow. &nbsp;Indeed, the cosigners =
definitely must not simply trust the leader to compute c correctly. =
&nbsp;What section 5.1.3 should say is that the leader sends out the =
aggregate commitment R, which all participants use to compute c =3D =
SHA512(R || A || M) independently based on that R, ensuring that the =
responses they produced are only good for a particular message M =
they=E2=80=99ve seen and approved. &nbsp;(And the hash might of course =
be further extended to cover additional information, such as the bit =
mask, depending on the outcome of other orthogonal discussions raised by =
others.) &nbsp;We=E2=80=99ll make sure that fix gets into the next =
version of the spec - thanks for pointing out the bug.</div><br =
class=3D""><blockquote type=3D"cite" class=3D""><div class=3D""><div =
dir=3D"ltr" class=3D""><div class=3D"">2. EdDSA is designed to withstand =
collision attacks against the hash function used in the signature. On =
the other hand, the protocol suggested is susceptible to such attacks. A =
hostile leader and participant, together, could wait for all other =
participants to select their commitments. They could then choose a =
commitment such that SHA512(R||A||msg)=3DSHA512(R'||A||msg'), providing =
them with a signature of msg'. This would of course have to be done in =
real-time, and given the strength of SHA512 is in no way practical. This =
kind of attack would be difficult to avoid without substantial =
modifications to the scheme, but this does not seem to be a significant =
threat.</div></div></div></blockquote><div><br class=3D""></div><div>Nice =
observation, thanks. &nbsp;Agreed, it=E2=80=99s not clear that there=E2=80=
=99s a straightforward way to protect against such attacks in the event =
the hash function has collision weaknesses - but hopefully SHA512 will =
be strong enough for long enough that this shouldn=E2=80=99t be an issue =
in practice.</div><div><br =
class=3D""></div><div>Cheers</div><div>Bryan</div><br =
class=3D""><blockquote type=3D"cite" class=3D""><div class=3D""><div =
dir=3D"ltr" class=3D""><div class=3D"">Thomas G.</div></div><div =
class=3D"gmail_extra"><br class=3D""><div class=3D"gmail_quote">On Wed, =
Jul 5, 2017 at 2:11 PM, Bryan Ford <span dir=3D"ltr" class=3D"">&lt;<a =
href=3D"mailto:brynosaurus@gmail.com" target=3D"_blank" =
class=3D"">brynosaurus@gmail.com</a>&gt;</span> wrote:<br =
class=3D""><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 =
.8ex;border-left:1px #ccc solid;padding-left:1ex"><div =
style=3D"word-wrap:break-word" class=3D"">Hi Daniel, thanks for your =
thoughts on the commitment-to-the-bitmask issue.<div class=3D""><br =
class=3D""></div><div class=3D"">Your proposal of using a chameleon =
hash, to allow the leader to =E2=80=9Cadjust=E2=80=9D the bit mask after =
the commit c has been established, is an interesting idea. However, if I =
understand it correctly, if the leader holds the trapdoor key for the =
chameleon hash, wouldn=E2=80=99t that still make the final collective =
signature malleable for the leader (or for anyone the leader=E2=80=99s =
trapdoor key might leak to)?&nbsp; The CoSi protocol as currently =
defined is intended to ensure that the leader has no special privilege =
or trust with respect to other cosigners: i.e., the leader is merely an =
ordinary participant, but is simply the one who for whatever reason =
decides to initiate the cosigning operation.&nbsp; Giving the leader =
special powers - e.g., making the signature malleable to the leader but =
not to others - would break this principle and need to be extremely =
carefully considered I think.</div><div class=3D""><br =
class=3D""></div><div class=3D"">To follow up on my last message to =
Oleg, again I suggest reading section IV of our CoSi paper from IEEE =
S&amp;P last year (<a =
href=3D"http://dedis.cs.yale.edu/dissent/papers/witness-abs" =
target=3D"_blank" class=3D"">http://dedis.cs.yale.edu/<wbr =
class=3D"">dissent/papers/witness-abs</a>), as it discusses several =
related issues, especially the potential desire to allow the leader to =
complete a collective signing procedure even with only a subset of =
=E2=80=9Ccommitted=E2=80=9D participants remaining present in the =
=E2=80=9Cresponse=E2=80=9D phase.&nbsp; In particular, the leader can =
form all the individual Schnorr commits into a Merkle tree, and make the =
real commit c be the root of that Merkle tree.&nbsp; In this way, the =
leader is committing not so much to a particular collective Schnorr =
commit but rather to *all possible* Schnorr commits that can be composed =
from any subset of the individual Schnorr commits within that Merkle =
tree.&nbsp; This way, if some of the participants whose commits are =
present in that Merkle tree remain available during the response phase =
but others drop out, the leader can still use the commit c and form a =
correct and verifiable collective signature against the particular =
subset of Schnorr commits from nodes that remained available throughout =
the process, without restarting.</div><div class=3D""><br =
class=3D""></div><div class=3D"">I guess this approach does, in a =
slightly different way, make the resulting collective signatures =
slightly malleable to the leader: from a given set of commit-time and =
response-time information, the leader could put together distinct =
collective signatures representing different subsets of response-time =
participants.&nbsp; Some form of =E2=80=9Cleader-malleability=E2=80=9D =
of this kind seems unavoidably essential to enabling the leader to =
complete a collective signing round in the presence of partial failures =
without restarting.&nbsp; Perhaps the same limited leader-malleability =
is more-or-less the same property your suggestion of using chameleon =
hashes has, although I haven=E2=80=99t had a chance to compare them =
deeply yet. &nbsp;</div><div class=3D""><br class=3D""></div><div =
class=3D"">But at any rate, the higher-level tradeoff here to consider =
is whether it=E2=80=99s better to (a) enforce strict non-malleability of =
collective signatures (by anyone, leader included), at the cost of =
O(N)-round DoS attack vulnerability during signing due to the need to =
restart partially failed rounds, or (b) provide some limited form of =
limited leader-malleability in order to support restart-free operation =
and avoid DoS attacks during signing, at the cost of a more complex =
protocol (and perhaps slightly more =E2=80=9Cspecial=E2=80=9D trust in =
the leader than we might like).</div><div class=3D""><br =
class=3D""></div><div class=3D"">Again, further thoughts on this and =
other topics are most welcome.</div><div class=3D""><br =
class=3D""></div><div class=3D"">Thanks</div><div =
class=3D"">Bryan</div><div class=3D""><br class=3D""><div =
class=3D""><blockquote type=3D"cite" class=3D""><div class=3D"">On Jul =
3, 2017, at 7:34 PM, Daniel Slamanig &lt;<a =
href=3D"mailto:daniel.slamanig@tugraz.at" target=3D"_blank" =
class=3D"">daniel.slamanig@tugraz.at</a>&gt; wrote:</div><br =
class=3D"m_3610228578482648793Apple-interchange-newline"><div =
class=3D""><div class=3D"">Hi Philipp,<br class=3D""><br class=3D"">looks =
interesting!<br class=3D""><br class=3D"">After looking at the protocol =
I also have some security concerns (related to what has been raised by =
Oleg in a previous mail).<br class=3D""><br class=3D"">Not committing to =
Z as well as the actual sum of signers public keys A' in the computation =
of the hash c for the signature seems to be problematic.<br class=3D""><br=
 class=3D"">It seems to me that committing Z in the signature in plain =
as well as A' does not work given the later application of the signing =
procedure (where till the end of the protocol it is not clear who =
actually participates in the signing but c must be known at the =
beginning).<br class=3D""><br class=3D"">Committing to neither of both =
however seems problematic as it does not fix the set of actual =
signers.<br class=3D""><br class=3D"">This could be circumvented by =
allowing an honest leader to adapt the commitment to the final Z (and =
A') after it knows the signers without modifying the initially computed =
c using a chameleon hash (trapdoor commitment). I use P as a generator =
below, omit the brackets [a]P notation for scalar multiplication and =
write it from the perspective of the leader, i.e., the signer that =
initiates the protocol.<br class=3D""><br class=3D"">The leader could =
choose chameleon hash parameters sk_ch=3Dy for random y and =
pk_ch=3D(P,Y=3DyP) and add pk_ch and chameleon hash CH(Z'):=3Dh(Z')P+u'Y =
for randomly chosen u' to the computation of c, i.e., set =
c=3DH(R||A||pk_ch||CH(Z')||S), where h() is a collision resistant hash =
function (this is just the standard way of constructing a chameleon hash =
from DL for arbitrary message spaces as propsed in [1]). If Z' is not =
yet known one simply sets Z' to some fixed string at the beginning, =
e.g., Z':=3D0. At the end of the protocol, when the leader knows the =
exact signers, it can update Z' to the final value Z and use sk_ch to =
compute a collision in the chameleon hash, i.e., such that CH(Z)=3DCH(Z') =
by solving h(Z')+u'y =3D h(Z)+uy for u. He then adds u and Z as well as =
pk_ch to the signature, i.e., sets it as (R,s,u,Z,pk_ch) and discards =
sk_ch and u'. If Z is known beforehand, one simply computes the =
chameleon hash once and does not need to compute a collision. Clearly, =
the use of a chameleon hash allows to simply adapt to the actual set of =
signers representing Z without modifying c (with the knowledge of sk_ch =
- but it does not work without the knowledge of sk_ch). This would =
resolve the issue with the unknown Z at the time of signing.<br =
class=3D""><br class=3D"">Also, A is committed in the signature, but not =
the concrete A'=3D\sum A_i of keys used for computing the signature (I =
guess also due to the reason that one does not know the correct set of =
signers when computing the hash c). That can be problematic in a rogue =
key scenario in the current protocol, i.e., when not all signers need to =
prove knowledge of the secret key when they register their public keys =
but their public keys could be functions of other public keys (guess =
this could be a problem here). For instance, a malicious A^* could just =
take some key from A, say A_j, and compute and publish A^*=3Da^*A_j. And =
then given a collective signature (R,s,Z) where A_j participated, the =
signer can update s to s^* =3D s+a^*c as well as Z^* to exclude A_j and =
include A^* (as Z is not committed in the signature generation) and the =
signature (R,s^*,Z^*) will be a valid signature that certifies that A^* =
participated in signing - although he didn't.<br class=3D""><br =
class=3D"">If Z is committed as proposed above and it is checked during =
the verification, then this should no longer work. One could also adapt =
the hash c=3DH(R||pk_ch||CH(Z'||A)||S) to include a chameleon hash to =
CH(Z||A'), where A' is the real set of signers that participated in the =
signature generation and is adapted before finalizing the signature when =
known as above.<br class=3D""><br class=3D"">I hope that what I proposed =
is not just complete nonsense :) Also it produces quite a bit of an =
overhead. There may also be easier ways to avoid the issues.<br =
class=3D""><br class=3D"">Some editorial issues: the message to be =
signed is sometimes called a satement S and later then message msg. S =
could be confusing as part of the signature is s and your semantic is =
that scalars are lowercase and points are uppercase. Also in 4.2 =
"Signature Generation" steps 2 and 3 are confusing as I guess that in =
the protocol all the signer compute their own [r_i]B values and R=3D\sum =
R_i instead of R=3D[r]B which would mean that they would send their =
r_i's (hope they will not do so).<br class=3D""><br class=3D"">Also I =
find it somewhat confusing that the bitmask Z identifies the non-signers =
with a bit set to 1. Why not identifying the signers with a bit set to =
1?<br class=3D""><br class=3D"">Cheers,<br class=3D"">Daniel<br =
class=3D""><br class=3D""><br class=3D"">[1] Hugo Krawczyk, Tal Rabin: =
Chameleon Signatures. NDSS 2000<span class=3D""><br class=3D""><br =
class=3D"">On 01.07.2017 23:58, Philipp Jovanovic wrote:<br =
class=3D""><blockquote type=3D"cite" class=3D"">Hi CFRG,<br =
class=3D"">Here=E2=80=99s a first version of an Internet-Draft on =
=E2=80=9CCollective Edwards-Curve Digital Signature Algorithms=E2=80=9D =
based on Ed25519 and Ed448: <a =
href=3D"https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/" =
target=3D"_blank" class=3D"">https://datatracker.ietf.org/<wbr =
class=3D"">doc/draft-ford-cfrg-cosi/</a><br class=3D"">We plan to give a =
short presentation on that topic at the next CFRG meeting in Prague.<br =
class=3D"">Any feedback is more than welcome. Thanks!<br class=3D"">All =
the best,<br class=3D"">Philipp<br =
class=3D"">______________________________<wbr =
class=3D"">_________________<br class=3D"">Cfrg mailing list<br =
class=3D""><a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank" =
class=3D"">Cfrg@irtf.org</a><br class=3D""><a =
href=3D"https://www.irtf.org/mailman/listinfo/cfrg" target=3D"_blank" =
class=3D"">https://www.irtf.org/mailman/<wbr =
class=3D"">listinfo/cfrg</a><br class=3D""></blockquote><br class=3D""><br=
 class=3D""></span><span class=3D"HOEnZb"><font color=3D"#888888" =
class=3D"">--<br class=3D"">Dr. Daniel Slamanig<br class=3D"">Institute =
for Applied Information Processing and Communications<br class=3D"">Graz =
University of Technology<br class=3D"">Inffeldgasse 16a, 8010 Graz, =
Austria.<br class=3D"">Phone: <a href=3D"tel:+43%20316%208735509" =
value=3D"+433168735509" target=3D"_blank" class=3D"">+43 316 873 =
5509</a><br class=3D""><a href=3D"http://www.iaik.tugraz.at/" =
target=3D"_blank" =
class=3D"">http://www.iaik.tugraz.at</a></font></span><span class=3D""><br=
 class=3D""><br class=3D"">______________________________<wbr =
class=3D"">_________________<br class=3D"">Cfrg mailing list<br =
class=3D""><a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank" =
class=3D"">Cfrg@irtf.org</a><br class=3D""><a =
href=3D"https://www.irtf.org/mailman/listinfo/cfrg" target=3D"_blank" =
class=3D"">https://www.irtf.org/mailman/<wbr =
class=3D"">listinfo/cfrg</a><br =
class=3D""></span></div></div></blockquote></div><br =
class=3D""></div></div><br class=3D"">______________________________<wbr =
class=3D"">_________________<br class=3D"">
Cfrg mailing list<br class=3D"">
<a href=3D"mailto:Cfrg@irtf.org" class=3D"">Cfrg@irtf.org</a><br =
class=3D"">
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" =
target=3D"_blank" class=3D"">https://www.irtf.org/mailman/<wbr =
class=3D"">listinfo/cfrg</a><br class=3D"">
<br class=3D""></blockquote></div><br class=3D""></div>
</div></blockquote></div><br class=3D""></div></body></html>=

--Apple-Mail=_B73CB522-DE56-4B30-967E-A4ECA65EE493--

--Apple-Mail=_821CAADD-B3B5-40A3-BF93-B12AD20EDA74
Content-Transfer-Encoding: 7bit
Content-Disposition: attachment;
	filename=signature.asc
Content-Type: application/pgp-signature;
	name=signature.asc
Content-Description: Message signed with OpenPGP

-----BEGIN PGP SIGNATURE-----
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=wuak
-----END PGP SIGNATURE-----

--Apple-Mail=_821CAADD-B3B5-40A3-BF93-B12AD20EDA74--


From nobody Wed Jul  5 11:23:28 2017
Return-Path: <sfluhrer@cisco.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 2C599131B5F for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 11:23:27 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -14.521
X-Spam-Level: 
X-Spam-Status: No, score=-14.521 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_HI=-5, RCVD_IN_MSPIKE_H3=-0.01, RCVD_IN_MSPIKE_WL=-0.01, RP_MATCHES_RCVD=-0.001, SPF_HELO_PASS=-0.001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001, USER_IN_DEF_DKIM_WL=-7.5] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=cisco.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id n66kxT_EgtCF for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 11:23:25 -0700 (PDT)
Received: from alln-iport-5.cisco.com (alln-iport-5.cisco.com [173.37.142.92]) (using TLSv1.2 with cipher DHE-RSA-SEED-SHA (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 73C1B13184B for <cfrg@irtf.org>; Wed,  5 Jul 2017 11:23:25 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=cisco.com; i=@cisco.com; l=8091; q=dns/txt; s=iport; t=1499279005; x=1500488605; h=from:to:cc:subject:date:message-id:mime-version; bh=/UzDhYRte9UvBZ0LSi8t3eiiRyL7yxuoH4UOdZ7Jhw4=; b=NwvlAHbdtaVDoF2e8CIo+Pe0Dx77oNgDZKOfezbmhSl2uMoZDM3EPsiz hkXIsDPfP/FcN/OFqrFxRq7s1iJG35ynhtAktqQCETwW9qkF8msm8tEOO UwQ80gQB8CVzqdybDSnc7KdSK1rv9EtkunQAycysKqzi9ZqNRGgMKCWMR g=;
X-IronPort-Anti-Spam-Filtered: true
X-IronPort-Anti-Spam-Result: =?us-ascii?q?A0A4AgCDLV1Z/4ENJK1dGgEBAQECAQEBA?= =?us-ascii?q?QgBAQEBgm9qY4EQB7A9hSyCESyFcIMeQRYBAgEBAQEBAQFrHQuFHS9MEgGBACY?= =?us-ascii?q?BBA4NiUNkELBoiz8BAQEBAQEBAQEBAQEBAQEBAQEBAQEdgyeDTIFhgySBJIk6B?= =?us-ascii?q?Zcph10CgWOFYow1gmuPPHCUQgEPFwUsP0t1FYVbHYFmdgGHdYENAQEB?=
X-IronPort-AV: E=Sophos;i="5.40,312,1496102400";  d="scan'208,217";a="448868576"
Received: from alln-core-9.cisco.com ([173.36.13.129]) by alln-iport-5.cisco.com with ESMTP/TLS/DHE-RSA-AES256-SHA; 05 Jul 2017 18:23:24 +0000
Received: from XCH-RTP-001.cisco.com (xch-rtp-001.cisco.com [64.101.220.141]) by alln-core-9.cisco.com (8.14.5/8.14.5) with ESMTP id v65INO98002509 (version=TLSv1/SSLv3 cipher=AES256-SHA bits=256 verify=FAIL) for <cfrg@irtf.org>; Wed, 5 Jul 2017 18:23:24 GMT
Received: from xch-rtp-006.cisco.com (64.101.220.146) by XCH-RTP-001.cisco.com (64.101.220.141) with Microsoft SMTP Server (TLS) id 15.0.1210.3; Wed, 5 Jul 2017 14:23:23 -0400
Received: from xch-rtp-006.cisco.com ([64.101.220.146]) by XCH-RTP-006.cisco.com ([64.101.220.146]) with mapi id 15.00.1210.000; Wed, 5 Jul 2017 14:23:23 -0400
From: "Scott Fluhrer (sfluhrer)" <sfluhrer@cisco.com>
To: "cfrg@irtf.org" <cfrg@irtf.org>
CC: "David McGrew (mcgrew)" <mcgrew@cisco.com>
Thread-Topic: Request for a slot to discuss the LMS hash based signatures at Prague
Thread-Index: AdL1u8jStyGum1IMQimgMKynsUjIXg==
Date: Wed, 5 Jul 2017 18:23:23 +0000
Message-ID: <05a9099ce483405ea988bc6053ceff66@XCH-RTP-006.cisco.com>
Accept-Language: en-US
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
x-ms-exchange-transport-fromentityheader: Hosted
x-originating-ip: [10.98.2.55]
Content-Type: multipart/alternative; boundary="_000_05a9099ce483405ea988bc6053ceff66XCHRTP006ciscocom_"
MIME-Version: 1.0
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/O9EFoxShbp-bGraRhwiPvakJyJw>
Subject: [Cfrg] Request for a slot to discuss the LMS hash based signatures at Prague
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 18:23:27 -0000

--_000_05a9099ce483405ea988bc6053ceff66XCHRTP006ciscocom_
Content-Type: text/plain; charset="us-ascii"
Content-Transfer-Encoding: quoted-printable

Hi,

   I would ask to request a slot to discuss the LMS hash based signatures a=
t the CRFG in-person meeting at Prague.  I will not be there in person, how=
ever David McGrew will be (and I'll be attending virtually).

   We have:


-          The latest version of the LMS draft: https://datatracker.ietf.or=
g/doc/draft-mcgrew-hash-sigs/

-          A proof of security (in the Random Oracle model, where the hash =
compression function is considered the random Oracle): http://eprint.iacr.o=
rg/2017/553.pdf

-          A comparison of this proposal with the XMSS proposal under consi=
deration by the CRFG: http://eprint.iacr.org/2017/349.pdf

-          A practical implementation of this draft: https://github.com/cis=
co/hash-sigs

Thank you!

--_000_05a9099ce483405ea988bc6053ceff66XCHRTP006ciscocom_
Content-Type: text/html; charset="us-ascii"
Content-Transfer-Encoding: quoted-printable

<html xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-micr=
osoft-com:office:office" xmlns:w=3D"urn:schemas-microsoft-com:office:word" =
xmlns:m=3D"http://schemas.microsoft.com/office/2004/12/omml" xmlns=3D"http:=
//www.w3.org/TR/REC-html40">
<head>
<meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3Dus-ascii"=
>
<meta name=3D"Generator" content=3D"Microsoft Word 14 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
	{font-family:Wingdings;
	panose-1:5 0 0 0 0 0 0 0 0 0;}
@font-face
	{font-family:Wingdings;
	panose-1:5 0 0 0 0 0 0 0 0 0;}
@font-face
	{font-family:Calibri;
	panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
	{font-family:Tahoma;
	panose-1:2 11 6 4 3 5 4 4 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
	{margin:0in;
	margin-bottom:.0001pt;
	font-size:11.0pt;
	font-family:"Calibri","sans-serif";}
a:link, span.MsoHyperlink
	{mso-style-priority:99;
	color:blue;
	text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
	{mso-style-priority:99;
	color:purple;
	text-decoration:underline;}
p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
	{mso-style-priority:99;
	mso-style-link:"Balloon Text Char";
	margin:0in;
	margin-bottom:.0001pt;
	font-size:8.0pt;
	font-family:"Tahoma","sans-serif";}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
	{mso-style-priority:34;
	margin-top:0in;
	margin-right:0in;
	margin-bottom:0in;
	margin-left:.5in;
	margin-bottom:.0001pt;
	font-size:11.0pt;
	font-family:"Calibri","sans-serif";}
span.EmailStyle17
	{mso-style-type:personal-compose;
	font-family:"Calibri","sans-serif";
	color:windowtext;}
span.BalloonTextChar
	{mso-style-name:"Balloon Text Char";
	mso-style-priority:99;
	mso-style-link:"Balloon Text";
	font-family:"Tahoma","sans-serif";}
.MsoChpDefault
	{mso-style-type:export-only;
	font-family:"Calibri","sans-serif";}
@page WordSection1
	{size:8.5in 11.0in;
	margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
	{page:WordSection1;}
/* List Definitions */
@list l0
	{mso-list-id:2087996282;
	mso-list-type:hybrid;
	mso-list-template-ids:1606474692 1187801136 67698691 67698693 67698689 676=
98691 67698693 67698689 67698691 67698693;}
@list l0:level1
	{mso-level-start-at:2;
	mso-level-number-format:bullet;
	mso-level-text:-;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-.25in;
	font-family:"Calibri","sans-serif";
	mso-fareast-font-family:Calibri;
	mso-bidi-font-family:"Times New Roman";}
@list l0:level2
	{mso-level-number-format:bullet;
	mso-level-text:o;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-.25in;
	font-family:"Courier New";}
@list l0:level3
	{mso-level-number-format:bullet;
	mso-level-text:\F0A7;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-.25in;
	font-family:Wingdings;}
@list l0:level4
	{mso-level-number-format:bullet;
	mso-level-text:\F0B7;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-.25in;
	font-family:Symbol;}
@list l0:level5
	{mso-level-number-format:bullet;
	mso-level-text:o;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-.25in;
	font-family:"Courier New";}
@list l0:level6
	{mso-level-number-format:bullet;
	mso-level-text:\F0A7;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-.25in;
	font-family:Wingdings;}
@list l0:level7
	{mso-level-number-format:bullet;
	mso-level-text:\F0B7;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-.25in;
	font-family:Symbol;}
@list l0:level8
	{mso-level-number-format:bullet;
	mso-level-text:o;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-.25in;
	font-family:"Courier New";}
@list l0:level9
	{mso-level-number-format:bullet;
	mso-level-text:\F0A7;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-.25in;
	font-family:Wingdings;}
ol
	{margin-bottom:0in;}
ul
	{margin-bottom:0in;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext=3D"edit" spidmax=3D"1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext=3D"edit">
<o:idmap v:ext=3D"edit" data=3D"1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang=3D"EN-US" link=3D"blue" vlink=3D"purple">
<div class=3D"WordSection1">
<p class=3D"MsoNormal">Hi,<o:p></o:p></p>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
<p class=3D"MsoNormal">&nbsp;&nbsp; I would ask to request a slot to discus=
s the LMS hash based signatures at the CRFG in-person meeting at Prague.&nb=
sp; I will not be there in person, however David McGrew will be (and I&#821=
7;ll be attending virtually).<o:p></o:p></p>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
<p class=3D"MsoNormal">&nbsp;&nbsp; We have:<o:p></o:p></p>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
<p class=3D"MsoListParagraph" style=3D"text-indent:-.25in;mso-list:l0 level=
1 lfo1"><![if !supportLists]><span style=3D"mso-list:Ignore">-<span style=
=3D"font:7.0pt &quot;Times New Roman&quot;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;
</span></span><![endif]>The latest version of the LMS draft: <a href=3D"htt=
ps://datatracker.ietf.org/doc/draft-mcgrew-hash-sigs/">
https://datatracker.ietf.org/doc/draft-mcgrew-hash-sigs/</a><o:p></o:p></p>
<p class=3D"MsoListParagraph" style=3D"text-indent:-.25in;mso-list:l0 level=
1 lfo1"><![if !supportLists]><span style=3D"mso-list:Ignore">-<span style=
=3D"font:7.0pt &quot;Times New Roman&quot;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;
</span></span><![endif]>A proof of security (in the Random Oracle model, wh=
ere the hash compression function is considered the random Oracle):
<a href=3D"http://eprint.iacr.org/2017/553.pdf">http://eprint.iacr.org/2017=
/553.pdf</a><o:p></o:p></p>
<p class=3D"MsoListParagraph" style=3D"text-indent:-.25in;mso-list:l0 level=
1 lfo1"><![if !supportLists]><span style=3D"mso-list:Ignore">-<span style=
=3D"font:7.0pt &quot;Times New Roman&quot;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;
</span></span><![endif]>A comparison of this proposal with the XMSS proposa=
l under consideration by the CRFG:
<a href=3D"http://eprint.iacr.org/2017/349.pdf">http://eprint.iacr.org/2017=
/349.pdf</a><o:p></o:p></p>
<p class=3D"MsoListParagraph" style=3D"text-indent:-.25in;mso-list:l0 level=
1 lfo1"><![if !supportLists]><span style=3D"mso-list:Ignore">-<span style=
=3D"font:7.0pt &quot;Times New Roman&quot;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;
</span></span><![endif]>A practical implementation of this draft: <a href=
=3D"https://github.com/cisco/hash-sigs">
https://github.com/cisco/hash-sigs</a><o:p></o:p></p>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
<p class=3D"MsoNormal">Thank you!<o:p></o:p></p>
</div>
</body>
</html>

--_000_05a9099ce483405ea988bc6053ceff66XCHRTP006ciscocom_--


From nobody Wed Jul  5 11:38:27 2017
Return-Path: <hallam@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id F136E131D9E for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 11:38:25 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.398
X-Spam-Level: 
X-Spam-Status: No, score=-2.398 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, FREEMAIL_FORGED_FROMDOMAIN=0.199, FREEMAIL_FROM=0.001, HEADER_FROM_DIFFERENT_DOMAINS=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 2Vl1YwqBHwPr for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 11:38:24 -0700 (PDT)
Received: from mail-lf0-x235.google.com (mail-lf0-x235.google.com [IPv6:2a00:1450:4010:c07::235]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 03D2C131DB2 for <cfrg@irtf.org>; Wed,  5 Jul 2017 11:38:21 -0700 (PDT)
Received: by mail-lf0-x235.google.com with SMTP id z78so98191480lff.0 for <cfrg@irtf.org>; Wed, 05 Jul 2017 11:38:20 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:sender:from:date:message-id:subject:to; bh=IEtX10uknXUUmHfb547Us78T5keHcPRrmU85yAoBAPo=; b=Qdi3trVC0QAfhfrUMJyXRWm0Z3lzcPQbcB/vujK8gZgAzekTjgDEpiaBjQcge7Bt/d JMxC8kPdPgp1TsoAPLYMtvlefhTFCDh7W5B7IlBpOGwznd9MLZqdyEBPhiGLm0ERLiVY pRM4AvzkyW2lZpPY64oVSi6Epl0K2Hhm1ep1yfT7L6uHy/dqpUPpUuz2r7uH0iRF1OAK 0P589pULNEoLgqPkILj0GHeyV7n5SXvL95wjwP17k+x0EV4cmtyoVLRT0+DPJv1n0fDc 33RkcpVKfTipOSVgy6DaL6w7hn3f5W4w/elaMUf0NLbJlp+kA49r3XXbd7KCCK+ylEZk 8ehA==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:sender:from:date:message-id:subject :to; bh=IEtX10uknXUUmHfb547Us78T5keHcPRrmU85yAoBAPo=; b=CwNLkh5F4rfx9pwS4bYadS2B5tlLU2JssYFtOdjmVRSj/rItHsadk9xcO9wMkuZzHi tU2ABYy6liO0K+NFvYV1b/TB+FgdmG7dHIuegbd3SaZSaG+dGycEbfqj7ODtUsjpeBNO VbJbHiUzNX/GGr1C61WR5b5WtRiDjUYtsS02v1C5ha9pFEkMldo3KoYWRX6NgmfVQ9EG AB8VA3AhdUEw1AiCBNS3Pp3J5A+3NhB3Hx6n3xWjP8DlJmyWAQZN6Ej3n6Z6N72Yj8ed 0UAsYkC8R3T4GUgq5MJT3NB4ueQNw6Zz1TT/dXNg/6UI+H5xeM+jTcX1vocD8tLGQmOL PTRw==
X-Gm-Message-State: AKS2vOwR61p0sNhnqj19wpXadK2GYqF5vCbKd8vs8HN7H/vSRJL44I8B EnjKz4TGgp7nKjiBLPDHsxAOVpBwsCaf
X-Received: by 10.46.82.199 with SMTP id n68mr12158438lje.99.1499279898840; Wed, 05 Jul 2017 11:38:18 -0700 (PDT)
MIME-Version: 1.0
Sender: hallam@gmail.com
Received: by 10.25.181.214 with HTTP; Wed, 5 Jul 2017 11:38:18 -0700 (PDT)
From: Phillip Hallam-Baker <phill@hallambaker.com>
Date: Wed, 5 Jul 2017 14:38:18 -0400
X-Google-Sender-Auth: e4LArwlx7mQ3iyeQbSf5L1fBfzY
Message-ID: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com>
To: "cfrg@irtf.org" <cfrg@irtf.org>
Content-Type: multipart/alternative; boundary="001a113be372ca138d0553964dff"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/V1JXfnf05uE88huYaQVKi7iZ6mY>
Subject: [Cfrg] Side channel attack and Edwards curves...
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 18:38:26 -0000

--001a113be372ca138d0553964dff
Content-Type: text/plain; charset="UTF-8"

http://thehackernews.com/2017/07/gnupg-libgcrypt-rsa-encryption.html?m=1

Just another side channel attack and not something that bothers me writing
reference code. But have we maybe put our eggs in the Montgomery ladder
basket when maybe we should have gone for 'randomly split the private key
into two parts, perform two separate multiplications with each part and add
the result'.

We can play the blinding game in Edwards or Montgomery but it is easier in
Edwards.

Anyone got code for adding points in compressed Montgomery?



Thoughts?

--001a113be372ca138d0553964dff
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_default"><a href=3D"http://thehackerne=
ws.com/2017/07/gnupg-libgcrypt-rsa-encryption.html?m=3D1">http://thehackern=
ews.com/2017/07/gnupg-libgcrypt-rsa-encryption.html?m=3D1</a><br></div><div=
 class=3D"gmail_default"><br></div><div class=3D"gmail_default">Just anothe=
r side channel attack and not something that bothers me writing reference c=
ode. But have we maybe put our eggs in the Montgomery ladder basket when ma=
ybe we should have gone for &#39;randomly split the private key into two pa=
rts, perform two separate multiplications with each part and add the result=
&#39;.</div><div class=3D"gmail_default"><br></div><div class=3D"gmail_defa=
ult">We can play the blinding game in Edwards or Montgomery but it is easie=
r in Edwards.</div><div class=3D"gmail_default"><br></div><div class=3D"gma=
il_default">Anyone got code for adding points in compressed Montgomery?</di=
v><div class=3D"gmail_default"><br></div><div class=3D"gmail_default"><br><=
/div><div class=3D"gmail_default"><br></div><div class=3D"gmail_default">Th=
oughts?</div><div class=3D"gmail_default"><br></div><div class=3D"gmail_def=
ault"><br></div></div>

--001a113be372ca138d0553964dff--


From nobody Wed Jul  5 14:03:18 2017
Return-Path: <campbell@mumble.net>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 3F2391200E5 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 14:03:17 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.901
X-Spam-Level: 
X-Spam-Status: No, score=-1.901 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, RCVD_IN_DNSWL_NONE=-0.0001, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id pPN8GxjnMQz3 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 14:03:15 -0700 (PDT)
Received: from jupiter.mumble.net (jupiter.mumble.net [74.50.56.165]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 14616131A20 for <cfrg@irtf.org>; Wed,  5 Jul 2017 14:03:14 -0700 (PDT)
Received: by jupiter.mumble.net (Postfix, from userid 1014) id E58C860AA2; Wed,  5 Jul 2017 21:03:58 +0000 (UTC)
From: Taylor R Campbell <campbell+cfrg@mumble.net>
To: Phillip Hallam-Baker <phill@hallambaker.com>
CC: cfrg@irtf.org
In-reply-to: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com> (phill@hallambaker.com)
Date: Wed, 5 Jul 2017 21:03:20 +0000
Sender: Taylor R Campbell <campbell@mumble.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: quoted-printable
Message-Id: <20170705210358.E58C860AA2@jupiter.mumble.net>
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/SK4sRMbG9fL54Tu_-Ikf3PwcG7A>
Subject: Re: [Cfrg] Side channel attack and Edwards curves...
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 21:03:17 -0000

> Date: Wed, 5 Jul 2017 14:38:18 -0400
> From: Phillip Hallam-Baker <phill@hallambaker.com>
>=20
> http://thehackernews.com/2017/07/gnupg-libgcrypt-rsa-encryption.html?m=3D1
>=20
> Just another side channel attack and not something that bothers me writing
> reference code. But have we maybe put our eggs in the Montgomery ladder
> basket when maybe we should have gone for 'randomly split the private key
> into two parts, perform two separate multiplications with each part and a=
dd
> the result'.
>=20
> We can play the blinding game in Edwards or Montgomery but it is easier in
> Edwards.

You can always convert from Montgomery x to Edwards (x, y) and back
without losing anything and costing only one field element inversion;
see XEdDSA <https://whispersystems.org/docs/specifications/xeddsa/>
for something similar.

But there is no reason to flail around with blinding when you can just
use constant-time code for both Edwards and Montgomery arithmetic.

You can even do RSA in constant time, but it's hard if you naively
start with a generic bignum library that automatically normalizes away
high-order zeros for in-memory representations of secret integers.

Unfortunately, both OpenSSL and libgcrypt did just that, and generally
made basic mistakes for writing constant-time code in C.  Not even
anything interesting, like code that just happens to be `optimized' by
a fancy compiler into variable-time -- they just have unnecessary
explicit branches and array indices that are dependent on secrets.

I wrote some details on and recommendations for libgcrypt a while
back:

https://lists.gnupg.org/pipermail/gcrypt-devel/2015-November/003618.html

The easy bugs I observed in twisted Edwards scalarmult were fixed
immediately; the harder bugs about generic bignum arithmetic were not
fixed when I last checked.


From nobody Wed Jul  5 14:56:23 2017
Return-Path: <hallam@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id EE5C6120725 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 14:56:22 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.398
X-Spam-Level: 
X-Spam-Status: No, score=-2.398 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, FREEMAIL_FORGED_FROMDOMAIN=0.199, FREEMAIL_FROM=0.001, HEADER_FROM_DIFFERENT_DOMAINS=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id ZI_qLUBD-hrJ for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 14:56:20 -0700 (PDT)
Received: from mail-lf0-x235.google.com (mail-lf0-x235.google.com [IPv6:2a00:1450:4010:c07::235]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id E2EEB1270AC for <cfrg@irtf.org>; Wed,  5 Jul 2017 14:56:18 -0700 (PDT)
Received: by mail-lf0-x235.google.com with SMTP id z78so1161668lff.0 for <cfrg@irtf.org>; Wed, 05 Jul 2017 14:56:18 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:sender:in-reply-to:references:from:date:message-id :subject:to:cc; bh=ugm3hWT1A3N52i9W+IfoPrbUq9EOkktuRlWCKlzOEmM=; b=I2haJyIFteU+R7Fv6iFynmsQMlA1blPYdqQwYwCNI4FfaTGQMtXAAS12ex2SPQ/69h dPrtDp6AH6mN68PXyDaSKlgB11DYe81FXW53mtLxghvXyTEk8XRRPEHjqm9i+8wTAeGB Xk4pw8Ies0/Lb6vWOgd0Jcbh6zneCo5scS+MckhQoPE7bCMfnmlZ93NaPx0aaxbFZ9gG y7owAlwhe8fW4Op7VC2M6cEqFLW+/0tBjgDWAl5/uuyTWbIkIKTF3j0XWqT9T3bPNnaB aDq+XXBO3JsmBKfDT4MFE5FUgxhnMi2fpybnO+ATYsQd9Aabsw6vLSqBtX75VqAHCmWl LU6w==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:sender:in-reply-to:references:from :date:message-id:subject:to:cc; bh=ugm3hWT1A3N52i9W+IfoPrbUq9EOkktuRlWCKlzOEmM=; b=pB/E6cpbCDCzSbSA5cUIQzARJxk5LbMMISWsUCU6ByjdX8Iw5m2sej33Sjcc/sRx06 ugRFi3vHMrou1+tli7oL2CSh4hWyV816uOWSGv6YueB1UytxStnLUhcEgoZ2nINKcAys WN72tK68reac+V6W0SaNQ25BjvCpnKZpt72KLDGzdtbjNcaHjd2qT1WlS/mthkCi+nVD S1ehR5SaRDFlpX1nd4140vECMYEbBmHytwkKAF3DZONy+2vH+gPoRgFJ7lCLDxhekhfo xN5yDXE8YRjVViZdSnvDoae4bMkkGM4MfmylLYVgImaGLnhjkc2ZUSO9fSyD15jxHGjr SUjw==
X-Gm-Message-State: AIVw110Ya7BO7Z9T4WCc0JfjRwC9fKWUlQSQjrGk9q57JuRTUbPBltPS A7xF+FiodNsmS53FkfPwNC+CCPxmXw==
X-Received: by 10.25.159.11 with SMTP id i11mr4744705lfe.178.1499291777138; Wed, 05 Jul 2017 14:56:17 -0700 (PDT)
MIME-Version: 1.0
Sender: hallam@gmail.com
Received: by 10.25.181.214 with HTTP; Wed, 5 Jul 2017 14:56:16 -0700 (PDT)
In-Reply-To: <20170705210358.E58C860AA2@jupiter.mumble.net>
References: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com> <20170705210358.E58C860AA2@jupiter.mumble.net>
From: Phillip Hallam-Baker <phill@hallambaker.com>
Date: Wed, 5 Jul 2017 17:56:16 -0400
X-Google-Sender-Auth: 7Lq_igjoWCpITbCYV83AsiJp9GE
Message-ID: <CAMm+LwjKcTpwMzu4=DzO2nb3pKvwgZ=7iHUeK2TKUukZ1N=jjA@mail.gmail.com>
To: Taylor R Campbell <campbell+cfrg@mumble.net>
Cc: "cfrg@irtf.org" <cfrg@irtf.org>
Content-Type: multipart/alternative; boundary="001a114109eaca867f055399117d"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/tmG-g_gyyB8GhO9wUNAjzvtCgRg>
Subject: Re: [Cfrg] Side channel attack and Edwards curves...
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 21:56:23 -0000

--001a114109eaca867f055399117d
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

On Wed, Jul 5, 2017 at 5:03 PM, Taylor R Campbell <campbell+cfrg@mumble.net=
>
wrote:

> > Date: Wed, 5 Jul 2017 14:38:18 -0400
> > From: Phillip Hallam-Baker <phill@hallambaker.com>
> >
> > http://thehackernews.com/2017/07/gnupg-libgcrypt-rsa-encryption.html?m=
=3D1
> >
> > Just another side channel attack and not something that bothers me
> writing
> > reference code. But have we maybe put our eggs in the Montgomery ladder
> > basket when maybe we should have gone for 'randomly split the private k=
ey
> > into two parts, perform two separate multiplications with each part and
> add
> > the result'.
> >
> > We can play the blinding game in Edwards or Montgomery but it is easier
> in
> > Edwards.
>
> You can always convert from Montgomery x to Edwards (x, y) and back
> without losing anything and costing only one field element inversion;
> see XEdDSA <https://whispersystems.org/docs/specifications/xeddsa/>
> for something similar.
>
> But there is no reason to flail around with blinding when you can just
> use constant-time code for both Edwards and Montgomery arithmetic.
>

'=E2=80=8BJust use =E2=80=8Bfinely ground unicorn powder'.

I don't think the constant time code survives modern optimizers or hardware
accelerations nearly as robustly as you imagine. I would much rather go
with an approach that does not depend on the vagaries of implementation.

=E2=80=8BThe main reason not to do this was the Kocher patents on blinding.=
 But
those are expiring soon.=E2=80=8B

--001a114109eaca867f055399117d
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_default" style=3D"font-size:small"><br=
></div><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">On Wed, Ju=
l 5, 2017 at 5:03 PM, Taylor R Campbell <span dir=3D"ltr">&lt;<a href=3D"ma=
ilto:campbell+cfrg@mumble.net" target=3D"_blank">campbell+cfrg@mumble.net</=
a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0=
 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">&gt; Date: Wed, 5 Ju=
l 2017 14:38:18 -0400<br>
&gt; From: Phillip Hallam-Baker &lt;<a href=3D"mailto:phill@hallambaker.com=
">phill@hallambaker.com</a>&gt;<br>
<span class=3D"">&gt;<br>
&gt; <a href=3D"http://thehackernews.com/2017/07/gnupg-libgcrypt-rsa-encryp=
tion.html?m=3D1" rel=3D"noreferrer" target=3D"_blank">http://thehackernews.=
com/2017/<wbr>07/gnupg-libgcrypt-rsa-<wbr>encryption.html?m=3D1</a><br>
&gt;<br>
&gt; Just another side channel attack and not something that bothers me wri=
ting<br>
&gt; reference code. But have we maybe put our eggs in the Montgomery ladde=
r<br>
&gt; basket when maybe we should have gone for &#39;randomly split the priv=
ate key<br>
&gt; into two parts, perform two separate multiplications with each part an=
d add<br>
&gt; the result&#39;.<br>
&gt;<br>
&gt; We can play the blinding game in Edwards or Montgomery but it is easie=
r in<br>
&gt; Edwards.<br>
<br>
</span>You can always convert from Montgomery x to Edwards (x, y) and back<=
br>
without losing anything and costing only one field element inversion;<br>
see XEdDSA &lt;<a href=3D"https://whispersystems.org/docs/specifications/xe=
ddsa/" rel=3D"noreferrer" target=3D"_blank">https://whispersystems.org/<wbr=
>docs/specifications/xeddsa/</a>&gt;<br>
for something similar.<br>
<br>
But there is no reason to flail around with blinding when you can just<br>
use constant-time code for both Edwards and Montgomery arithmetic.<br></blo=
ckquote><div><br></div><div><div class=3D"gmail_default" style=3D"font-size=
:small">&#39;=E2=80=8BJust use =E2=80=8Bfinely ground unicorn powder&#39;.<=
/div><div class=3D"gmail_default" style=3D"font-size:small"><br></div><div =
class=3D"gmail_default" style=3D"font-size:small">I don&#39;t think the con=
stant time code survives modern optimizers or hardware accelerations nearly=
 as robustly as you imagine. I would much rather go with an approach that d=
oes not depend on the vagaries of implementation.</div><br></div><div><div =
class=3D"gmail_default" style=3D"font-size:small">=E2=80=8BThe main reason =
not to do this was the Kocher patents on blinding. But those are expiring s=
oon.=E2=80=8B</div></div></div></div></div>

--001a114109eaca867f055399117d--


From nobody Wed Jul  5 15:01:39 2017
Return-Path: <bascule@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 2B29313169F for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 15:01:38 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.998
X-Spam-Level: 
X-Spam-Status: No, score=-1.998 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 5yhm1hon3gQj for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 15:01:36 -0700 (PDT)
Received: from mail-yb0-x229.google.com (mail-yb0-x229.google.com [IPv6:2607:f8b0:4002:c09::229]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id EC03C131545 for <cfrg@irtf.org>; Wed,  5 Jul 2017 15:01:32 -0700 (PDT)
Received: by mail-yb0-x229.google.com with SMTP id s15so673769ybe.2 for <cfrg@irtf.org>; Wed, 05 Jul 2017 15:01:32 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=/9bAixlAYrcDr8r67axy27lN4BtF0kCq40N4ryEAdQY=; b=Kj+YE90/0fanRARwua7T5HDQkssmUr/BInqj5Q8ueesJQbvSTqieJIWh2gIjCh8sTL FeYLF3aYsBaIOuxqLajsGMpLvzxM7Ahg1sWgVWl8ZCM8uxZO89ksnRlDVyD9K+sjfHRA 2bQOytleBYemxTqy4fYjo+HIV/pu0KS0ehAmzzdLuqlZ+Nt2UAeNL42sFTU007oaH8i7 caAOF1AInFCVJ5dFLUN+AWptJArYXG41Lm4Iz0WWq/GS0hlxUapKNC55f29z16JZCw4W H6eKGI3TrO/S4v6XrD4oVEhNyMZnTkocj/zT/HIf2tc2NdTyBJxLW3QQ+3XflFXsyhE3 zw5Q==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=/9bAixlAYrcDr8r67axy27lN4BtF0kCq40N4ryEAdQY=; b=FepL6n0Y/z3YwTfmOl2x9TXH2Dcf27fRpfNz9pTkMRgqyObZ3m+q78ej2RJVF9aF1s 6N6kpQVHZM7aSkToooEfwj+VF3FBJ/7OklSEhDCdJil+9w7ZXuKLjd8wzWy4js/+1voo wJVRhDopccwQjuS9FzKGVqB8ILojReQ2ako6rzjbC6gQYuLBw9fizUgy8XYY2qv9mWbI QuaoG1UskPu+2JIpOnflsmrGb4j55w1AWYFgXJC2cvbw+REt7sDw/G+Jwaqwjc2cq01m /k/m64ViMerVImYgFJnLozqqYgtxoFMx2N+hTN9a4XaK9iZLepJQYEl9M0aWJY+0vwcA S0LA==
X-Gm-Message-State: AIVw110r4sBe0zjKpayitlstIeRc/+pDRe4s/ogS3Wm+9p5beULAi8zM 3nPEqyUGOk2zAElsa4YsbPsjb2k+yg==
X-Received: by 10.37.203.139 with SMTP id b133mr224971ybg.209.1499292091718; Wed, 05 Jul 2017 15:01:31 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.37.228.134 with HTTP; Wed, 5 Jul 2017 15:01:11 -0700 (PDT)
In-Reply-To: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com>
References: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com>
From: Tony Arcieri <bascule@gmail.com>
Date: Wed, 5 Jul 2017 15:01:11 -0700
Message-ID: <CAHOTMVLyB6+r6XX3z5ifi7Ey7Qpi1uiZDLsGREsWhgxjqotPxQ@mail.gmail.com>
To: Phillip Hallam-Baker <phill@hallambaker.com>
Cc: "cfrg@irtf.org" <cfrg@irtf.org>
Content-Type: multipart/alternative; boundary="001a114faf108abb6a0553992417"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/QqM5RrsPRFcGKgJygEo82cO4JBQ>
Subject: Re: [Cfrg] Side channel attack and Edwards curves...
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 22:01:38 -0000

--001a114faf108abb6a0553992417
Content-Type: text/plain; charset="UTF-8"

On Wed, Jul 5, 2017 at 11:38 AM, Phillip Hallam-Baker <phill@hallambaker.com
> wrote:

> Just another side channel attack and not something that bothers me writing
> reference code. But have we maybe put our eggs in the Montgomery ladder
> basket when maybe we should have gone for 'randomly split the private key
> into two parts, perform two separate multiplications with each part and add
> the result'.
>

I'm not sure why you're talking about Montgomery vs Edwards here. This is a
Flush+Reload attack similar to:

- "Just A Little Bit": https://eprint.iacr.org/2014/161.pdf
- "Just A Little Bit More": https://eprint.iacr.org/2014/434.pdf
- Cachebleed: https://eprint.iacr.org/2016/224.pdf

If there was a conclusion I drew from these attacks, it's the need to
include random values, as the security proofs say we should do.

I will note that BoringSSL was not vulnerable to Cachebleed because they
continued to use random blinding in addition to Intel's allegedly "constant
time" RSA code. Though many are quick to dismiss it, random blinding seems
to provide defenses against a multitude of attacks, not just cache timing
but DPA as well.

-- 
Tony Arcieri

--001a114faf108abb6a0553992417
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_extra"><div class=3D"gmail_quote">On W=
ed, Jul 5, 2017 at 11:38 AM, Phillip Hallam-Baker <span dir=3D"ltr">&lt;<a =
href=3D"mailto:phill@hallambaker.com" target=3D"_blank">phill@hallambaker.c=
om</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"marg=
in:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1e=
x"><div dir=3D"ltr"><div>Just another side channel attack and not something=
 that bothers me writing reference code. But have we maybe put our eggs in =
the Montgomery ladder basket when maybe we should have gone for &#39;random=
ly split the private key into two parts, perform two separate multiplicatio=
ns with each part and add the result&#39;.</div></div></blockquote><div><br=
></div><div>I&#39;m not sure why you&#39;re talking about Montgomery vs Edw=
ards here. This is a Flush+Reload attack similar to:</div><div><br></div><d=
iv>- &quot;Just A Little Bit&quot;:=C2=A0<a href=3D"https://eprint.iacr.org=
/2014/161.pdf">https://eprint.iacr.org/2014/161.pdf</a></div><div>- &quot;J=
ust A Little Bit More&quot;:=C2=A0<a href=3D"https://eprint.iacr.org/2014/4=
34.pdf">https://eprint.iacr.org/2014/434.pdf</a></div><div>- Cachebleed:=C2=
=A0<a href=3D"https://eprint.iacr.org/2016/224.pdf">https://eprint.iacr.org=
/2016/224.pdf</a></div><div><br></div><div>If there was a conclusion I drew=
 from these attacks, it&#39;s the need to include random values, as the sec=
urity proofs say we should do.</div><div><br></div><div>I will note that Bo=
ringSSL was not vulnerable to Cachebleed because they continued to use rand=
om blinding in addition to Intel&#39;s allegedly &quot;constant time&quot; =
RSA code. Though many are quick to dismiss it, random blinding seems to pro=
vide defenses against a multitude of attacks, not just cache timing but DPA=
 as well.</div><div>=C2=A0</div></div>-- <br><div class=3D"gmail_signature"=
>Tony Arcieri<br></div>
</div></div>

--001a114faf108abb6a0553992417--


From nobody Wed Jul  5 16:16:31 2017
Return-Path: <hallam@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 5187A12EA95 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 16:16:29 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.398
X-Spam-Level: 
X-Spam-Status: No, score=-2.398 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, FREEMAIL_FORGED_FROMDOMAIN=0.199, FREEMAIL_FROM=0.001, HEADER_FROM_DIFFERENT_DOMAINS=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id M6bSHDP24JLP for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 16:16:27 -0700 (PDT)
Received: from mail-lf0-x231.google.com (mail-lf0-x231.google.com [IPv6:2a00:1450:4010:c07::231]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id EACDA129482 for <cfrg@irtf.org>; Wed,  5 Jul 2017 16:16:26 -0700 (PDT)
Received: by mail-lf0-x231.google.com with SMTP id t72so1897671lff.1 for <cfrg@irtf.org>; Wed, 05 Jul 2017 16:16:26 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:sender:in-reply-to:references:from:date:message-id :subject:to:cc; bh=Qu6YhYtzmZUfwMeH0usRnfhb17q9DlJrPMt8IRv8bKE=; b=b1kl18wST3kUholQejM+hv3s+Qu04xKmHLH99t91jB5LC1F2Vy2CtA2zqmxnqmQgZI IePexXxBbiC9HI5je0vi02SFbmzEQvWXAzjGAuLKN1OU/ZARyNRqanc2peSlH9vo+kXj i8+Cy7MfVIqcAmM57IxEZahJxphrTqiM2tHPngJleNcIZDkFl7o3ZZTCWWqMc6lYjQnT fCOGw3MIJjDvbe7nToWpDSqWuBNfogoBpPY4DlaowTmfhXU21RJ2DcTR4CG8q5qPpAWP bcuAZnuwe2Cmq5eavLIT/C4g4RS7E1XQNeyLvEdbyLYRJxzFb0fLX1JiJDLYrzP1tfgW z7Lg==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:sender:in-reply-to:references:from :date:message-id:subject:to:cc; bh=Qu6YhYtzmZUfwMeH0usRnfhb17q9DlJrPMt8IRv8bKE=; b=K09sL4kVzI7fu/hh6eCSiTQnBrD0skLmraMZX2L7SXj96j3khKaTMKMIdqbfzbW437 1nI+7msom0hWziQssy8wAiyZNrp1aqYUL4XhZPyKxRI9K+ehSTErNEKnFn01ArI+WIfj IbsgeXkp0J9ReQ/dyo+BdfOxqGZKwn/PnpUgF0LZj+tA+Wkv5hoQvLR06SnyilQWcxgI 1dEJJigWd62VRAIlNeHsNi04OcGCRFldG1Gmuowp3SQMZcifbpHefZBgjZzP+HbxfqKw QbSc/KzmG0od71OwW9RDpSmeX1AmxkriMScwvM//mgQMGlkpkj4IKzddo7EDXnal9VoK KY6Q==
X-Gm-Message-State: AKS2vOxJ2fH4FG91pyhDWRIDx5gzBeOZ3TGfV3+OsseDjP5pUdwYNlaJ cPx3cyuzoE4OvTk/dF6aNK1RT0BGAg==
X-Received: by 10.46.77.84 with SMTP id a81mr14490174ljb.73.1499296585116; Wed, 05 Jul 2017 16:16:25 -0700 (PDT)
MIME-Version: 1.0
Sender: hallam@gmail.com
Received: by 10.25.181.214 with HTTP; Wed, 5 Jul 2017 16:16:24 -0700 (PDT)
In-Reply-To: <CAHOTMVLyB6+r6XX3z5ifi7Ey7Qpi1uiZDLsGREsWhgxjqotPxQ@mail.gmail.com>
References: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com> <CAHOTMVLyB6+r6XX3z5ifi7Ey7Qpi1uiZDLsGREsWhgxjqotPxQ@mail.gmail.com>
From: Phillip Hallam-Baker <phill@hallambaker.com>
Date: Wed, 5 Jul 2017 19:16:24 -0400
X-Google-Sender-Auth: _Y3NthpjCFcHaXIDh5iR3qjibJg
Message-ID: <CAMm+LwiKUJSOEZefABwwkF8H_p+_WTZNGzzrezjCncVZzLd_dA@mail.gmail.com>
To: Tony Arcieri <bascule@gmail.com>
Cc: "cfrg@irtf.org" <cfrg@irtf.org>
Content-Type: multipart/alternative; boundary="94eb2c1aac365e728705539a3061"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/lM0kLEW4N7-ZEM0p1lktbONaVbs>
Subject: Re: [Cfrg] Side channel attack and Edwards curves...
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 23:16:29 -0000

--94eb2c1aac365e728705539a3061
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

On Wed, Jul 5, 2017 at 6:01 PM, Tony Arcieri <bascule@gmail.com> wrote:

> On Wed, Jul 5, 2017 at 11:38 AM, Phillip Hallam-Baker <
> phill@hallambaker.com> wrote:
>
>> Just another side channel attack and not something that bothers me
>> writing reference code. But have we maybe put our eggs in the Montgomery
>> ladder basket when maybe we should have gone for 'randomly split the
>> private key into two parts, perform two separate multiplications with ea=
ch
>> part and add the result'.
>>
>
> I'm not sure why you're talking about Montgomery vs Edwards here. This is
> a Flush+Reload attack similar to:
>

=E2=80=8BYou can blind in either. But if you are going to blind then a lot =
of the
advantages of Montgomery start to collapse. because you have to do that add
stage.



> - "Just A Little Bit": https://eprint.iacr.org/2014/161.pdf
> - "Just A Little Bit More": https://eprint.iacr.org/2014/434.pdf
> - Cachebleed: https://eprint.iacr.org/2016/224.pdf
>
> If there was a conclusion I drew from these attacks, it's the need to
> include random values, as the security proofs say we should do.
>
> I will note that BoringSSL was not vulnerable to Cachebleed because they
> continued to use random blinding in addition to Intel's allegedly "consta=
nt
> time" RSA code. Though many are quick to dismiss it, random blinding seem=
s
> to provide defenses against a multitude of attacks, not just cache timing
> but DPA as well.
>
> --
> Tony Arcieri
>

--94eb2c1aac365e728705539a3061
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_default" style=3D"font-size:small"><br=
></div><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">On Wed, Ju=
l 5, 2017 at 6:01 PM, Tony Arcieri <span dir=3D"ltr">&lt;<a href=3D"mailto:=
bascule@gmail.com" target=3D"_blank">bascule@gmail.com</a>&gt;</span> wrote=
:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-le=
ft:1px #ccc solid;padding-left:1ex"><div dir=3D"ltr"><div class=3D"gmail_ex=
tra"><div class=3D"gmail_quote"><span class=3D"">On Wed, Jul 5, 2017 at 11:=
38 AM, Phillip Hallam-Baker <span dir=3D"ltr">&lt;<a href=3D"mailto:phill@h=
allambaker.com" target=3D"_blank">phill@hallambaker.com</a>&gt;</span> wrot=
e:<br><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;b=
order-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir=3D"ltr"><d=
iv>Just another side channel attack and not something that bothers me writi=
ng reference code. But have we maybe put our eggs in the Montgomery ladder =
basket when maybe we should have gone for &#39;randomly split the private k=
ey into two parts, perform two separate multiplications with each part and =
add the result&#39;.</div></div></blockquote><div><br></div></span><div>I&#=
39;m not sure why you&#39;re talking about Montgomery vs Edwards here. This=
 is a Flush+Reload attack similar to:</div></div></div></div></blockquote><=
div><br></div><div><div class=3D"gmail_default" style=3D"font-size:small">=
=E2=80=8BYou can blind in either. But if you are going to blind then a lot =
of the advantages of Montgomery start to collapse. because you have to do t=
hat add stage.</div><div class=3D"gmail_default" style=3D"font-size:small">=
<br></div></div><div>=C2=A0</div><blockquote class=3D"gmail_quote" style=3D=
"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir=3D=
"ltr"><div class=3D"gmail_extra"><div class=3D"gmail_quote"><div>- &quot;Ju=
st A Little Bit&quot;:=C2=A0<a href=3D"https://eprint.iacr.org/2014/161.pdf=
" target=3D"_blank">https://eprint.iacr.org/<wbr>2014/161.pdf</a></div><div=
>- &quot;Just A Little Bit More&quot;:=C2=A0<a href=3D"https://eprint.iacr.=
org/2014/434.pdf" target=3D"_blank">https://eprint.iacr.<wbr>org/2014/434.p=
df</a></div><div>- Cachebleed:=C2=A0<a href=3D"https://eprint.iacr.org/2016=
/224.pdf" target=3D"_blank">https://eprint.<wbr>iacr.org/2016/224.pdf</a></=
div><div><br></div><div>If there was a conclusion I drew from these attacks=
, it&#39;s the need to include random values, as the security proofs say we=
 should do.</div><div><br></div><div>I will note that BoringSSL was not vul=
nerable to Cachebleed because they continued to use random blinding in addi=
tion to Intel&#39;s allegedly &quot;constant time&quot; RSA code. Though ma=
ny are quick to dismiss it, random blinding seems to provide defenses again=
st a multitude of attacks, not just cache timing but DPA as well.</div><spa=
n class=3D"HOEnZb"><font color=3D"#888888"><div>=C2=A0</div></font></span><=
/div><span class=3D"HOEnZb"><font color=3D"#888888">-- <br><div class=3D"m_=
8525802127365536270gmail_signature">Tony Arcieri<br></div>
</font></span></div></div>
</blockquote></div><br></div></div>

--94eb2c1aac365e728705539a3061--


From nobody Wed Jul  5 16:29:24 2017
Return-Path: <bascule@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id A289212EE46 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 16:29:23 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.998
X-Spam-Level: 
X-Spam-Status: No, score=-1.998 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id tkKqgXnyrfDV for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 16:29:22 -0700 (PDT)
Received: from mail-yb0-x231.google.com (mail-yb0-x231.google.com [IPv6:2607:f8b0:4002:c09::231]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 2888C12ECBB for <cfrg@irtf.org>; Wed,  5 Jul 2017 16:29:22 -0700 (PDT)
Received: by mail-yb0-x231.google.com with SMTP id f194so1129295yba.3 for <cfrg@irtf.org>; Wed, 05 Jul 2017 16:29:22 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=IosnFZFmVwvsTrV1gY14keO4BhGcARh82JryrfXHcZA=; b=kcPJevIvWBC6bm0Kp7AxlzfReBcRTlJ3ILCKn8OVymeVzXcL8eZSZepOut5xMKgPYJ 3qjMV4zQlLE5/FaKXk7nnVkNxI01uwlMOQScXbmn7STN2s8oEAqjl0WJRqOF8aJvLXc4 dkZMy5XX9qHqn9WXMcXOXRKK5bYmBeOElsZ8nTQ4zj/z8Yav8TR5ZPRgEheuzCEFp3+i aEBShwqT9LZVzeX5mjws4iFoRrAwj2TUsgo2jmjh/fqAbj4FrDXQJvz07QL00ZRkdVj+ EDgu2SEflnI6QqK0np0Jd6OzqrYPzDYFWm1ZVL4M9bQE9NHwnXOV21jkuUcC7W41RpDU n8zg==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=IosnFZFmVwvsTrV1gY14keO4BhGcARh82JryrfXHcZA=; b=OMKeJALY7wvdRxYDKeG7YchuTS2rwh1ZiP9/dI2do03z20GoZ+9VwjBIhVg7oCXau4 vQx4dLXkNhyaL1GJTGAVUvMIypBmra5pL0p1PUDEg0zzuP2O7xbEN1WT0u/AKKKtcEY9 kVtF6ul9+kM7wW5yP0KzspUm2NfiMQBf9vkSYCI4vn6Ks55wa/nmvK2gw2/fsknuJB25 Bf8aw889jrITTiR2JvVOr/nsZVdAtfJFhISAVBcdCeVgB/pu7u/AJN2G58/H0ZI60FOf wCKXJuz1Oct2UNmUMS/A3Who82M7swfSZhVeckS/SNUKLewqbkkzcDqdyAlLacnohqSS VuiA==
X-Gm-Message-State: AIVw111WVedWl87nOg9OJdSeTs3YTuRwXQUUUjXOfwjWFwzirqJdvMCJ xxxeIme5Rs/0RFOfombOrk9Btj4Ag83c
X-Received: by 10.37.221.196 with SMTP id u187mr444439ybg.173.1499297361397; Wed, 05 Jul 2017 16:29:21 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.37.228.134 with HTTP; Wed, 5 Jul 2017 16:29:00 -0700 (PDT)
In-Reply-To: <CAMm+LwiKUJSOEZefABwwkF8H_p+_WTZNGzzrezjCncVZzLd_dA@mail.gmail.com>
References: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com> <CAHOTMVLyB6+r6XX3z5ifi7Ey7Qpi1uiZDLsGREsWhgxjqotPxQ@mail.gmail.com> <CAMm+LwiKUJSOEZefABwwkF8H_p+_WTZNGzzrezjCncVZzLd_dA@mail.gmail.com>
From: Tony Arcieri <bascule@gmail.com>
Date: Wed, 5 Jul 2017 16:29:00 -0700
Message-ID: <CAHOTMVK8J5YRD0t516mn1twVq2d-z+h6smxYxL1EOW0yy_Xtzw@mail.gmail.com>
To: Phillip Hallam-Baker <phill@hallambaker.com>
Cc: "cfrg@irtf.org" <cfrg@irtf.org>
Content-Type: multipart/alternative; boundary="001a114bc35aa3949105539a5e5d"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/Bt6ct3IziYJ_7byeREvb153wXzc>
Subject: Re: [Cfrg] Side channel attack and Edwards curves...
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 05 Jul 2017 23:29:23 -0000

--001a114bc35aa3949105539a5e5d
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

On Wed, Jul 5, 2017 at 4:16 PM, Phillip Hallam-Baker <phill@hallambaker.com=
>
wrote:

> =E2=80=8BYou can blind in either. But if you are going to blind then a lo=
t of the
> advantages of Montgomery start to collapse. because you have to do that a=
dd
> stage.
>

Ephemeral Montgomery keys, of the sort used by TLS ECDHE, are another
example of a use case which (if proper deployment procedures are followed)
shouldn't be vulnerable to this sort of attack.

I would agree that for long-term static keys, for this and other reasons
perhaps Edwards would be preferable.

--=20
Tony Arcieri

--001a114bc35aa3949105539a5e5d
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_extra"><div class=3D"gmail_quote">On W=
ed, Jul 5, 2017 at 4:16 PM, Phillip Hallam-Baker <span dir=3D"ltr">&lt;<a h=
ref=3D"mailto:phill@hallambaker.com" target=3D"_blank">phill@hallambaker.co=
m</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margi=
n:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir=3D"ltr">=
<div style=3D"font-size:small">=E2=80=8BYou can blind in either. But if you=
 are going to blind then a lot of the advantages of Montgomery start to col=
lapse. because you have to do that add stage.</div></div></blockquote><div>=
<br></div><div>Ephemeral Montgomery keys, of the sort used by TLS ECDHE, ar=
e another example of a use case which (if proper deployment procedures are =
followed) shouldn&#39;t be vulnerable to this sort of attack.</div><div><br=
></div><div>I would agree that for long-term static keys, for this and othe=
r reasons perhaps Edwards would be preferable.</div><div><br></div></div>--=
 <br><div class=3D"gmail_signature" data-smartmail=3D"gmail_signature">Tony=
 Arcieri<br></div>
</div></div>

--001a114bc35aa3949105539a5e5d--


From nobody Wed Jul  5 17:07:25 2017
Return-Path: <bascule@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 3EE2312F5DB for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 17:07:24 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.998
X-Spam-Level: 
X-Spam-Status: No, score=-1.998 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id csrifOQDDkfK for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 17:07:22 -0700 (PDT)
Received: from mail-yb0-x231.google.com (mail-yb0-x231.google.com [IPv6:2607:f8b0:4002:c09::231]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 673C2127286 for <cfrg@irtf.org>; Wed,  5 Jul 2017 17:07:22 -0700 (PDT)
Received: by mail-yb0-x231.google.com with SMTP id e201so1327720ybb.1 for <cfrg@irtf.org>; Wed, 05 Jul 2017 17:07:22 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=iO1JVqhavsssPBrtNx5VmyvdFcYp9Qmu2q5wi9VQj8A=; b=D3YB1PgxflcUI5o/xAK9k6Z1LDVfwfYv+0EGFYGknV8khKNXCFxY3QFPsqh1RY9N8J YMXQwWPpe4+zJOYDOXOb+LQCAzziMQ8XqZgNxNBeK07mJOf5FJhTXPzC48y9j66sDzAt QnEBFpU1D1jndMCnNxDS5HuuWkFKNullGxVxa6MabtvFO44bvRwg/XbhBnq+EEcslkUs tJZTX/PHUNJk3cDx+9sBXAct/8L0RbiPmbPwWIAIp8RKhkkX9e+oIrRKzFLjNKhoniP6 /zWhzoz/ESA+4+cCWglVUJPplbdemMrN9GY+gAFYEgKkPs5T87zIh5Jgo5tocz4rFzZH ePvQ==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=iO1JVqhavsssPBrtNx5VmyvdFcYp9Qmu2q5wi9VQj8A=; b=MZm0t0Qq/0nTsyQQt5Ck75yfKOkFjYyeu4Wxys/WP3FODXixhgtVmUmtFpLQGpCj7X UryNnP55CMWEOdShvw7K7kw74yS+jwk68x2pnWqr2nJEoqSXSOlvUrJ9bk4/9N6bAUjA 3Jbih5MG/VQDbu/oKmoP0zP/hwpMgsKJu4i7TYEyMeElZSWwzoXpana8y3YRcYSmB8sA bbLFuarS8HyL/5hgFMVPa29mwXtGetjSBM88pREpVV2NZusuk3ekFv0wVir6t1mNd2c3 t71Lo8lw12wpezDIFJDyS6B3lYVC+O/D3/sjJMyZwldUL+4zG7wLsLfpUZqoV7890qOx HxeQ==
X-Gm-Message-State: AIVw112Ka+Mvb+cDol58SKJNMFw3h69N8GH8mE5U8HXEBFLpxtbFZh7t L1yRqJHYA5gdAnmBzOrr8OTeonsZIg==
X-Received: by 10.37.221.196 with SMTP id u187mr529608ybg.173.1499299641595; Wed, 05 Jul 2017 17:07:21 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.37.228.134 with HTTP; Wed, 5 Jul 2017 17:07:01 -0700 (PDT)
In-Reply-To: <CAMm+LwiKUJSOEZefABwwkF8H_p+_WTZNGzzrezjCncVZzLd_dA@mail.gmail.com>
References: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com> <CAHOTMVLyB6+r6XX3z5ifi7Ey7Qpi1uiZDLsGREsWhgxjqotPxQ@mail.gmail.com> <CAMm+LwiKUJSOEZefABwwkF8H_p+_WTZNGzzrezjCncVZzLd_dA@mail.gmail.com>
From: Tony Arcieri <bascule@gmail.com>
Date: Wed, 5 Jul 2017 17:07:01 -0700
Message-ID: <CAHOTMVL0hbxZ0PtHhMxjM7eXh+Mg57R=ReFteiMPViNZO4BtBg@mail.gmail.com>
To: Phillip Hallam-Baker <phill@hallambaker.com>
Cc: "cfrg@irtf.org" <cfrg@irtf.org>
Content-Type: multipart/alternative; boundary="001a114bc35a8cd73f05539ae63a"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/hK0bkDa5OG2gp2rAOlmBIXhVpGw>
Subject: Re: [Cfrg] Side channel attack and Edwards curves...
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Thu, 06 Jul 2017 00:07:24 -0000

--001a114bc35a8cd73f05539ae63a
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

On Wed, Jul 5, 2017 at 4:16 PM, Phillip Hallam-Baker <phill@hallambaker.com=
>
wrote:

> =E2=80=8BYou can blind in either. But if you are going to blind then a lo=
t of the
> advantages of Montgomery start to collapse. because you have to do that a=
dd
> stage.
>

What if you blinded kP with r using:

    r*([k r^-1]*P)

which only requires inversions?

--=20
Tony Arcieri

--001a114bc35a8cd73f05539ae63a
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_extra"><div class=3D"gmail_quote">On W=
ed, Jul 5, 2017 at 4:16 PM, Phillip Hallam-Baker <span dir=3D"ltr">&lt;<a h=
ref=3D"mailto:phill@hallambaker.com" target=3D"_blank">phill@hallambaker.co=
m</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margi=
n:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex=
"><div dir=3D"ltr"><div style=3D"font-size:small">=E2=80=8BYou can blind in=
 either. But if you are going to blind then a lot of the advantages of Mont=
gomery start to collapse. because you have to do that add stage.</div></div=
></blockquote><div><br></div><div>What if you blinded kP with r using:</div=
><div><br></div><div>=C2=A0 =C2=A0 r*([k r^-1]*P)=C2=A0</div></div><div><br=
></div><div>which only requires inversions?</div><div><br></div>-- <br><div=
 class=3D"gmail_signature">Tony Arcieri<br></div>
</div></div>

--001a114bc35a8cd73f05539ae63a--


From nobody Wed Jul  5 17:36:14 2017
Return-Path: <samuel.c.p.neves@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 32065129562 for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 17:36:13 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.999
X-Spam-Level: 
X-Spam-Status: No, score=-1.999 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id GrObEqlMvmsP for <cfrg@ietfa.amsl.com>; Wed,  5 Jul 2017 17:36:11 -0700 (PDT)
Received: from mail-wr0-x232.google.com (mail-wr0-x232.google.com [IPv6:2a00:1450:400c:c0c::232]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id D52901292F5 for <cfrg@irtf.org>; Wed,  5 Jul 2017 17:36:10 -0700 (PDT)
Received: by mail-wr0-x232.google.com with SMTP id c11so6502621wrc.3 for <cfrg@irtf.org>; Wed, 05 Jul 2017 17:36:10 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :content-transfer-encoding; bh=1hM1JInjqew/mNCHXoeMcvvMdSTLtL3q51sGxIzYyQU=; b=GroWgnCC30qLwC+mfVQlgwywhT8wL7nzXy0f+Cc4YiVtlwKqtvBn5InufHLStqkl0x qGBa1+BH2N6kAgR4+TJ0Z9lXGeJb8j6nnIdG2Pkr1smgi5K++IAv55Z2u5/RN+tFw3Hk LJTJO/1CGlPMiAMyJInNY09HIpLXsKC6F41+0NuNUxd4JfKQWGpfWpD+7r/nO2D0BdjG xpXn5n+TPSeVPhUP8+5zjSp+QbEs/TQdRtSh73mzLy0EakaRWB8ecciqqBVwAsaHeQlW +oEKZoubWPOSeJbYbxP3e9keG6c7Xb0PtKxawN3MhZenurTKPmbpwvv3cBqyBbUW0wIC EB8Q==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:content-transfer-encoding; bh=1hM1JInjqew/mNCHXoeMcvvMdSTLtL3q51sGxIzYyQU=; b=Kd/RIbdA5bAc4ZeDkPFf59+/8OT7ma1wn9HVUFLCRf8tgCQ6qiuhsbtlbSXAy8vU3Z 75bjZohSXpcLa2CxYECFCyGDPdPJx9nDOyQj1xQIQkOhGnCqSkpLAhEd1mwaK2g+HVcn AYOELY8Y47utaxLMXh/VfWgtg3yi17YYb6ER6reydYTVndGtlsemGDcaJ6qGn3AYqAN7 OuxyPmzocM3tsUCXCpJ814z/4klUBWcXDu9HQDrhCMWNf1d5kuVVDngnljgWy9UQJZOs wwp9E0ob4H0Kb1hvHdaBUFWPAzwDPJjSos5N3GkZleI2bLwPbBv4ftb3uLPxYrsHbMu3 at0w==
X-Gm-Message-State: AKS2vOyxMNEK2X8gKNI9yZGpxNQTi59BTVtAFDROd+7oI5J1K05/8dSi 3ZynlA5J3oY/ueBgo2JaVKhXTxaXVf4nDqI=
X-Received: by 10.80.164.241 with SMTP id x46mr24041531edb.114.1499301369330;  Wed, 05 Jul 2017 17:36:09 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.80.151.199 with HTTP; Wed, 5 Jul 2017 17:35:29 -0700 (PDT)
In-Reply-To: <CAHOTMVL0hbxZ0PtHhMxjM7eXh+Mg57R=ReFteiMPViNZO4BtBg@mail.gmail.com>
References: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com> <CAHOTMVLyB6+r6XX3z5ifi7Ey7Qpi1uiZDLsGREsWhgxjqotPxQ@mail.gmail.com> <CAMm+LwiKUJSOEZefABwwkF8H_p+_WTZNGzzrezjCncVZzLd_dA@mail.gmail.com> <CAHOTMVL0hbxZ0PtHhMxjM7eXh+Mg57R=ReFteiMPViNZO4BtBg@mail.gmail.com>
From: Samuel Neves <samuel.c.p.neves@gmail.com>
Date: Thu, 6 Jul 2017 01:35:29 +0100
Message-ID: <CAEX_ruGD5V7nus20d8507q09PMSJghv6xh-a-_fbHbs1nF33EQ@mail.gmail.com>
To: "cfrg@irtf.org" <cfrg@irtf.org>
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/fMgcnV1V5Z60Vwh2aSm0D0Lf-CE>
Subject: Re: [Cfrg] Side channel attack and Edwards curves...
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Thu, 06 Jul 2017 00:36:13 -0000

Coron's countermeasures [1, =C2=A75]---the first and third one, in
particular---work well with Montgomery coordinates.

[1] http://www.jscoron.fr/publications/dpaecc.pdf

On Thu, Jul 6, 2017 at 1:07 AM, Tony Arcieri <bascule@gmail.com> wrote:
> On Wed, Jul 5, 2017 at 4:16 PM, Phillip Hallam-Baker <phill@hallambaker.c=
om>
> wrote:
>>
>> You can blind in either. But if you are going to blind then a lot of the
>> advantages of Montgomery start to collapse. because you have to do that =
add
>> stage.
>
>
> What if you blinded kP with r using:
>
>     r*([k r^-1]*P)
>
> which only requires inversions?
>
> --
> Tony Arcieri
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>


From nobody Thu Jul  6 01:34:50 2017
Return-Path: <daniel.slamanig@tugraz.at>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id D008812EB69 for <cfrg@ietfa.amsl.com>; Thu,  6 Jul 2017 01:34:48 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -4.302
X-Spam-Level: 
X-Spam-Status: No, score=-4.302 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, RCVD_IN_DNSWL_MED=-2.3, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=tugraz.at
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 5waHpx5huRXa for <cfrg@ietfa.amsl.com>; Thu,  6 Jul 2017 01:34:45 -0700 (PDT)
Received: from mailrelay.tugraz.at (mailrelay.tugraz.at [129.27.2.202]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 95CE9126B6D for <cfrg@irtf.org>; Thu,  6 Jul 2017 01:34:44 -0700 (PDT)
Received: from [10.27.152.210] (nat-hiding.iaik.tugraz.at [129.27.152.126]) (authenticated bits=0) by mailrelay2.tugraz.at (8.14.9/8.14.9) with ESMTP id v668YboV010680 (version=TLSv1/SSLv3 cipher=ECDHE-RSA-AES256-GCM-SHA384 bits=256 verify=NO); Thu, 6 Jul 2017 10:34:38 +0200
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=tugraz.at; s=mailrelay; t=1499330081; bh=Rn5nCYH4P21Vqc7j3lNlvracpkMuib+YvK6nmy4/r40=; h=Subject:To:Cc:References:From:Date:In-Reply-To; b=UrXWu2sWGgPxCwoqai/RhJTHsYYQR2N6iKURjAshOvSPTn1WyStIAt07gceg021PN 8cpHlfQrWDQXs2BgtcPfiDxIs81uADdbBMtMXPmFZJdQsjE1k1N3ffU9KIfghw6Ksh 9YlBLSxbfwaf1n+yWy6+QpmUyxhOSfCMfw4Ecx8E=
To: Bryan Ford <brynosaurus@gmail.com>
Cc: Philipp Jovanovic <philipp@jovanovic.io>, cfrg@irtf.org
References: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io> <11cc5d3f-ecf9-2fd0-825c-c8b441bd2813@tugraz.at> <A423CB6E-D649-4320-BB76-2E3783D6AFE0@gmail.com>
From: Daniel Slamanig <daniel.slamanig@tugraz.at>
Message-ID: <1e0faffa-370c-bf81-4973-55bfd36de510@tugraz.at>
Date: Thu, 6 Jul 2017 10:34:36 +0200
User-Agent: Mozilla/5.0 (Windows NT 6.3; WOW64; rv:52.0) Gecko/20100101 Thunderbird/52.2.1
MIME-Version: 1.0
In-Reply-To: <A423CB6E-D649-4320-BB76-2E3783D6AFE0@gmail.com>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
X-TUG-Backscatter-control: lAa1Aa+Pa1hp/miybLoRww
X-Spam-Scanner: SpamAssassin 3.003001 
X-Spam-Score-relay: -1.7
X-Scanned-By: MIMEDefang 2.74
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/MBVLP-Nw4LqN3BKMrZuyzI1cwnA>
Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Thu, 06 Jul 2017 08:34:49 -0000

Hi Bryan,

thank you very much for your detailed comments. I have to admit that I 
was not aware of the S&P paper before reading the draft and so I 
somewhat missed the big picture and simply "analyzed" the collective 
signing as described in the draft without specific context.

You are correct in that with a chameleon hash (CH) the leader needs to 
be somehow trusted (it however does not seem to me that the leader has 
more power than producing invalid signatures by messing up with the CH - 
which would work in any case - but I guess one needs to evaluate that in 
a bit more details). Moreover, in such a CH approach the leader must be 
involved in the final step of the signature generation. It seems to me 
that this is not the case in your approach as everyone could complete 
the multi-signature. Clearly, the CH approach is much more susceptible 
to DoS attacks.

Another observation regarding committing to the bitmask Z. If you do not 
commit to the bitmask Z, then users could cooperate in setting up their 
public keys, lets say A_i and A_j cooperate. Then one of them could take 
part in the signing, but in the end one could use the attack with the 
rogue keys outlined in my initial mail so that A_j can claim that he 
took part in the signing process although A_i actually took part. As far 
as I see not even using a delinearization scheme would help here. 
Nevertheless, it seems to me that this is not a valid attack vector when 
I look at the paper (but as you do not formally specify a security model 
for your approach in the paper this is hard to tell). Note that such an 
attack would even work if users have to register the public keys and 
prove that they know the secret key corresponding to the public key, 
e.g., via a (NI)ZK proof of the secret key - which I have seen is 
mentioned in the paper, but not discussed in the draft. Summing up, 
without commiting to Z in the signature, you would trivially not be able 
to achieve strong EUF-CMA security of the multi-signature due to the 
malleability, but as far as I see standard EUF-CMA should still hold 
(which seems sufficient for your application).

Thanks and cheers,
Daniel

On 05.07.2017 15:11, Bryan Ford wrote:
> Hi Daniel, thanks for your thoughts on the commitment-to-the-bitmask issue.
> 
> Your proposal of using a chameleon hash, to allow the leader to “adjust” 
> the bit mask after the commit c has been established, is an interesting 
> idea. However, if I understand it correctly, if the leader holds the 
> trapdoor key for the chameleon hash, wouldn’t that still make the final 
> collective signature malleable for the leader (or for anyone the 
> leader’s trapdoor key might leak to)?  The CoSi protocol as currently 
> defined is intended to ensure that the leader has no special privilege 
> or trust with respect to other cosigners: i.e., the leader is merely an 
> ordinary participant, but is simply the one who for whatever reason 
> decides to initiate the cosigning operation.  Giving the leader special 
> powers - e.g., making the signature malleable to the leader but not to 
> others - would break this principle and need to be extremely carefully 
> considered I think.
> 
> To follow up on my last message to Oleg, again I suggest reading section 
> IV of our CoSi paper from IEEE S&P last year 
> (http://dedis.cs.yale.edu/dissent/papers/witness-abs), as it discusses 
> several related issues, especially the potential desire to allow the 
> leader to complete a collective signing procedure even with only a 
> subset of “committed” participants remaining present in the “response” 
> phase.  In particular, the leader can form all the individual Schnorr 
> commits into a Merkle tree, and make the real commit c be the root of 
> that Merkle tree.  In this way, the leader is committing not so much to 
> a particular collective Schnorr commit but rather to *all possible* 
> Schnorr commits that can be composed from any subset of the individual 
> Schnorr commits within that Merkle tree.  This way, if some of the 
> participants whose commits are present in that Merkle tree remain 
> available during the response phase but others drop out, the leader can 
> still use the commit c and form a correct and verifiable collective 
> signature against the particular subset of Schnorr commits from nodes 
> that remained available throughout the process, without restarting.
> 
> I guess this approach does, in a slightly different way, make the 
> resulting collective signatures slightly malleable to the leader: from a 
> given set of commit-time and response-time information, the leader could 
> put together distinct collective signatures representing different 
> subsets of response-time participants.  Some form of 
> “leader-malleability” of this kind seems unavoidably essential to 
> enabling the leader to complete a collective signing round in the 
> presence of partial failures without restarting.  Perhaps the same 
> limited leader-malleability is more-or-less the same property your 
> suggestion of using chameleon hashes has, although I haven’t had a 
> chance to compare them deeply yet.
> 
> But at any rate, the higher-level tradeoff here to consider is whether 
> it’s better to (a) enforce strict non-malleability of collective 
> signatures (by anyone, leader included), at the cost of O(N)-round DoS 
> attack vulnerability during signing due to the need to restart partially 
> failed rounds, or (b) provide some limited form of limited 
> leader-malleability in order to support restart-free operation and avoid 
> DoS attacks during signing, at the cost of a more complex protocol (and 
> perhaps slightly more “special” trust in the leader than we might like).
> 
> Again, further thoughts on this and other topics are most welcome.
> 
> Thanks
> Bryan
> 
>> On Jul 3, 2017, at 7:34 PM, Daniel Slamanig <daniel.slamanig@tugraz.at 
>> <mailto:daniel.slamanig@tugraz.at>> wrote:
>>
>> Hi Philipp,
>>
>> looks interesting!
>>
>> After looking at the protocol I also have some security concerns 
>> (related to what has been raised by Oleg in a previous mail).
>>
>> Not committing to Z as well as the actual sum of signers public keys 
>> A' in the computation of the hash c for the signature seems to be 
>> problematic.
>>
>> It seems to me that committing Z in the signature in plain as well as 
>> A' does not work given the later application of the signing procedure 
>> (where till the end of the protocol it is not clear who actually 
>> participates in the signing but c must be known at the beginning).
>>
>> Committing to neither of both however seems problematic as it does not 
>> fix the set of actual signers.
>>
>> This could be circumvented by allowing an honest leader to adapt the 
>> commitment to the final Z (and A') after it knows the signers without 
>> modifying the initially computed c using a chameleon hash (trapdoor 
>> commitment). I use P as a generator below, omit the brackets [a]P 
>> notation for scalar multiplication and write it from the perspective 
>> of the leader, i.e., the signer that initiates the protocol.
>>
>> The leader could choose chameleon hash parameters sk_ch=y for random y 
>> and pk_ch=(P,Y=yP) and add pk_ch and chameleon hash CH(Z'):=h(Z')P+u'Y 
>> for randomly chosen u' to the computation of c, i.e., set 
>> c=H(R||A||pk_ch||CH(Z')||S), where h() is a collision resistant hash 
>> function (this is just the standard way of constructing a chameleon 
>> hash from DL for arbitrary message spaces as propsed in [1]). If Z' is 
>> not yet known one simply sets Z' to some fixed string at the 
>> beginning, e.g., Z':=0. At the end of the protocol, when the leader 
>> knows the exact signers, it can update Z' to the final value Z and use 
>> sk_ch to compute a collision in the chameleon hash, i.e., such that 
>> CH(Z)=CH(Z') by solving h(Z')+u'y = h(Z)+uy for u. He then adds u and 
>> Z as well as pk_ch to the signature, i.e., sets it as (R,s,u,Z,pk_ch) 
>> and discards sk_ch and u'. If Z is known beforehand, one simply 
>> computes the chameleon hash once and does not need to compute a 
>> collision. Clearly, the use of a chameleon hash allows to simply adapt 
>> to the actual set of signers representing Z without modifying c (with 
>> the knowledge of sk_ch - but it does not work without the knowledge of 
>> sk_ch). This would resolve the issue with the unknown Z at the time of 
>> signing.
>>
>> Also, A is committed in the signature, but not the concrete A'=\sum 
>> A_i of keys used for computing the signature (I guess also due to the 
>> reason that one does not know the correct set of signers when 
>> computing the hash c). That can be problematic in a rogue key scenario 
>> in the current protocol, i.e., when not all signers need to prove 
>> knowledge of the secret key when they register their public keys but 
>> their public keys could be functions of other public keys (guess this 
>> could be a problem here). For instance, a malicious A^* could just 
>> take some key from A, say A_j, and compute and publish A^*=a^*A_j. And 
>> then given a collective signature (R,s,Z) where A_j participated, the 
>> signer can update s to s^* = s+a^*c as well as Z^* to exclude A_j and 
>> include A^* (as Z is not committed in the signature generation) and 
>> the signature (R,s^*,Z^*) will be a valid signature that certifies 
>> that A^* participated in signing - although he didn't.
>>
>> If Z is committed as proposed above and it is checked during the 
>> verification, then this should no longer work. One could also adapt 
>> the hash c=H(R||pk_ch||CH(Z'||A)||S) to include a chameleon hash to 
>> CH(Z||A'), where A' is the real set of signers that participated in 
>> the signature generation and is adapted before finalizing the 
>> signature when known as above.
>>
>> I hope that what I proposed is not just complete nonsense :) Also it 
>> produces quite a bit of an overhead. There may also be easier ways to 
>> avoid the issues.
>>
>> Some editorial issues: the message to be signed is sometimes called a 
>> satement S and later then message msg. S could be confusing as part of 
>> the signature is s and your semantic is that scalars are lowercase and 
>> points are uppercase. Also in 4.2 "Signature Generation" steps 2 and 3 
>> are confusing as I guess that in the protocol all the signer compute 
>> their own [r_i]B values and R=\sum R_i instead of R=[r]B which would 
>> mean that they would send their r_i's (hope they will not do so).
>>
>> Also I find it somewhat confusing that the bitmask Z identifies the 
>> non-signers with a bit set to 1. Why not identifying the signers with 
>> a bit set to 1?
>>
>> Cheers,
>> Daniel
>>
>>
>> [1] Hugo Krawczyk, Tal Rabin: Chameleon Signatures. NDSS 2000
>>
>> On 01.07.2017 23:58, Philipp Jovanovic wrote:
>>> Hi CFRG,
>>> Here’s a first version of an Internet-Draft on “Collective 
>>> Edwards-Curve Digital Signature Algorithms” based on Ed25519 and 
>>> Ed448: https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/
>>> We plan to give a short presentation on that topic at the next CFRG 
>>> meeting in Prague.
>>> Any feedback is more than welcome. Thanks!
>>> All the best,
>>> Philipp
>>> _______________________________________________
>>> Cfrg mailing list
>>> Cfrg@irtf.org <mailto:Cfrg@irtf.org>
>>> https://www.irtf.org/mailman/listinfo/cfrg
>>
>>
>> --
>> Dr. Daniel Slamanig
>> Institute for Applied Information Processing and Communications
>> Graz University of Technology
>> Inffeldgasse 16a, 8010 Graz, Austria.
>> Phone: +43 316 873 5509
>> http://www.iaik.tugraz.at
>>
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org
>> https://www.irtf.org/mailman/listinfo/cfrg
> 


--
Dr. Daniel Slamanig
Institute for Applied Information Processing and Communications
Graz University of Technology
Inffeldgasse 16a, 8010 Graz, Austria.
Phone: +43 316 873 5509
http://www.iaik.tugraz.at


From nobody Fri Jul  7 00:17:49 2017
Return-Path: <Kenny.Paterson@rhul.ac.uk>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id ADFA4131A4F for <cfrg@ietfa.amsl.com>; Fri,  7 Jul 2017 00:17:48 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.92
X-Spam-Level: 
X-Spam-Status: No, score=-1.92 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, RCVD_IN_DNSWL_NONE=-0.0001, RCVD_IN_MSPIKE_H4=-0.01, RCVD_IN_MSPIKE_WL=-0.01, SPF_HELO_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=rhul.onmicrosoft.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id fzlaV2w7alab for <cfrg@ietfa.amsl.com>; Fri,  7 Jul 2017 00:17:46 -0700 (PDT)
Received: from EUR01-HE1-obe.outbound.protection.outlook.com (mail-he1eur01on0066.outbound.protection.outlook.com [104.47.0.66]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id C4B84131A45 for <cfrg@irtf.org>; Fri,  7 Jul 2017 00:17:45 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=rhul.onmicrosoft.com;  s=selector1-rhul-ac-uk; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version; bh=5/Qetdcn8TRY3GToTdKx7dY9VPZIKX+Juo6LNyP/nkc=; b=wWJ8R9CoFBc6zC02qfvqvsWe2gD3vayQILBv8cRNlw629Xf5FgJiT6yswa96Z1oQ//XuzG3hiflXH47LLjium0psaKfH/2LZ1qktDlp9q6Uiv7+Ich+punv1xK838YuRrVpuJCR67wv/0WBWRtoSqvFrDzu8TijHi0/JebkBS1Q=
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com (10.168.2.156) by AM4PR0301MB1906.eurprd03.prod.outlook.com (10.168.2.156) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256) id 15.1.1220.11; Fri, 7 Jul 2017 07:17:43 +0000
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a]) by AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a%14]) with mapi id 15.01.1220.018; Fri, 7 Jul 2017 07:17:42 +0000
From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: "Scott Fluhrer (sfluhrer)" <sfluhrer@cisco.com>, "cfrg@irtf.org" <cfrg@irtf.org>
CC: "David McGrew (mcgrew)" <mcgrew@cisco.com>
Thread-Topic: [Cfrg] Request for a slot to discuss the LMS hash based signatures at Prague
Thread-Index: AQHS9vEfY3kvF7g0tEaqUCtswSOC1Q==
Date: Fri, 7 Jul 2017 07:17:42 +0000
Message-ID: <D584F3F7.981A2%kenny.paterson@rhul.ac.uk>
Accept-Language: en-GB, en-US
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
user-agent: Microsoft-MacOutlook/14.7.1.161129
authentication-results: cisco.com; dkim=none (message not signed) header.d=none;cisco.com; dmarc=none action=none header.from=rhul.ac.uk;
x-originating-ip: [134.219.227.30]
x-ms-publictraffictype: Email
x-microsoft-exchange-diagnostics: 1; AM4PR0301MB1906; 7: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
x-forefront-antispam-report: SFV:SKI; SCL:-1SFV:NSPM; SFS:(10009020)(6009001)(39840400002)(39410400002)(39400400002)(39850400002)(39450400003)(24454002)(74482002)(6506006)(2906002)(6246003)(50986999)(54356999)(6512007)(305945005)(99286003)(7736002)(53936002)(38730400002)(42882006)(36756003)(66066001)(8676002)(8936002)(6306002)(6116002)(2900100001)(2501003)(3280700002)(189998001)(229853002)(478600001)(25786009)(6436002)(3660700001)(72206003)(3846002)(53546010)(102836003)(14454004)(81166006)(83506001)(6486002)(86362001)(4001350100001)(5660300001)(5250100002); DIR:OUT; SFP:1101; SCL:1; SRVR:AM4PR0301MB1906; H:AM4PR0301MB1906.eurprd03.prod.outlook.com; FPR:; SPF:None; MLV:sfv; LANG:en; 
x-ms-office365-filtering-correlation-id: 7204c42a-c2ac-4036-2ff4-08d4c508421c
x-microsoft-antispam: UriScan:; BCL:0; PCL:0; RULEID:(300000500095)(300135000095)(300000501095)(300135300095)(22001)(300000502095)(300135100095)(2017030254075)(300000503095)(300135400095)(2017052603031)(201703131423075)(201703031133081)(300000504095)(300135200095)(300000505095)(300135600095)(300000506095)(300135500095); SRVR:AM4PR0301MB1906; 
x-ms-traffictypediagnostic: AM4PR0301MB1906:
x-microsoft-antispam-prvs: <AM4PR0301MB1906A161D2715D4DA11FB5F9BCAA0@AM4PR0301MB1906.eurprd03.prod.outlook.com>
x-exchange-antispam-report-test: UriScan:(120809045254105)(166708455590820)(236129657087228)(192374486261705)(48057245064654)(95692535739014)(209349559609743);
x-exchange-antispam-report-cfa-test: BCL:0; PCL:0; RULEID:(100000700101)(100105000095)(100000701101)(100105300095)(100000702101)(100105100095)(6040450)(601004)(2401047)(5005006)(2017060910059)(8121501046)(10201501046)(100000703101)(100105400095)(93006095)(93001095)(3002001)(6041248)(20161123562025)(20161123555025)(201703131423075)(201702281528075)(201702281529075)(201703061421075)(201703061406153)(20161123564025)(20161123558100)(20161123560025)(6072148)(100000704101)(100105200095)(100000705101)(100105500095); SRVR:AM4PR0301MB1906; BCL:0; PCL:0; RULEID:(100000800101)(100110000095)(100000801101)(100110300095)(100000802101)(100110100095)(100000803101)(100110400095)(100000804101)(100110200095)(100000805101)(100110500095); SRVR:AM4PR0301MB1906; 
x-forefront-prvs: 0361212EA8
spamdiagnosticoutput: 1:99
spamdiagnosticmetadata: NSPM
Content-Type: text/plain; charset="utf-8"
Content-ID: <50F9CF0F67210D4083ECBA37C553167F@eurprd03.prod.outlook.com>
Content-Transfer-Encoding: base64
MIME-Version: 1.0
X-OriginatorOrg: rhul.ac.uk
X-MS-Exchange-CrossTenant-originalarrivaltime: 07 Jul 2017 07:17:42.5167 (UTC)
X-MS-Exchange-CrossTenant-fromentityheader: Hosted
X-MS-Exchange-CrossTenant-id: 2efd699a-1922-4e69-b601-108008d28a2e
X-MS-Exchange-Transport-CrossTenantHeadersStamped: AM4PR0301MB1906
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/HPQLe3hommPCvEB-YdSsYgwPTbc>
Subject: Re: [Cfrg] Request for a slot to discuss the LMS hash based signatures at Prague
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 07 Jul 2017 07:17:49 -0000
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From nobody Sun Jul  9 09:43:31 2017
Return-Path: <Kenny.Paterson@rhul.ac.uk>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id ABF32129B8B for <cfrg@ietfa.amsl.com>; Sun,  9 Jul 2017 09:43:29 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.92
X-Spam-Level: 
X-Spam-Status: No, score=-1.92 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, RCVD_IN_DNSWL_NONE=-0.0001, RCVD_IN_MSPIKE_H3=-0.01, RCVD_IN_MSPIKE_WL=-0.01, SPF_HELO_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=rhul.onmicrosoft.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id SvG_0u0ef6RB for <cfrg@ietfa.amsl.com>; Sun,  9 Jul 2017 09:43:27 -0700 (PDT)
Received: from EUR03-AM5-obe.outbound.protection.outlook.com (mail-eopbgr30061.outbound.protection.outlook.com [40.107.3.61]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 44D24129B19 for <cfrg@irtf.org>; Sun,  9 Jul 2017 09:43:26 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=rhul.onmicrosoft.com;  s=selector1-rhul-ac-uk; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version; bh=uTTEF4GuQe1ezurxCb6RXFV5gDFedH3exw76DeytYtw=; b=Q/WjrGsryY1XRM2qWhQae1yalaH7u1PKpwhSImT/s5uVQQdeIGUaXWpXxJbliBAoIQThhiOUtBEIRmKwa43UwdJ01A5J6izZbW5UqUwxDm59BY9UpLEzAxFY7EiRxJdgdvmNrUEzGVa+SL5QDasNhwkEAWETiNNq+LylKqKD9Eg=
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com (10.168.2.156) by AM4PR0301MB1907.eurprd03.prod.outlook.com (10.168.3.7) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256) id 15.1.1240.13; Sun, 9 Jul 2017 16:43:24 +0000
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a]) by AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a%14]) with mapi id 15.01.1240.013; Sun, 9 Jul 2017 16:43:22 +0000
From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: Preliminary agenda for CFRG meeting at IETF99
Thread-Index: AQHS+NJ6ey1CJFJrdUOmRvOoeL1R6Q==
Date: Sun, 9 Jul 2017 16:43:22 +0000
Message-ID: <D5881BC7.98535%kenny.paterson@rhul.ac.uk>
Accept-Language: en-GB, en-US
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
user-agent: Microsoft-MacOutlook/14.7.1.161129
authentication-results: irtf.org; dkim=none (message not signed) header.d=none;irtf.org; dmarc=none action=none header.from=rhul.ac.uk;
x-originating-ip: [78.146.77.209]
x-ms-publictraffictype: Email
x-microsoft-exchange-diagnostics: 1; AM4PR0301MB1907; 7: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
x-forefront-antispam-report: SFV:SKI; SCL:-1SFV:NSPM; SFS:(10009020)(6009001)(39840400002)(39410400002)(39400400002)(39450400003)(6916009)(6436002)(3846002)(2501003)(2351001)(42882006)(478600001)(6116002)(102836003)(110136004)(38730400002)(72206003)(6306002)(6512007)(6486002)(6506006)(5250100002)(53936002)(966005)(413944005)(5640700003)(99286003)(36756003)(5660300001)(4001350100001)(3660700001)(54356999)(50986999)(83506001)(305945005)(3280700002)(74482002)(2900100001)(66066001)(14454004)(189998001)(7736002)(86362001)(1730700003)(8936002)(81166006)(25786009)(2906002)(8676002); DIR:OUT; SFP:1101; SCL:1; SRVR:AM4PR0301MB1907; H:AM4PR0301MB1906.eurprd03.prod.outlook.com; FPR:; SPF:None; MLV:sfv; LANG:en; 
x-ms-office365-filtering-correlation-id: b9a50fe7-b3cd-446e-194d-08d4c6e99cfc
x-microsoft-antispam: UriScan:; BCL:0; PCL:0; RULEID:(300000500095)(300135000095)(300000501095)(300135300095)(22001)(300000502095)(300135100095)(2017030254075)(300000503095)(300135400095)(2017052603031)(201703131423075)(201703031133081)(201702281549075)(300000504095)(300135200095)(300000505095)(300135600095)(300000506095)(300135500095); SRVR:AM4PR0301MB1907; 
x-ms-traffictypediagnostic: AM4PR0301MB1907:
x-microsoft-antispam-prvs: <AM4PR0301MB19075529528C5A1DEB8F27C9BCA80@AM4PR0301MB1907.eurprd03.prod.outlook.com>
x-exchange-antispam-report-test: UriScan:(120809045254105)(166708455590820)(236129657087228)(48057245064654)(92977632026198)(167848164394848);
x-exchange-antispam-report-cfa-test: BCL:0; PCL:0; RULEID:(100000700101)(100105000095)(100000701101)(100105300095)(100000702101)(100105100095)(6040450)(601004)(2401047)(5005006)(8121501046)(2017060910075)(3002001)(10201501046)(100000703101)(100105400095)(93006095)(93001095)(6041248)(20161123558100)(20161123564025)(20161123555025)(201703131423075)(201702281528075)(201702281529075)(201703061421075)(201703061406153)(20161123562025)(20161123560025)(6072148)(100000704101)(100105200095)(100000705101)(100105500095); SRVR:AM4PR0301MB1907; BCL:0; PCL:0; RULEID:(100000800101)(100110000095)(100000801101)(100110300095)(100000802101)(100110100095)(100000803101)(100110400095)(100000804101)(100110200095)(100000805101)(100110500095); SRVR:AM4PR0301MB1907; 
x-forefront-prvs: 03630A6A4A
spamdiagnosticoutput: 1:99
spamdiagnosticmetadata: NSPM
Content-Type: text/plain; charset="utf-8"
Content-ID: <B17DEDD4AC47BF499CE767D39C2EFB66@eurprd03.prod.outlook.com>
Content-Transfer-Encoding: base64
MIME-Version: 1.0
X-OriginatorOrg: rhul.ac.uk
X-MS-Exchange-CrossTenant-originalarrivaltime: 09 Jul 2017 16:43:22.8435 (UTC)
X-MS-Exchange-CrossTenant-fromentityheader: Hosted
X-MS-Exchange-CrossTenant-id: 2efd699a-1922-4e69-b601-108008d28a2e
X-MS-Exchange-Transport-CrossTenantHeadersStamped: AM4PR0301MB1907
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/GYz4JI_U9t_xa-HIsrBaIWfI204>
Subject: [Cfrg] Preliminary agenda for CFRG meeting at IETF99
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Sun, 09 Jul 2017 16:43:30 -0000
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From nobody Tue Jul 11 03:29:14 2017
Return-Path: <brynosaurus@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id E3AE2127180 for <cfrg@ietfa.amsl.com>; Tue, 11 Jul 2017 03:29:12 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.998
X-Spam-Level: 
X-Spam-Status: No, score=-1.998 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id p4C7kz7BKTJe for <cfrg@ietfa.amsl.com>; Tue, 11 Jul 2017 03:29:09 -0700 (PDT)
Received: from mail-wr0-x22b.google.com (mail-wr0-x22b.google.com [IPv6:2a00:1450:400c:c0c::22b]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 37931126BF3 for <cfrg@irtf.org>; Tue, 11 Jul 2017 03:29:09 -0700 (PDT)
Received: by mail-wr0-x22b.google.com with SMTP id r103so177163248wrb.0 for <cfrg@irtf.org>; Tue, 11 Jul 2017 03:29:09 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=from:message-id:mime-version:subject:date:in-reply-to:cc:to :references; bh=hLuXhCzKolEQJ9MHcVVkQgaMYT7HDH+7lhH2CnDPDXw=; b=Q52+X0MO2fICPPkLAm4Ykty2kjFHZEqMoJnQw4yaHtDO3NbKLORwtAnYbXxHEsWIHU 9GfS/xhs+//ESWJENX5+dCYnN44FUmuJx2hEeNxXm4kvp7hNQgs9TiI1JOL5C7cjuAcj pkwVPLs19t4QLBZhrpxOeUcHNFEqqVjzwgeUjxPCzYU5KIrF/fQT+wQRCni0abABeaPR +n5su7O6HIAVRVcDqaaoiSjx92FKJbgg8rYu69YhTbvyu1zoU5LCMNzcPEQZjAkekvew wUNSUWwCjoS3t8960tX2t7Hu4QESNSdZiK1t58uEZpan18lZM2PLSVbk//4v4R36ljmT /Z2A==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:from:message-id:mime-version:subject:date :in-reply-to:cc:to:references; bh=hLuXhCzKolEQJ9MHcVVkQgaMYT7HDH+7lhH2CnDPDXw=; b=KGcNotF9XjZq7SI6xciwDtLGJgOzAv3KkROPXCHgRFbCqV26Us3f4nDdsI62DlVrgG w8ARAQ/ryGh8THFUNWu+42hUssUT2AHD6J84y4GILXk9E+Gb++oiWct7rcHYpzXva9MW /MoOPLyvAuQz8GHnXWZXJDU4Ird8ZCbzp51BjxNx4+LcktPCXWxm1oXO8Y0KFHDBNCGN 7xIo9mmLG2s/wzT+RAtauBeHsyJnoiuR3eOyGCEedXNKnl5sJlHkSITf0dlQ8KDyJ8I7 4vgPuPhxw8qQNV/G9j11ZDy2k3AUnGUhAk/6ovHFhKkX7lOR+DrUPG3tY2SiPTDG/cQ+ MzIw==
X-Gm-Message-State: AIVw111TIxwq0XXUAS7sY2mX9Ypc5EUuNTU71qYlrCBVt/mCMv62/CaC CAHkILvwcZB9mXpw24g=
X-Received: by 10.80.183.98 with SMTP id g89mr2002621ede.105.1499768947538; Tue, 11 Jul 2017 03:29:07 -0700 (PDT)
Received: from [172.20.10.2] (78.227.197.178.dynamic.wless.zhbmb00p-cgnat.res.cust.swisscom.ch. [178.197.227.78]) by smtp.gmail.com with ESMTPSA id h18sm777749eda.46.2017.07.11.03.29.04 (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Tue, 11 Jul 2017 03:29:04 -0700 (PDT)
From: Bryan Ford <brynosaurus@gmail.com>
Message-Id: <870B4583-2FF4-4B5F-A19C-5D39FA81559B@gmail.com>
Content-Type: multipart/signed; boundary="Apple-Mail=_4D1010BB-2068-406E-BB75-7089D31ED14A"; protocol="application/pgp-signature"; micalg=pgp-sha256
Mime-Version: 1.0 (Mac OS X Mail 10.3 \(3273\))
Date: Tue, 11 Jul 2017 12:29:02 +0200
In-Reply-To: <1e0faffa-370c-bf81-4973-55bfd36de510@tugraz.at>
Cc: Philipp Jovanovic <philipp@jovanovic.io>, cfrg@irtf.org
To: Daniel Slamanig <daniel.slamanig@tugraz.at>
References: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io> <11cc5d3f-ecf9-2fd0-825c-c8b441bd2813@tugraz.at> <A423CB6E-D649-4320-BB76-2E3783D6AFE0@gmail.com> <1e0faffa-370c-bf81-4973-55bfd36de510@tugraz.at>
X-Mailer: Apple Mail (2.3273)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/qzQ2Fw1QgexmBs1tePhgCPYL-YA>
Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Tue, 11 Jul 2017 10:29:13 -0000

--Apple-Mail=_4D1010BB-2068-406E-BB75-7089D31ED14A
Content-Type: multipart/alternative;
	boundary="Apple-Mail=_7B1AD11C-2390-4290-A1A2-EAFEAE3244C8"


--Apple-Mail=_7B1AD11C-2390-4290-A1A2-EAFEAE3244C8
Content-Transfer-Encoding: quoted-printable
Content-Type: text/plain;
	charset=utf-8

Hi Daniel, sorry about the slow followup=E2=80=A6

> On Jul 6, 2017, at 10:34 AM, Daniel Slamanig =
<daniel.slamanig@tugraz.at> wrote:
> Another observation regarding committing to the bitmask Z. If you do =
not commit to the bitmask Z, then users could cooperate in setting up =
their public keys, lets say A_i and A_j cooperate. Then one of them =
could take part in the signing, but in the end one could use the attack =
with the rogue keys outlined in my initial mail so that A_j can claim =
that he took part in the signing process although A_i actually took =
part. As far as I see not even using a delinearization scheme would help =
here. Nevertheless, it seems to me that this is not a valid attack =
vector when I look at the paper (but as you do not formally specify a =
security model for your approach in the paper this is hard to tell).

Correct - when two users A_i and A_j collude in such fashion, we just =
count both of them as =E2=80=9Cmalicious=E2=80=9D in our threat model.  =
In practice, if two nodes want to collude in this way, there are easier =
attacks that have nothing to do with collective signing but would work =
equally well with the =E2=80=9Cbase-case=E2=80=9D approach of collecting =
a bunch of individual signatures.  For example, A_i simply uses A_j=E2=80=99=
s private key (which A_j shares with A_i because they=E2=80=99re =
colluding) to pretend to be A_j and sign on A_j=E2=80=99s behalf, =
individually or collectively.  Or vice versa.

> Note that such an attack would even work if users have to register the =
public keys and prove that they know the secret key corresponding to the =
public key, e.g., via a (NI)ZK proof of the secret key - which I have =
seen is mentioned in the paper, but not discussed in the draft. Summing =
up, without commiting to Z in the signature, you would trivially not be =
able to achieve strong EUF-CMA security of the multi-signature due to =
the malleability, but as far as I see standard EUF-CMA should still hold =
(which seems sufficient for your application).

Agreed.  The critical question is then whether to prioritize strict =
non-malleability, or to allow just enough malleability to allow for =
stronger protection against DoS attacks.  The tradeoff is subtle and the =
ideal balance is not clear to me at least.

Cheers
Bryan

> Thanks and cheers,
> Daniel
>=20
> On 05.07.2017 15:11, Bryan Ford wrote:
>> Hi Daniel, thanks for your thoughts on the commitment-to-the-bitmask =
issue.
>> Your proposal of using a chameleon hash, to allow the leader to =
=E2=80=9Cadjust=E2=80=9D the bit mask after the commit c has been =
established, is an interesting idea. However, if I understand it =
correctly, if the leader holds the trapdoor key for the chameleon hash, =
wouldn=E2=80=99t that still make the final collective signature =
malleable for the leader (or for anyone the leader=E2=80=99s trapdoor =
key might leak to)?  The CoSi protocol as currently defined is intended =
to ensure that the leader has no special privilege or trust with respect =
to other cosigners: i.e., the leader is merely an ordinary participant, =
but is simply the one who for whatever reason decides to initiate the =
cosigning operation.  Giving the leader special powers - e.g., making =
the signature malleable to the leader but not to others - would break =
this principle and need to be extremely carefully considered I think.
>> To follow up on my last message to Oleg, again I suggest reading =
section IV of our CoSi paper from IEEE S&P last year =
(http://dedis.cs.yale.edu/dissent/papers/witness-abs), as it discusses =
several related issues, especially the potential desire to allow the =
leader to complete a collective signing procedure even with only a =
subset of =E2=80=9Ccommitted=E2=80=9D participants remaining present in =
the =E2=80=9Cresponse=E2=80=9D phase.  In particular, the leader can =
form all the individual Schnorr commits into a Merkle tree, and make the =
real commit c be the root of that Merkle tree.  In this way, the leader =
is committing not so much to a particular collective Schnorr commit but =
rather to *all possible* Schnorr commits that can be composed from any =
subset of the individual Schnorr commits within that Merkle tree.  This =
way, if some of the participants whose commits are present in that =
Merkle tree remain available during the response phase but others drop =
out, the leader can still use the commit c and form a correct and =
verifiable collective signature against the particular subset of Schnorr =
commits from nodes that remained available throughout the process, =
without restarting.
>> I guess this approach does, in a slightly different way, make the =
resulting collective signatures slightly malleable to the leader: from a =
given set of commit-time and response-time information, the leader could =
put together distinct collective signatures representing different =
subsets of response-time participants.  Some form of =
=E2=80=9Cleader-malleability=E2=80=9D of this kind seems unavoidably =
essential to enabling the leader to complete a collective signing round =
in the presence of partial failures without restarting.  Perhaps the =
same limited leader-malleability is more-or-less the same property your =
suggestion of using chameleon hashes has, although I haven=E2=80=99t had =
a chance to compare them deeply yet.
>> But at any rate, the higher-level tradeoff here to consider is =
whether it=E2=80=99s better to (a) enforce strict non-malleability of =
collective signatures (by anyone, leader included), at the cost of =
O(N)-round DoS attack vulnerability during signing due to the need to =
restart partially failed rounds, or (b) provide some limited form of =
limited leader-malleability in order to support restart-free operation =
and avoid DoS attacks during signing, at the cost of a more complex =
protocol (and perhaps slightly more =E2=80=9Cspecial=E2=80=9D trust in =
the leader than we might like).
>> Again, further thoughts on this and other topics are most welcome.
>> Thanks
>> Bryan
>>> On Jul 3, 2017, at 7:34 PM, Daniel Slamanig =
<daniel.slamanig@tugraz.at <mailto:daniel.slamanig@tugraz.at> =
<mailto:daniel.slamanig@tugraz.at <mailto:daniel.slamanig@tugraz.at>>> =
wrote:
>>>=20
>>> Hi Philipp,
>>>=20
>>> looks interesting!
>>>=20
>>> After looking at the protocol I also have some security concerns =
(related to what has been raised by Oleg in a previous mail).
>>>=20
>>> Not committing to Z as well as the actual sum of signers public keys =
A' in the computation of the hash c for the signature seems to be =
problematic.
>>>=20
>>> It seems to me that committing Z in the signature in plain as well =
as A' does not work given the later application of the signing procedure =
(where till the end of the protocol it is not clear who actually =
participates in the signing but c must be known at the beginning).
>>>=20
>>> Committing to neither of both however seems problematic as it does =
not fix the set of actual signers.
>>>=20
>>> This could be circumvented by allowing an honest leader to adapt the =
commitment to the final Z (and A') after it knows the signers without =
modifying the initially computed c using a chameleon hash (trapdoor =
commitment). I use P as a generator below, omit the brackets [a]P =
notation for scalar multiplication and write it from the perspective of =
the leader, i.e., the signer that initiates the protocol.
>>>=20
>>> The leader could choose chameleon hash parameters sk_ch=3Dy for =
random y and pk_ch=3D(P,Y=3DyP) and add pk_ch and chameleon hash =
CH(Z'):=3Dh(Z')P+u'Y for randomly chosen u' to the computation of c, =
i.e., set c=3DH(R||A||pk_ch||CH(Z')||S), where h() is a collision =
resistant hash function (this is just the standard way of constructing a =
chameleon hash from DL for arbitrary message spaces as propsed in [1]). =
If Z' is not yet known one simply sets Z' to some fixed string at the =
beginning, e.g., Z':=3D0. At the end of the protocol, when the leader =
knows the exact signers, it can update Z' to the final value Z and use =
sk_ch to compute a collision in the chameleon hash, i.e., such that =
CH(Z)=3DCH(Z') by solving h(Z')+u'y =3D h(Z)+uy for u. He then adds u =
and Z as well as pk_ch to the signature, i.e., sets it as =
(R,s,u,Z,pk_ch) and discards sk_ch and u'. If Z is known beforehand, one =
simply computes the chameleon hash once and does not need to compute a =
collision. Clearly, the use of a chameleon hash allows to simply adapt =
to the actual set of signers representing Z without modifying c (with =
the knowledge of sk_ch - but it does not work without the knowledge of =
sk_ch). This would resolve the issue with the unknown Z at the time of =
signing.
>>>=20
>>> Also, A is committed in the signature, but not the concrete A'=3D\sum =
A_i of keys used for computing the signature (I guess also due to the =
reason that one does not know the correct set of signers when computing =
the hash c). That can be problematic in a rogue key scenario in the =
current protocol, i.e., when not all signers need to prove knowledge of =
the secret key when they register their public keys but their public =
keys could be functions of other public keys (guess this could be a =
problem here). For instance, a malicious A^* could just take some key =
from A, say A_j, and compute and publish A^*=3Da^*A_j. And then given a =
collective signature (R,s,Z) where A_j participated, the signer can =
update s to s^* =3D s+a^*c as well as Z^* to exclude A_j and include A^* =
(as Z is not committed in the signature generation) and the signature =
(R,s^*,Z^*) will be a valid signature that certifies that A^* =
participated in signing - although he didn't.
>>>=20
>>> If Z is committed as proposed above and it is checked during the =
verification, then this should no longer work. One could also adapt the =
hash c=3DH(R||pk_ch||CH(Z'||A)||S) to include a chameleon hash to =
CH(Z||A'), where A' is the real set of signers that participated in the =
signature generation and is adapted before finalizing the signature when =
known as above.
>>>=20
>>> I hope that what I proposed is not just complete nonsense :) Also it =
produces quite a bit of an overhead. There may also be easier ways to =
avoid the issues.
>>>=20
>>> Some editorial issues: the message to be signed is sometimes called =
a satement S and later then message msg. S could be confusing as part of =
the signature is s and your semantic is that scalars are lowercase and =
points are uppercase. Also in 4.2 "Signature Generation" steps 2 and 3 =
are confusing as I guess that in the protocol all the signer compute =
their own [r_i]B values and R=3D\sum R_i instead of R=3D[r]B which would =
mean that they would send their r_i's (hope they will not do so).
>>>=20
>>> Also I find it somewhat confusing that the bitmask Z identifies the =
non-signers with a bit set to 1. Why not identifying the signers with a =
bit set to 1?
>>>=20
>>> Cheers,
>>> Daniel
>>>=20
>>>=20
>>> [1] Hugo Krawczyk, Tal Rabin: Chameleon Signatures. NDSS 2000
>>>=20
>>> On 01.07.2017 23:58, Philipp Jovanovic wrote:
>>>> Hi CFRG,
>>>> Here=E2=80=99s a first version of an Internet-Draft on =
=E2=80=9CCollective Edwards-Curve Digital Signature Algorithms=E2=80=9D =
based on Ed25519 and Ed448: =
https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/ =
<https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/>
>>>> We plan to give a short presentation on that topic at the next CFRG =
meeting in Prague.
>>>> Any feedback is more than welcome. Thanks!
>>>> All the best,
>>>> Philipp
>>>> _______________________________________________
>>>> Cfrg mailing list
>>>> Cfrg@irtf.org <mailto:Cfrg@irtf.org> <mailto:Cfrg@irtf.org =
<mailto:Cfrg@irtf.org>>
>>>> https://www.irtf.org/mailman/listinfo/cfrg =
<https://www.irtf.org/mailman/listinfo/cfrg>
>>>=20
>>>=20
>>> --
>>> Dr. Daniel Slamanig
>>> Institute for Applied Information Processing and Communications
>>> Graz University of Technology
>>> Inffeldgasse 16a, 8010 Graz, Austria.
>>> Phone: +43 316 873 5509
>>> http://www.iaik.tugraz.at <http://www.iaik.tugraz.at/>
>>>=20
>>> _______________________________________________
>>> Cfrg mailing list
>>> Cfrg@irtf.org <mailto:Cfrg@irtf.org>
>>> https://www.irtf.org/mailman/listinfo/cfrg =
<https://www.irtf.org/mailman/listinfo/cfrg>
>=20
>=20
> --
> Dr. Daniel Slamanig
> Institute for Applied Information Processing and Communications
> Graz University of Technology
> Inffeldgasse 16a, 8010 Graz, Austria.
> Phone: +43 316 873 5509
> http://www.iaik.tugraz.at <http://www.iaik.tugraz.at/>

--Apple-Mail=_7B1AD11C-2390-4290-A1A2-EAFEAE3244C8
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html;
	charset=utf-8

<html><head><meta http-equiv=3D"Content-Type" content=3D"text/html =
charset=3Dutf-8"></head><body style=3D"word-wrap: break-word; =
-webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" =
class=3D"">Hi Daniel, sorry about the slow followup=E2=80=A6<div =
class=3D""><br class=3D""></div><div class=3D""><div><blockquote =
type=3D"cite" class=3D""><div class=3D"">On Jul 6, 2017, at 10:34 AM, =
Daniel Slamanig &lt;<a href=3D"mailto:daniel.slamanig@tugraz.at" =
class=3D"">daniel.slamanig@tugraz.at</a>&gt; wrote:</div><div =
class=3D""><span style=3D"font-family: Helvetica; font-size: 11px; =
font-style: normal; font-variant-caps: normal; font-weight: normal; =
letter-spacing: normal; text-align: start; text-indent: 0px; =
text-transform: none; white-space: normal; word-spacing: 0px; =
-webkit-text-stroke-width: 0px; float: none; display: inline =
!important;" class=3D"">Another observation regarding committing to the =
bitmask Z. If you do not commit to the bitmask Z, then users could =
cooperate in setting up their public keys, lets say A_i and A_j =
cooperate. Then one of them could take part in the signing, but in the =
end one could use the attack with the rogue keys outlined in my initial =
mail so that A_j can claim that he took part in the signing process =
although A_i actually took part. As far as I see not even using a =
delinearization scheme would help here. Nevertheless, it seems to me =
that this is not a valid attack vector when I look at the paper (but as =
you do not formally specify a security model for your approach in the =
paper this is hard to tell). </span></div></blockquote><div><br =
class=3D""></div><div>Correct - when two users A_i and A_j collude in =
such fashion, we just count both of them as =E2=80=9Cmalicious=E2=80=9D =
in our threat model. &nbsp;In practice, if two nodes want to collude in =
this way, there are easier attacks that have nothing to do with =
collective signing but would work equally well with the =E2=80=9Cbase-case=
=E2=80=9D approach of collecting a bunch of individual signatures. =
&nbsp;For example, A_i simply uses A_j=E2=80=99s private key (which A_j =
shares with A_i because they=E2=80=99re colluding) to pretend to be A_j =
and sign on A_j=E2=80=99s behalf, individually or collectively. &nbsp;Or =
vice versa.</div><br class=3D""><blockquote type=3D"cite" class=3D""><div =
class=3D""><span style=3D"font-family: Helvetica; font-size: 11px; =
font-style: normal; font-variant-caps: normal; font-weight: normal; =
letter-spacing: normal; text-align: start; text-indent: 0px; =
text-transform: none; white-space: normal; word-spacing: 0px; =
-webkit-text-stroke-width: 0px; float: none; display: inline =
!important;" class=3D"">Note that such an attack would even work if =
users have to register the public keys and prove that they know the =
secret key corresponding to the public key, e.g., via a (NI)ZK proof of =
the secret key - which I have seen is mentioned in the paper, but not =
discussed in the draft. Summing up, without commiting to Z in the =
signature, you would trivially not be able to achieve strong EUF-CMA =
security of the multi-signature due to the malleability, but as far as I =
see standard EUF-CMA should still hold (which seems sufficient for your =
application).</span><br style=3D"font-family: Helvetica; font-size: =
11px; font-style: normal; font-variant-caps: normal; font-weight: =
normal; letter-spacing: normal; text-align: start; text-indent: 0px; =
text-transform: none; white-space: normal; word-spacing: 0px; =
-webkit-text-stroke-width: 0px;" class=3D""></div></blockquote><div><br =
class=3D""></div><div>Agreed. &nbsp;The critical question is then =
whether to prioritize strict non-malleability, or to allow just enough =
malleability to allow for stronger protection against DoS attacks. =
&nbsp;The tradeoff is subtle and the ideal balance is not clear to me at =
least.</div><div><br class=3D""></div><div>Cheers</div><div>Bryan</div><br=
 class=3D""><blockquote type=3D"cite" class=3D""><div class=3D""><span =
style=3D"font-family: Helvetica; font-size: 11px; font-style: normal; =
font-variant-caps: normal; font-weight: normal; letter-spacing: normal; =
text-align: start; text-indent: 0px; text-transform: none; white-space: =
normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; =
display: inline !important;" class=3D"">Thanks and cheers,</span><br =
style=3D"font-family: Helvetica; font-size: 11px; font-style: normal; =
font-variant-caps: normal; font-weight: normal; letter-spacing: normal; =
text-align: start; text-indent: 0px; text-transform: none; white-space: =
normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" =
class=3D""><span style=3D"font-family: Helvetica; font-size: 11px; =
font-style: normal; font-variant-caps: normal; font-weight: normal; =
letter-spacing: normal; text-align: start; text-indent: 0px; =
text-transform: none; white-space: normal; word-spacing: 0px; =
-webkit-text-stroke-width: 0px; float: none; display: inline =
!important;" class=3D"">Daniel</span><br style=3D"font-family: =
Helvetica; font-size: 11px; font-style: normal; font-variant-caps: =
normal; font-weight: normal; letter-spacing: normal; text-align: start; =
text-indent: 0px; text-transform: none; white-space: normal; =
word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=3D""><br =
style=3D"font-family: Helvetica; font-size: 11px; font-style: normal; =
font-variant-caps: normal; font-weight: normal; letter-spacing: normal; =
text-align: start; text-indent: 0px; text-transform: none; white-space: =
normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" =
class=3D""><span style=3D"font-family: Helvetica; font-size: 11px; =
font-style: normal; font-variant-caps: normal; font-weight: normal; =
letter-spacing: normal; text-align: start; text-indent: 0px; =
text-transform: none; white-space: normal; word-spacing: 0px; =
-webkit-text-stroke-width: 0px; float: none; display: inline =
!important;" class=3D"">On 05.07.2017 15:11, Bryan Ford wrote:</span><br =
style=3D"font-family: Helvetica; font-size: 11px; font-style: normal; =
font-variant-caps: normal; font-weight: normal; letter-spacing: normal; =
text-align: start; text-indent: 0px; text-transform: none; white-space: =
normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" =
class=3D""><blockquote type=3D"cite" style=3D"font-family: Helvetica; =
font-size: 11px; font-style: normal; font-variant-caps: normal; =
font-weight: normal; letter-spacing: normal; orphans: auto; text-align: =
start; text-indent: 0px; text-transform: none; white-space: normal; =
widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; =
-webkit-text-stroke-width: 0px;" class=3D"">Hi Daniel, thanks for your =
thoughts on the commitment-to-the-bitmask issue.<br class=3D"">Your =
proposal of using a chameleon hash, to allow the leader to =E2=80=9Cadjust=
=E2=80=9D the bit mask after the commit c has been established, is an =
interesting idea. However, if I understand it correctly, if the leader =
holds the trapdoor key for the chameleon hash, wouldn=E2=80=99t that =
still make the final collective signature malleable for the leader (or =
for anyone the leader=E2=80=99s trapdoor key might leak to)? &nbsp;The =
CoSi protocol as currently defined is intended to ensure that the leader =
has no special privilege or trust with respect to other cosigners: i.e., =
the leader is merely an ordinary participant, but is simply the one who =
for whatever reason decides to initiate the cosigning operation. =
&nbsp;Giving the leader special powers - e.g., making the signature =
malleable to the leader but not to others - would break this principle =
and need to be extremely carefully considered I think.<br class=3D"">To =
follow up on my last message to Oleg, again I suggest reading section IV =
of our CoSi paper from IEEE S&amp;P last year (<a =
href=3D"http://dedis.cs.yale.edu/dissent/papers/witness-abs" =
class=3D"">http://dedis.cs.yale.edu/dissent/papers/witness-abs</a>), as =
it discusses several related issues, especially the potential desire to =
allow the leader to complete a collective signing procedure even with =
only a subset of =E2=80=9Ccommitted=E2=80=9D participants remaining =
present in the =E2=80=9Cresponse=E2=80=9D phase. &nbsp;In particular, =
the leader can form all the individual Schnorr commits into a Merkle =
tree, and make the real commit c be the root of that Merkle tree. =
&nbsp;In this way, the leader is committing not so much to a particular =
collective Schnorr commit but rather to *all possible* Schnorr commits =
that can be composed from any subset of the individual Schnorr commits =
within that Merkle tree. &nbsp;This way, if some of the participants =
whose commits are present in that Merkle tree remain available during =
the response phase but others drop out, the leader can still use the =
commit c and form a correct and verifiable collective signature against =
the particular subset of Schnorr commits from nodes that remained =
available throughout the process, without restarting.<br class=3D"">I =
guess this approach does, in a slightly different way, make the =
resulting collective signatures slightly malleable to the leader: from a =
given set of commit-time and response-time information, the leader could =
put together distinct collective signatures representing different =
subsets of response-time participants. &nbsp;Some form of =
=E2=80=9Cleader-malleability=E2=80=9D of this kind seems unavoidably =
essential to enabling the leader to complete a collective signing round =
in the presence of partial failures without restarting. &nbsp;Perhaps =
the same limited leader-malleability is more-or-less the same property =
your suggestion of using chameleon hashes has, although I haven=E2=80=99t =
had a chance to compare them deeply yet.<br class=3D"">But at any rate, =
the higher-level tradeoff here to consider is whether it=E2=80=99s =
better to (a) enforce strict non-malleability of collective signatures =
(by anyone, leader included), at the cost of O(N)-round DoS attack =
vulnerability during signing due to the need to restart partially failed =
rounds, or (b) provide some limited form of limited leader-malleability =
in order to support restart-free operation and avoid DoS attacks during =
signing, at the cost of a more complex protocol (and perhaps slightly =
more =E2=80=9Cspecial=E2=80=9D trust in the leader than we might =
like).<br class=3D"">Again, further thoughts on this and other topics =
are most welcome.<br class=3D"">Thanks<br class=3D"">Bryan<br =
class=3D""><blockquote type=3D"cite" class=3D"">On Jul 3, 2017, at 7:34 =
PM, Daniel Slamanig &lt;<a href=3D"mailto:daniel.slamanig@tugraz.at" =
class=3D"">daniel.slamanig@tugraz.at</a><span =
class=3D"Apple-converted-space">&nbsp;</span>&lt;<a =
href=3D"mailto:daniel.slamanig@tugraz.at" =
class=3D"">mailto:daniel.slamanig@tugraz.at</a>&gt;&gt; wrote:<br =
class=3D""><br class=3D"">Hi Philipp,<br class=3D""><br class=3D"">looks =
interesting!<br class=3D""><br class=3D"">After looking at the protocol =
I also have some security concerns (related to what has been raised by =
Oleg in a previous mail).<br class=3D""><br class=3D"">Not committing to =
Z as well as the actual sum of signers public keys A' in the computation =
of the hash c for the signature seems to be problematic.<br class=3D""><br=
 class=3D"">It seems to me that committing Z in the signature in plain =
as well as A' does not work given the later application of the signing =
procedure (where till the end of the protocol it is not clear who =
actually participates in the signing but c must be known at the =
beginning).<br class=3D""><br class=3D"">Committing to neither of both =
however seems problematic as it does not fix the set of actual =
signers.<br class=3D""><br class=3D"">This could be circumvented by =
allowing an honest leader to adapt the commitment to the final Z (and =
A') after it knows the signers without modifying the initially computed =
c using a chameleon hash (trapdoor commitment). I use P as a generator =
below, omit the brackets [a]P notation for scalar multiplication and =
write it from the perspective of the leader, i.e., the signer that =
initiates the protocol.<br class=3D""><br class=3D"">The leader could =
choose chameleon hash parameters sk_ch=3Dy for random y and =
pk_ch=3D(P,Y=3DyP) and add pk_ch and chameleon hash CH(Z'):=3Dh(Z')P+u'Y =
for randomly chosen u' to the computation of c, i.e., set =
c=3DH(R||A||pk_ch||CH(Z')||S), where h() is a collision resistant hash =
function (this is just the standard way of constructing a chameleon hash =
from DL for arbitrary message spaces as propsed in [1]). If Z' is not =
yet known one simply sets Z' to some fixed string at the beginning, =
e.g., Z':=3D0. At the end of the protocol, when the leader knows the =
exact signers, it can update Z' to the final value Z and use sk_ch to =
compute a collision in the chameleon hash, i.e., such that CH(Z)=3DCH(Z') =
by solving h(Z')+u'y =3D h(Z)+uy for u. He then adds u and Z as well as =
pk_ch to the signature, i.e., sets it as (R,s,u,Z,pk_ch) and discards =
sk_ch and u'. If Z is known beforehand, one simply computes the =
chameleon hash once and does not need to compute a collision. Clearly, =
the use of a chameleon hash allows to simply adapt to the actual set of =
signers representing Z without modifying c (with the knowledge of sk_ch =
- but it does not work without the knowledge of sk_ch). This would =
resolve the issue with the unknown Z at the time of signing.<br =
class=3D""><br class=3D"">Also, A is committed in the signature, but not =
the concrete A'=3D\sum A_i of keys used for computing the signature (I =
guess also due to the reason that one does not know the correct set of =
signers when computing the hash c). That can be problematic in a rogue =
key scenario in the current protocol, i.e., when not all signers need to =
prove knowledge of the secret key when they register their public keys =
but their public keys could be functions of other public keys (guess =
this could be a problem here). For instance, a malicious A^* could just =
take some key from A, say A_j, and compute and publish A^*=3Da^*A_j. And =
then given a collective signature (R,s,Z) where A_j participated, the =
signer can update s to s^* =3D s+a^*c as well as Z^* to exclude A_j and =
include A^* (as Z is not committed in the signature generation) and the =
signature (R,s^*,Z^*) will be a valid signature that certifies that A^* =
participated in signing - although he didn't.<br class=3D""><br =
class=3D"">If Z is committed as proposed above and it is checked during =
the verification, then this should no longer work. One could also adapt =
the hash c=3DH(R||pk_ch||CH(Z'||A)||S) to include a chameleon hash to =
CH(Z||A'), where A' is the real set of signers that participated in the =
signature generation and is adapted before finalizing the signature when =
known as above.<br class=3D""><br class=3D"">I hope that what I proposed =
is not just complete nonsense :) Also it produces quite a bit of an =
overhead. There may also be easier ways to avoid the issues.<br =
class=3D""><br class=3D"">Some editorial issues: the message to be =
signed is sometimes called a satement S and later then message msg. S =
could be confusing as part of the signature is s and your semantic is =
that scalars are lowercase and points are uppercase. Also in 4.2 =
"Signature Generation" steps 2 and 3 are confusing as I guess that in =
the protocol all the signer compute their own [r_i]B values and R=3D\sum =
R_i instead of R=3D[r]B which would mean that they would send their =
r_i's (hope they will not do so).<br class=3D""><br class=3D"">Also I =
find it somewhat confusing that the bitmask Z identifies the non-signers =
with a bit set to 1. Why not identifying the signers with a bit set to =
1?<br class=3D""><br class=3D"">Cheers,<br class=3D"">Daniel<br =
class=3D""><br class=3D""><br class=3D"">[1] Hugo Krawczyk, Tal Rabin: =
Chameleon Signatures. NDSS 2000<br class=3D""><br class=3D"">On =
01.07.2017 23:58, Philipp Jovanovic wrote:<br class=3D""><blockquote =
type=3D"cite" class=3D"">Hi CFRG,<br class=3D"">Here=E2=80=99s a first =
version of an Internet-Draft on =E2=80=9CCollective Edwards-Curve =
Digital Signature Algorithms=E2=80=9D based on Ed25519 and Ed448:<span =
class=3D"Apple-converted-space">&nbsp;</span><a =
href=3D"https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/" =
class=3D"">https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/</a><br =
class=3D"">We plan to give a short presentation on that topic at the =
next CFRG meeting in Prague.<br class=3D"">Any feedback is more than =
welcome. Thanks!<br class=3D"">All the best,<br class=3D"">Philipp<br =
class=3D"">_______________________________________________<br =
class=3D"">Cfrg mailing list<br class=3D""><a =
href=3D"mailto:Cfrg@irtf.org" class=3D"">Cfrg@irtf.org</a><span =
class=3D"Apple-converted-space">&nbsp;</span>&lt;<a =
href=3D"mailto:Cfrg@irtf.org" class=3D"">mailto:Cfrg@irtf.org</a>&gt;<br =
class=3D""><a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" =
class=3D"">https://www.irtf.org/mailman/listinfo/cfrg</a><br =
class=3D""></blockquote><br class=3D""><br class=3D"">--<br class=3D"">Dr.=
 Daniel Slamanig<br class=3D"">Institute for Applied Information =
Processing and Communications<br class=3D"">Graz University of =
Technology<br class=3D"">Inffeldgasse 16a, 8010 Graz, Austria.<br =
class=3D"">Phone: +43 316 873 5509<br class=3D""><a =
href=3D"http://www.iaik.tugraz.at/" =
class=3D"">http://www.iaik.tugraz.at</a><br class=3D""><br =
class=3D"">_______________________________________________<br =
class=3D"">Cfrg mailing list<br class=3D""><a =
href=3D"mailto:Cfrg@irtf.org" class=3D"">Cfrg@irtf.org</a><br =
class=3D""><a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" =
class=3D"">https://www.irtf.org/mailman/listinfo/cfrg</a><br =
class=3D""></blockquote></blockquote><br style=3D"font-family: =
Helvetica; font-size: 11px; font-style: normal; font-variant-caps: =
normal; font-weight: normal; letter-spacing: normal; text-align: start; =
text-indent: 0px; text-transform: none; white-space: normal; =
word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=3D""><br =
style=3D"font-family: Helvetica; font-size: 11px; font-style: normal; =
font-variant-caps: normal; font-weight: normal; letter-spacing: normal; =
text-align: start; text-indent: 0px; text-transform: none; white-space: =
normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" =
class=3D""><span style=3D"font-family: Helvetica; font-size: 11px; =
font-style: normal; font-variant-caps: normal; font-weight: normal; =
letter-spacing: normal; text-align: start; text-indent: 0px; =
text-transform: none; white-space: normal; word-spacing: 0px; =
-webkit-text-stroke-width: 0px; float: none; display: inline =
!important;" class=3D"">--</span><br style=3D"font-family: Helvetica; =
font-size: 11px; font-style: normal; font-variant-caps: normal; =
font-weight: normal; letter-spacing: normal; text-align: start; =
text-indent: 0px; text-transform: none; white-space: normal; =
word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=3D""><span =
style=3D"font-family: Helvetica; font-size: 11px; font-style: normal; =
font-variant-caps: normal; font-weight: normal; letter-spacing: normal; =
text-align: start; text-indent: 0px; text-transform: none; white-space: =
normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; =
display: inline !important;" class=3D"">Dr. Daniel Slamanig</span><br =
style=3D"font-family: Helvetica; font-size: 11px; font-style: normal; =
font-variant-caps: normal; font-weight: normal; letter-spacing: normal; =
text-align: start; text-indent: 0px; text-transform: none; white-space: =
normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" =
class=3D""><span style=3D"font-family: Helvetica; font-size: 11px; =
font-style: normal; font-variant-caps: normal; font-weight: normal; =
letter-spacing: normal; text-align: start; text-indent: 0px; =
text-transform: none; white-space: normal; word-spacing: 0px; =
-webkit-text-stroke-width: 0px; float: none; display: inline =
!important;" class=3D"">Institute for Applied Information Processing and =
Communications</span><br style=3D"font-family: Helvetica; font-size: =
11px; font-style: normal; font-variant-caps: normal; font-weight: =
normal; letter-spacing: normal; text-align: start; text-indent: 0px; =
text-transform: none; white-space: normal; word-spacing: 0px; =
-webkit-text-stroke-width: 0px;" class=3D""><span style=3D"font-family: =
Helvetica; font-size: 11px; font-style: normal; font-variant-caps: =
normal; font-weight: normal; letter-spacing: normal; text-align: start; =
text-indent: 0px; text-transform: none; white-space: normal; =
word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: =
inline !important;" class=3D"">Graz University of Technology</span><br =
style=3D"font-family: Helvetica; font-size: 11px; font-style: normal; =
font-variant-caps: normal; font-weight: normal; letter-spacing: normal; =
text-align: start; text-indent: 0px; text-transform: none; white-space: =
normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" =
class=3D""><span style=3D"font-family: Helvetica; font-size: 11px; =
font-style: normal; font-variant-caps: normal; font-weight: normal; =
letter-spacing: normal; text-align: start; text-indent: 0px; =
text-transform: none; white-space: normal; word-spacing: 0px; =
-webkit-text-stroke-width: 0px; float: none; display: inline =
!important;" class=3D"">Inffeldgasse 16a, 8010 Graz, Austria.</span><br =
style=3D"font-family: Helvetica; font-size: 11px; font-style: normal; =
font-variant-caps: normal; font-weight: normal; letter-spacing: normal; =
text-align: start; text-indent: 0px; text-transform: none; white-space: =
normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" =
class=3D""><span style=3D"font-family: Helvetica; font-size: 11px; =
font-style: normal; font-variant-caps: normal; font-weight: normal; =
letter-spacing: normal; text-align: start; text-indent: 0px; =
text-transform: none; white-space: normal; word-spacing: 0px; =
-webkit-text-stroke-width: 0px; float: none; display: inline =
!important;" class=3D"">Phone: +43 316 873 5509</span><br =
style=3D"font-family: Helvetica; font-size: 11px; font-style: normal; =
font-variant-caps: normal; font-weight: normal; letter-spacing: normal; =
text-align: start; text-indent: 0px; text-transform: none; white-space: =
normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=3D""><a =
href=3D"http://www.iaik.tugraz.at/" style=3D"font-family: Helvetica; =
font-size: 11px; font-style: normal; font-variant-caps: normal; =
font-weight: normal; letter-spacing: normal; orphans: auto; text-align: =
start; text-indent: 0px; text-transform: none; white-space: normal; =
widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; =
-webkit-text-stroke-width: 0px;" =
class=3D"">http://www.iaik.tugraz.at</a></div></blockquote></div><br =
class=3D""></div></body></html>=

--Apple-Mail=_7B1AD11C-2390-4290-A1A2-EAFEAE3244C8--

--Apple-Mail=_4D1010BB-2068-406E-BB75-7089D31ED14A
Content-Transfer-Encoding: 7bit
Content-Disposition: attachment;
	filename=signature.asc
Content-Type: application/pgp-signature;
	name=signature.asc
Content-Description: Message signed with OpenPGP

-----BEGIN PGP SIGNATURE-----
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=Cczo
-----END PGP SIGNATURE-----

--Apple-Mail=_4D1010BB-2068-406E-BB75-7089D31ED14A--


From nobody Tue Jul 11 03:51:01 2017
Return-Path: <stephen.farrell@cs.tcd.ie>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id AB102128BC8 for <cfrg@ietfa.amsl.com>; Tue, 11 Jul 2017 03:51:00 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -4.301
X-Spam-Level: 
X-Spam-Status: No, score=-4.301 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, RCVD_IN_DNSWL_MED=-2.3, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=cs.tcd.ie
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id HOR_xgEQ9Gxc for <cfrg@ietfa.amsl.com>; Tue, 11 Jul 2017 03:50:59 -0700 (PDT)
Received: from mercury.scss.tcd.ie (mercury.scss.tcd.ie [134.226.56.6]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 10186129B5E for <Cfrg@irtf.org>; Tue, 11 Jul 2017 03:50:59 -0700 (PDT)
Received: from localhost (localhost [127.0.0.1]) by mercury.scss.tcd.ie (Postfix) with ESMTP id CD182BF4C for <Cfrg@irtf.org>; Tue, 11 Jul 2017 11:50:57 +0100 (IST)
Received: from mercury.scss.tcd.ie ([127.0.0.1]) by localhost (mercury.scss.tcd.ie [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id af_Iz1TLoJpQ for <Cfrg@irtf.org>; Tue, 11 Jul 2017 11:50:57 +0100 (IST)
Received: from [134.226.36.93] (bilbo.dsg.cs.tcd.ie [134.226.36.93]) by mercury.scss.tcd.ie (Postfix) with ESMTPSA id 868E2BF48 for <Cfrg@irtf.org>; Tue, 11 Jul 2017 11:50:57 +0100 (IST)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=cs.tcd.ie; s=mail; t=1499770257; bh=Md4CMHfybURHwRuV7cB3GktH7+YP0VsIByu4MQq4LM0=; h=Subject:To:References:From:Date:In-Reply-To:From; b=mFUm+Kt7GmclwQY92zoKd0v781ANGbf72J7u90RJOSi8B3OIgyLCikKjmAb+XY9Xg SYPVVyphgGOc3CTUjs30Vyr9IqtbaWIRrMa0c3KMLM4krFJqSrsmQ3FNP0Hq6IH/Aw Q26YanoJd5vpT3RA08NUbUXW3kS5tZ2i0kvjInX0=
To: "cfrg@irtf.org" <Cfrg@irtf.org>
References: <1777c26d-4e8c-453d-422e-b1f238105bd5@cs.tcd.ie>
From: Stephen Farrell <stephen.farrell@cs.tcd.ie>
Openpgp: id=D66EA7906F0B897FB2E97D582F3C8736805F8DA2; url=
Message-ID: <cc0ded6b-e768-c7c2-9d90-eba380c56f76@cs.tcd.ie>
Date: Tue, 11 Jul 2017 11:50:54 +0100
User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.2.1
MIME-Version: 1.0
In-Reply-To: <1777c26d-4e8c-453d-422e-b1f238105bd5@cs.tcd.ie>
Content-Type: multipart/signed; micalg=pgp-sha256; protocol="application/pgp-signature"; boundary="lF5AvI0QuElgu80roAiUwL3mGeNGa9xBI"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/PNx-X6t83ng8qbHd7ZnFwQqGiGs>
Subject: Re: [Cfrg] [TLS] wiretapping draft - collecting rebuttal arguments
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Tue, 11 Jul 2017 10:51:01 -0000

This is an OpenPGP/MIME signed message (RFC 4880 and 3156)
--lF5AvI0QuElgu80roAiUwL3mGeNGa9xBI
Content-Type: multipart/mixed; boundary="QodADKSwsqT21Uh5cXe63DqE6KNvbAQu3";
 protected-headers="v1"
From: Stephen Farrell <stephen.farrell@cs.tcd.ie>
To: "cfrg@irtf.org" <Cfrg@irtf.org>
Message-ID: <cc0ded6b-e768-c7c2-9d90-eba380c56f76@cs.tcd.ie>
Subject: Re: [TLS] wiretapping draft - collecting rebuttal arguments
References: <1777c26d-4e8c-453d-422e-b1f238105bd5@cs.tcd.ie>
In-Reply-To: <1777c26d-4e8c-453d-422e-b1f238105bd5@cs.tcd.ie>

--QodADKSwsqT21Uh5cXe63DqE6KNvbAQu3
Content-Type: text/plain; charset=utf-8
Content-Language: en-GB
Content-Transfer-Encoding: quoted-printable


FYI. Contributions from folks here would be welcome
if you're interested,
Cheers,
S.

PS: This relates to ongoing discussion on the TLS list.

On 11/07/17 11:48, Stephen Farrell wrote:
>=20
> Hiya,
>=20
> I've asked the chairs for a slot in Prague to allow
> for rebutting the claims made by the proponents of
> the most recent wiretapping draft we're (sadly, still)
> discussing. [1]
>=20
> So far the chairs seem un-keen, but I'm gonna keep
> asking as I think having a rebuttal for this kind
> of bad idea is needed. (And again, I'd prefer the
> chairs ditch the entire idea of discussing this at
> all.)
>=20
> In any case, and perhaps with a view to longer-term
> documenting the arguments against the various "let's
> break TLS" proposals we continually see, I've started
> to collect some of those arguments in a github repo [2].
>=20
> I would welcome contributions to [2] however folks
> would like to provide 'em (but ideally via PRs) so
> we can provide a nice crowd-sourced rebuttal in
> Prague, either as a presentation or via a lively
> mic-line if need be.
>=20
> Cheers,
> S.
>=20
> PS: I've just started on this, but will go through
> the list archive to extract others' arguments and
> add acks. Not sure if that'll get done before we
> end up in Prague but please do let me know if I've
> used an argument you made so I can ack that later.
>=20
> [1] https://tools.ietf.org/html/draft-green-tls-static-dh-in-tls13-01
> [2] https://github.com/sftcd/tinfoil
>=20
>=20
>=20
> _______________________________________________
> TLS mailing list
> TLS@ietf.org
> https://www.ietf.org/mailman/listinfo/tls
>=20


--QodADKSwsqT21Uh5cXe63DqE6KNvbAQu3--

--lF5AvI0QuElgu80roAiUwL3mGeNGa9xBI
Content-Type: application/pgp-signature; name="signature.asc"
Content-Description: OpenPGP digital signature
Content-Disposition: attachment; filename="signature.asc"

-----BEGIN PGP SIGNATURE-----

iQEcBAEBCAAGBQJZZK2QAAoJEC88hzaAX42igpkIAIBAMOTTa9in20d6Ac2Rcpoo
0iyxQlrRoPHfRByawW6qowtPKbJ5WqdcIIYNXkUAtzspnFP3n+CFhKExPMq+TIA9
JoWqhYwFGpW6ZAfVTXDQkY3Qwb+PXeEMjAYd/Sli9v/Og5M3z90iuvM4m9Iot9Dd
thGyzleZJcE6fBtTt8ofqugQR1TdtBdQxS87bgGVMiDbGrSY7XZ/Mz1lKj+MfY0c
mXwBCvc9tBaY/UBHXRD50cu0TtH+s7gbwJ4XGAmJdEXEfljvV34hE70LnkLR2VkR
MxS5h6h043e9OIHF1CXqdl0IYzEOftqK6rl8OIMe8/Ub+HX8cZg5RDhA2v8Q/Dw=
=OxwR
-----END PGP SIGNATURE-----

--lF5AvI0QuElgu80roAiUwL3mGeNGa9xBI--


From nobody Tue Jul 11 19:18:26 2017
Return-Path: <dmjacobson@sbcglobal.net>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 329F7120725 for <cfrg@ietfa.amsl.com>; Tue, 11 Jul 2017 19:18:24 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.7
X-Spam-Level: 
X-Spam-Status: No, score=-2.7 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, RCVD_IN_DNSWL_LOW=-0.7] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=sbcglobal.net
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id WUcKjK1lP58u for <cfrg@ietfa.amsl.com>; Tue, 11 Jul 2017 19:18:22 -0700 (PDT)
Received: from nm18-vm4.access.bullet.mail.bf1.yahoo.com (nm18-vm4.access.bullet.mail.bf1.yahoo.com [216.109.115.83]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 8622A120454 for <cfrg@irtf.org>; Tue, 11 Jul 2017 19:18:22 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=sbcglobal.net; s=s2048; t=1499825901; bh=uCNFmpF+zqp7IBMHyo0dsKud7Tq6Tnu/SpOdK4GQz9Q=; h=Subject:To:References:From:Date:In-Reply-To:From:Subject; b=n1bHJ3MlOrDRVyLfDxt9zMTWOXWQ2OF8vVHoZ0JIi852PZL/GA2p9v5buobFQiN5hyS5fDWoqE7RxDVfY0gbiCpN1zi8NnKtYymIGifVxKKORGK5QzefXIApnSOh6BEe4q1ngJW7I1+sMK4gX3dnc0lAc2/FmRNR+d+KdQUh/mFlpvCCYhOJvkD75LO4T7tXNcLswnoTkB2oa8+TCoq2Sq12pD1f0QZp7+sTyMarQjN5hN6Vjeur44ucXv7IW6rRFxZbPdT/RJK551xETArImkJAY0icLE3AZIODsicl6i/2gOoAbPpB/8WADWI7yEJd43RD4EX4x/y0UhnnuGguUg==
Received: from [66.196.81.157] by nm18.access.bullet.mail.bf1.yahoo.com with NNFMP; 12 Jul 2017 02:18:21 -0000
Received: from [10.218.253.202] by tm3.access.bullet.mail.bf1.yahoo.com with NNFMP; 12 Jul 2017 02:18:21 -0000
Received: from [127.0.0.1] by smtp119.sbc.mail.ne1.yahoo.com with NNFMP; 12 Jul 2017 02:18:21 -0000
X-Yahoo-Newman-Id: 468197.53913.bm@smtp119.sbc.mail.ne1.yahoo.com
X-Yahoo-Newman-Property: ymail-3
X-YMail-OSG: MMgQT64VM1l2niu8M5pa0OI8aqBfkvkyPOu.KTBHfzfw51w ZbMFu8izQsyPkPBxrw.DWKIChzkKAsi0R6PAZ.mFoVptrhF4x80V0XmtKkcW Qwj1hRtvt.aEGMBDblyTTFlHl5B1lcFoQtRL4XvLcJHVyPgIIZGnWPBh46V2 wHAcnOdd_Q9vU5hIwIeNbJHXXGJLIv57lhCIMZ5bveQjF.WJ0uoc8tkrgZSs TkKELQh1dO5SglNVbpreOX51L.9eB_TO42YMl_MyeYbPLlEcDIpza5TT7AG7 zadLl435Dgvn33PV6dYqVQRB0w5ad4tiLH.cCaYrYyzZ.P05giJTwJ6JuHpu OWao2ZjSD._yq1Cv1qQN9Ms2xOvUyYofmTV7rRAHNZPh3I7No2Y2HV77.zM9 wOFklCwXQ.RAPeRAEY9NBN01xlxb4fOvIwwzkCzr_eykJMs78a.F7Mp2_4Kp KwyUnUZOIlTFVoGH.Sz2qna14f05fZ5dZAPX2ge_Dmro_z2GiIAs_PgpWwJA NUwhC84FD7yfLIkmC2MGTKxy72W8KWAp8ihFtQFSbLQ--
X-Yahoo-SMTP: nOrmCa6swBAE50FabWnlVFUpgFVJ9Gbi__8U5mpvhtQq7tTV1g--
To: Samuel Neves <samuel.c.p.neves@gmail.com>, "cfrg@irtf.org" <cfrg@irtf.org>
References: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com> <CAHOTMVLyB6+r6XX3z5ifi7Ey7Qpi1uiZDLsGREsWhgxjqotPxQ@mail.gmail.com> <CAMm+LwiKUJSOEZefABwwkF8H_p+_WTZNGzzrezjCncVZzLd_dA@mail.gmail.com> <CAHOTMVL0hbxZ0PtHhMxjM7eXh+Mg57R=ReFteiMPViNZO4BtBg@mail.gmail.com> <CAEX_ruGD5V7nus20d8507q09PMSJghv6xh-a-_fbHbs1nF33EQ@mail.gmail.com>
From: David Jacobson <dmjacobson@sbcglobal.net>
Message-ID: <838cb765-1ecb-5dbd-f308-bbd415e6321c@sbcglobal.net>
Date: Tue, 11 Jul 2017 19:18:18 -0700
User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.12; rv:45.0) Gecko/20100101 Thunderbird/45.8.0
MIME-Version: 1.0
In-Reply-To: <CAEX_ruGD5V7nus20d8507q09PMSJghv6xh-a-_fbHbs1nF33EQ@mail.gmail.com>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/k6KyAjMVOiD3PlhMwDjw4PmQhwQ>
Subject: Re: [Cfrg] Side channel attack and Edwards curves...
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 12 Jul 2017 02:18:24 -0000

On 7/5/17 5:35 PM, Samuel Neves wrote:
> Coron's countermeasures [1, §5]---the first and third one, in
> particular---work well with Montgomery coordinates.
>
> [1] http://www.jscoron.fr/publications/dpaecc.pdf
>
> On Thu, Jul 6, 2017 at 1:07 AM, Tony Arcieri <bascule@gmail.com> wrote:
>> On Wed, Jul 5, 2017 at 4:16 PM, Phillip Hallam-Baker <phill@hallambaker.com>
>> wrote:
>>> You can blind in either. But if you are going to blind then a lot of the
>>> advantages of Montgomery start to collapse. because you have to do that add
>>> stage.
>>
>> What if you blinded kP with r using:
>>
>>      r*([k r^-1]*P)
>>
>> which only requires inversions?
>>
>> --
>> Tony Arcieri
>>
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org
>> https://www.irtf.org/mailman/listinfo/cfrg
>>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg

I think you miscounted the cost.   You need an extra inversion and an 
extra point multiplication.

And even then the security is dubious.  The original motivation 
apparently was that you are worried that computing kP will leak k.  
Well, the proposal first leaks k r^-1, then it leaks r.  The attacker 
can just multiply the two leaked quantities and she has k.

    --David Jacobson






From nobody Wed Jul 12 02:42:43 2017
Return-Path: <sharon.goldbe@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id A51FC126B72 for <cfrg@ietfa.amsl.com>; Wed, 12 Jul 2017 02:42:41 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.699
X-Spam-Level: 
X-Spam-Status: No, score=-1.699 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, FREEMAIL_FORGED_FROMDOMAIN=0.199, FREEMAIL_FROM=0.001, HEADER_FROM_DIFFERENT_DOMAINS=0.001, HTML_MESSAGE=0.001, SPF_PASS=-0.001] autolearn=no autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id Xif7y51Empus for <cfrg@ietfa.amsl.com>; Wed, 12 Jul 2017 02:42:40 -0700 (PDT)
Received: from mail-it0-x229.google.com (mail-it0-x229.google.com [IPv6:2607:f8b0:4001:c0b::229]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 25C8B124E15 for <cfrg@irtf.org>; Wed, 12 Jul 2017 02:42:40 -0700 (PDT)
Received: by mail-it0-x229.google.com with SMTP id m68so8865199ith.1 for <cfrg@irtf.org>; Wed, 12 Jul 2017 02:42:40 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:sender:from:date:message-id:subject:to:cc; bh=EecCD57uzATR8fbxVB3wRbgrJmvC0VQ3feIcK+bcRmc=; b=f+Mjh6pxAg5UTboy1hTCq/39NpzTDDdD1DxzHEP+mA4wxfrZaSNG/f0AeSTXUF8ren eewtF1hvu5q2+vLP/dVJvGIHWQHt7pIHUcF9jhGk/rpxiG7KCMojWaSV8g9wYpQaerRu btrshci645e2SrnYelWOUbOVxEo6l6ee8QP7QuElkXrdIr5GemoA3Kgor1mRMk/CB1oh OCbiL5G2l2pH2ULU8vG/KeNMXC4zjW+pEA+/s8nv88bvhjrWAWSLVs1WYKFzEkrvh0qa bX5nmJWPd5iyjzOBWZMF2D80Z+ZvX0U3XBoYIgjFQgC86RL46tV/RrJlql74k4YlFON4 s9Kg==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:sender:from:date:message-id:subject :to:cc; bh=EecCD57uzATR8fbxVB3wRbgrJmvC0VQ3feIcK+bcRmc=; b=UaBNGPmtiDcOk+ZjX26tLIsGasW0o55ZJOPXIzVk2LuHgCgrYl/p0qWuG9wH8uSIp3 DKnlZPLo9l3WKkBwOkjUCQPuEKqSORtvM9Wsk8u1641cwdIOd23wdN/YijHnSGdrW+aa QUq+mjr6pWbxuF0jk3SooKL2n0B9d+2EIcEzzuHgbkr2az+h2u7gFuafEITYP4SlLHjT IB+/n4OwF/SxgkJCYzQ4sHsV4S9DRytBZwI1COAesiQ2e1w1FC40cdWwuT6TOUnSmjzw +nPCQZ6fmj1rnX5qgoJmJvZeYeWKqSE526kg3IbYZK9suI51WOzHzDFd1Sgu9jF1xdz0 iBbw==
X-Gm-Message-State: AIVw111a/b4EIrnaxltMIlffgHuv+mft6tDHAmPL88SxSfxrB82HwWJt eQXuDo9sRISg1dSzVCMqThGvdh6eNHak
X-Received: by 10.36.82.77 with SMTP id d74mr20485250itb.119.1499852559342; Wed, 12 Jul 2017 02:42:39 -0700 (PDT)
MIME-Version: 1.0
Sender: sharon.goldbe@gmail.com
Received: by 10.107.164.205 with HTTP; Wed, 12 Jul 2017 02:41:58 -0700 (PDT)
From: Sharon Goldberg <goldbe@cs.bu.edu>
Date: Wed, 12 Jul 2017 12:41:58 +0300
X-Google-Sender-Auth: mob62gXFptJbpNMYMuBkGPE4oT4
Message-ID: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com>
To: cfrg@irtf.org
Cc: Leonid Reyzin <reyzin@cs.bu.edu>, jan@ns1.com,  Dimitrios Papadopoulos <dipapado@umd.edu>
Content-Type: multipart/alternative; boundary="001a11448d8203e33205541ba3d9"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/NdeHrrXvqwgRbDE73FN6AdxwlEs>
Subject: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 12 Jul 2017 09:42:42 -0000

--001a11448d8203e33205541ba3d9
Content-Type: text/plain; charset="UTF-8"

Dear CFRG,

I'm presenting at next week's meeting on Verifiable Random Functions. A VRF
is the public-key version of keyed cryptographic hash. Only the holder of
the VRF secret key can compute the hash, but anyone with the public key can
verify it.  VRFs can be used to prevent dictionary attacks on hash-based
data structures, and have applications to key transparency (CONIKS), DNSSEC
(NSEC5), and cryptocurrencies (Algorand).

In advance of the meeting, please see:

1) Our substantially updated -01 draft:
https://datatracker.ietf.org/doc/draft-goldbe-vrf/

2) Our project page, with links to various VRF implementations:
https://www.cs.bu.edu/~goldbe/projects/vrf

Comments welcome.  Thanks,

Sharon

--
Sharon Goldberg
Computer Science, Boston University
http://www.cs.bu.edu/~goldbe

--001a11448d8203e33205541ba3d9
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Dear CFRG,<br><br>I&#39;m presenting at next week&#39;s me=
eting on Verifiable Random Functions. A VRF is the public-key version of ke=
yed cryptographic hash. Only the holder of the VRF secret key can compute t=
he hash, but anyone with the public key can verify it.=C2=A0 VRFs can be us=
ed to prevent dictionary attacks on hash-based data structures, and have ap=
plications to key transparency (CONIKS), DNSSEC (NSEC5), and cryptocurrenci=
es (Algorand).<br><br>In advance of the meeting, please see:<br><br>1) Our =
substantially updated -01 draft:<br><a href=3D"https://datatracker.ietf.org=
/doc/draft-goldbe-vrf/" target=3D"_blank">https://datatracker.ietf.org/<wbr=
>doc/draft-goldbe-vrf/</a><br><br>2) Our project page, with links to variou=
s VRF implementations:<br><a href=3D"https://www.cs.bu.edu/~goldbe/projects=
/vrf" target=3D"_blank">https://www.cs.bu.edu/~goldbe/<wbr>projects/vrf</a>=
<br><br>Comments welcome.=C2=A0 Thanks,<br><br>Sharon<br><br>--<br>Sharon G=
oldberg<br>Computer Science, Boston University<br><a href=3D"http://www.cs.=
bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu.edu/~goldbe</a></div>

--001a11448d8203e33205541ba3d9--


From nobody Wed Jul 12 05:43:54 2017
Return-Path: <sfluhrer@cisco.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 4582812783A for <cfrg@ietfa.amsl.com>; Wed, 12 Jul 2017 05:43:53 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -14.523
X-Spam-Level: 
X-Spam-Status: No, score=-14.523 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, RCVD_IN_DNSWL_HI=-5, RCVD_IN_MSPIKE_H3=-0.01, RCVD_IN_MSPIKE_WL=-0.01, RP_MATCHES_RCVD=-0.001, SPF_HELO_PASS=-0.001, SPF_PASS=-0.001, USER_IN_DEF_DKIM_WL=-7.5] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=cisco.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id gdJbZrjx-tnj for <cfrg@ietfa.amsl.com>; Wed, 12 Jul 2017 05:43:51 -0700 (PDT)
Received: from rcdn-iport-2.cisco.com (rcdn-iport-2.cisco.com [173.37.86.73]) (using TLSv1.2 with cipher DHE-RSA-SEED-SHA (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 728CF12EC30 for <cfrg@irtf.org>; Wed, 12 Jul 2017 05:43:51 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=cisco.com; i=@cisco.com; l=3672; q=dns/txt; s=iport; t=1499863431; x=1501073031; h=from:to:subject:date:message-id:references:in-reply-to: content-transfer-encoding:mime-version; bh=OKWikAKOVRWnrrYP9HRhoPftYpVHnppvJtZuM/Rbe+s=; b=i3SF8jl2pJ9sWdNDa5mV2+bJesBB6/OUjwB9uGM6tImAYP2QN06njYu/ xHBaUx5KXoLqI09tqrANnUFz/sbPr7u3HwxlZ2SJ2rl9LcCcFqbhTlVuH vdQhXllert1nR7XRY0wunCHFGyJ2IHd13kxQM9w7TiCXz1zofNd4AVPln s=;
X-IronPort-Anti-Spam-Filtered: true
X-IronPort-Anti-Spam-Result: =?us-ascii?q?A0AQAgA+GWZZ/4sNJK1dGgEBAQECAQEBA?= =?us-ascii?q?QgBAQEBg1pkgRQHn3KILo1VghEhC4VKAhqDM0AXAQIBAQEBAQEBayiFGAEBAQE?= =?us-ascii?q?BAgEBIRE6BhEEAgEIDgMEAQEBAgIjAwICAh8GCxQBCAgCBAESCBOJfAMVEKxvg?= =?us-ascii?q?iaHLw2DZAEBAQEBAQEBAQEBAQEBAQEBAQEBAR2BC4IZBIELgkKFBYJXKYIBgny?= =?us-ascii?q?CYQWebTsCjx+EZZIujAaJSgEhATWBCnUVSYcWdgGHS4ENAQEB?=
X-IronPort-AV: E=Sophos;i="5.40,349,1496102400"; d="scan'208";a="272070722"
Received: from alln-core-6.cisco.com ([173.36.13.139]) by rcdn-iport-2.cisco.com with ESMTP/TLS/DHE-RSA-AES256-SHA; 12 Jul 2017 12:43:31 +0000
Received: from XCH-RTP-008.cisco.com (xch-rtp-008.cisco.com [64.101.220.148]) by alln-core-6.cisco.com (8.14.5/8.14.5) with ESMTP id v6CChVPB018865 (version=TLSv1/SSLv3 cipher=AES256-SHA bits=256 verify=FAIL); Wed, 12 Jul 2017 12:43:31 GMT
Received: from xch-rtp-006.cisco.com (64.101.220.146) by XCH-RTP-008.cisco.com (64.101.220.148) with Microsoft SMTP Server (TLS) id 15.0.1210.3; Wed, 12 Jul 2017 08:43:30 -0400
Received: from xch-rtp-006.cisco.com ([64.101.220.146]) by XCH-RTP-006.cisco.com ([64.101.220.146]) with mapi id 15.00.1210.000; Wed, 12 Jul 2017 08:43:30 -0400
From: "Scott Fluhrer (sfluhrer)" <sfluhrer@cisco.com>
To: David Jacobson <dmjacobson@sbcglobal.net>, Samuel Neves <samuel.c.p.neves@gmail.com>, "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] Side channel attack and Edwards curves...
Thread-Index: AQHS9b3vZ+aOkxg3wUKP5VNbVUjcgaJGC/6AgAAVBACAAA4lgIAAB/SAgAmKtwCAAGlfIA==
Date: Wed, 12 Jul 2017 12:43:30 +0000
Message-ID: <63bd361b2bc543b4a84de3678cea196a@XCH-RTP-006.cisco.com>
References: <CAMm+LwiDbjq7nENzvqKGmsQnz=y49nBSVhU0boddtbz3dJAHfw@mail.gmail.com> <CAHOTMVLyB6+r6XX3z5ifi7Ey7Qpi1uiZDLsGREsWhgxjqotPxQ@mail.gmail.com> <CAMm+LwiKUJSOEZefABwwkF8H_p+_WTZNGzzrezjCncVZzLd_dA@mail.gmail.com> <CAHOTMVL0hbxZ0PtHhMxjM7eXh+Mg57R=ReFteiMPViNZO4BtBg@mail.gmail.com> <CAEX_ruGD5V7nus20d8507q09PMSJghv6xh-a-_fbHbs1nF33EQ@mail.gmail.com> <838cb765-1ecb-5dbd-f308-bbd415e6321c@sbcglobal.net>
In-Reply-To: <838cb765-1ecb-5dbd-f308-bbd415e6321c@sbcglobal.net>
Accept-Language: en-US
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
x-ms-exchange-transport-fromentityheader: Hosted
x-originating-ip: [10.150.34.172]
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: base64
MIME-Version: 1.0
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/cipIC99eer4FlFObgji7HxEzIS4>
Subject: Re: [Cfrg] Side channel attack and Edwards curves...
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 12 Jul 2017 12:43:53 -0000
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From nobody Fri Jul 14 08:52:39 2017
Return-Path: <khovratovich@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 74C51128961; Fri, 14 Jul 2017 08:52:37 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.699
X-Spam-Level: 
X-Spam-Status: No, score=-2.699 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id cQ869B8as8zO; Fri, 14 Jul 2017 08:52:34 -0700 (PDT)
Received: from mail-yw0-x22a.google.com (mail-yw0-x22a.google.com [IPv6:2607:f8b0:4002:c05::22a]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 9A620127ABE; Fri, 14 Jul 2017 08:52:34 -0700 (PDT)
Received: by mail-yw0-x22a.google.com with SMTP id l21so27046747ywb.1; Fri, 14 Jul 2017 08:52:34 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=8LzfEQVPNlqay360NtaKavT5FsjKv0lneeREZiXNiBM=; b=GyekS0RvZf9//RSPDTQQ5iTf0+TtaWvI+LHruwX8R6ggnHvhPo1QvlXWBX/rP+eVbM 26RPMn+Djkzhjc9mSWVby7ve5OK00/TBvFEapd2hOf79Xi0L0u02+GtRTd0gkXG/1xlS ckACHi34U5W/Wos2H921X0uEa14wgkTk23j/hNFkY+ASg0Pn+2Ff6WpthFRVNfQc4FkD R/FBfAbonNt3OztGzc9AUeq3S20ouPQWtidQtU/JeqL0GiQkBNRyNJL98q2InFvArlze yScRkZYVbkYs2Yzc0NWW1nnzO5BHtq69yYlrigTJkMTcOYpuYBbYFYTqZGRGBomifSSs OI1g==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=8LzfEQVPNlqay360NtaKavT5FsjKv0lneeREZiXNiBM=; b=oMnnpS+yz8VfTaDbdlo+6NcxqaOwZZBCboMl/4EfZBgCyWuvdmKQezJmTvYsLKLM+7 pO/bLg6npJdUYR1WhGFgtdfCXllnaCJPs9HNZfPbicFSZ158/1gO8uW+3OtBnyIycE6j ZzlETBdCNsscDrMJ1ANZHDSkW+v15KLmRPMSUPJTMvUZcJDvgljuj6CE75xRDMiq35T0 AWhN2/JMdibyfVveflN1FisgfQqE1FvD+YKnnKqYBtf0+OyQWT5XAqhjFtuOoJFFJnt0 zPTP60wTbScdrdajiM/XOlT9WEHXhETQ9TWNM9mnN2VDfP0N9XCNmFuKiucaPqcizP13 N8gw==
X-Gm-Message-State: AIVw110NO0zTx3Qm+iQWYctdwWgHemBx6NHpn0iLqh5MGgzBY3LG6bLS DF5HwwYP3PaN2/ea2DyFxbgeGzYrNw==
X-Received: by 10.129.200.7 with SMTP id n7mr7064427ywi.115.1500047553718; Fri, 14 Jul 2017 08:52:33 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.83.17.138 with HTTP; Fri, 14 Jul 2017 08:52:18 -0700 (PDT)
In-Reply-To: <D5815D6C.97F14%kenny.paterson@rhul.ac.uk>
References: <149061159741.30566.11599293166376872082@ietfa.amsl.com> <CALW8-7+BL5dLJiTh_yn_OD8pNNwLvEz5ZPhqK=-TfUH3xvohBg@mail.gmail.com> <D56853D6.96722%kenny.paterson@rhul.ac.uk> <D5815D6C.97F14%kenny.paterson@rhul.ac.uk>
From: Dmitry Khovratovich <khovratovich@gmail.com>
Date: Fri, 14 Jul 2017 17:52:18 +0200
Message-ID: <CALW8-7LLP=xnCWuGfyvHiH4P39zKjJay4_UEtst-OuzoByT_Uw@mail.gmail.com>
To: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
Cc: "draft-irtf-cfrg-argon2@ietf.org" <draft-irtf-cfrg-argon2@ietf.org>, "cfrg@ietf.org" <cfrg@ietf.org>
Content-Type: multipart/alternative; boundary="089e0821eb4095f16f0554490900"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/9iz6Wll2-hwiu9gRhoMgT_YWhNw>
Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-argon2-02.txt
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 14 Jul 2017 15:52:37 -0000

--089e0821eb4095f16f0554490900
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Dear Russ, Stanislav, Jeremiah,

thank you a lot for the efforts! The reviews make the document much better.
We are now working on integrating the comments into the draft, hopefully
finished next week.

We'll publish a document where every comment is accompanied with a note.

Best regards,
Dmitry, Alex

On Tue, Jul 4, 2017 at 4:06 PM, Paterson, Kenny <Kenny.Paterson@rhul.ac.uk>
wrote:

> Dear Argon2 authors,
>
>
> You will have seen the two recent CFRG review panel reviews for
> draft-irtf-cfrg-argon2-02.txt:
>
> https://www.ietf.org/mail-archive/web/cfrg/current/msg09199.html
>
> https://www.ietf.org/mail-archive/web/cfrg/current/msg09195.html
>
>
> - thanks to Russ Housley and Stanislav Smyshlyaev for preparing these.
>
> Please would you take these reviews into account when preparing the next
> version of your draft? It would helpful if you would post a response
> explaining how you have addressed the comments when you are ready.
>
> (Note also that there was a cutoff for new drafts this Monday past becaus=
e
> of the upcoming IETF meeting.)
>
> Regards
>
> Kenny (for the chairs)
>
>
> On 15/06/2017 15:16, "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk> wrote:
>
> >Dear CFRG,
> >
> >Dmitry Khovratovich kindly presented the latest draft for Argon2 at the
> >interim CFRG meeting in Paris. For those of you who could not attend, hi=
s
> >slides can be found here:
> >
> >https://www.ietf.org/proceedings/interim-2017-cfrg-
> 01/slides/slides-interi
> >m
> >-2017-cfrg-01-sessa-argon2-00.pdf
> >
> >
> >My sense from the constructive discussion that took place after Dmitry's
> >talk in Paris was that there are now no remaining serious objections to
> >the recommended parameters in the latest version of the draft:
> >
> >https://datatracker.ietf.org/doc/draft-irtf-cfrg-argon2/
> >
> >
> >If there are further substantive technical comments from the CFRG
> >membership, the chairs would be grateful if they could be brought to the
> >list in the next few days.
> >
> >Assuming we have indeed reached consensus, then we will be in a position
> >to move to last call for this ID.
> >
> >Thanks,
> >
> >Kenny (for the chairs)
> >
> >
> >On 27/03/2017 11:51, "Cfrg on behalf of Dmitry Khovratovich"
> ><cfrg-bounces@irtf.org on behalf of khovratovich@gmail.com> wrote:
> >
> >>Some comments on a new draft:VariantsArgon2 fills M bytes of memory in =
T
> >>iterations over
> >> it, with M and T being the parameters supplied to Argon2 and determini=
ng
> >>its performance. Speed on a typical server is linear in the MT product.
> >>
> >>The Argon2 family has three variants: I, D, and
> >> ID, which differ in the way of reusing memory that has been filled. Th=
e
> >>I variant makes queries with predictable addresses, whereas D determine=
s
> >>the addresses on the fly depending on the current state (and thus the
> >>password). The ID variant follows I for the
> >> first half of the memory used and D for the rest and while overwriting=
.
> >>Side-channelsThe side-channel attacks, which are of still rising
> >> concern in the security community, are applicable to the D variant as
> >>the memory addresses and thus information about the password or other
> >>secret inputs can be determined from the timing leaks. The I variant is
> >>completely invulnerable to this attack, and
> >> the ID variant provides only a constant factor improvement for the
> >>attacker.
> >>Hardware and tradeoffsThe M and T parameters determine the cost of
> >>bruteforcing
> >> passwords on custom hardware, which is proportional to M2T
> >> if we follow the traditional time-area product metric. The time-memory
> >>tradeoff analysis [2] shows that the bruteforce cost for the I variant
> >>can be changed to M2T/Q(M,T)
> >> for some quality function Q. For instance, Q(230,1)=3D5,
> >> Q(230,4)=3D2.5.
> >>
> >>The D variant is invulnerable to the approach [2],
> >> and the savings factor in the ID variant is upper bounded by factor 2
> >>for all parameters.
> >>Defender tradeoff and ultimate
> >> recommendationsIn public and private conversations with security
> >> architects in the industry we learned that the bottleneck in a system
> >>employing the password-hashing function is the function latency rather
> >>than memory costs. We then assume that a rational defender would like t=
o
> >>maximize the bruteforce costs for the attacker
> >> equipped with a list of hashes, salts, and timing information, for fix=
ed
> >>computing time on the
> >> defender=E2=80=99s machine.  In this assumption the defender keeps the=
 MT
> >>product constant and maximizes the losses M/Q(M,T).
> >> The authors of [2] provides us with attack cost estimates for constant
> >>MT =3D 228,230,232
> >> (measured in iteration-bytes)
> >>
> >>We ultimately recommend the ID variant with T=3D1 and maximum M as a
> >>default setting for all environments, which is secure
> >> against side-channel attacks and prohibit adversarial advantage on
> >>dedicated bruteforce hardware.
> >>
> >>
> >>References[1]
> >>=E2=80=9CEfficiently Computing Data-Independent
> >> Memory-Hard Functions=E2=80=9D <http://eprint.iacr.org/2016/115.pdf>
> >>[2]
> >>=E2=80=9CTowards Practical Attacks on
> >> Argon2i and Balloon Hashing=E2=80=9D  <http://eprint.iacr.org/2016/759=
.pdf>
> >>
> >>
> >>
> >>
> >>
> >>On Mon, Mar 27, 2017 at 12:46 PM, <internet-drafts@ietf.org> wrote:
> >>
> >>
> >>A New Internet-Draft is available from the on-line Internet-Drafts
> >>directories.
> >>This draft is a work item of the Crypto Forum of the IETF.
> >>
> >>        Title           : The memory-hard Argon2 password hash and
> >>proof-of-work function
> >>        Authors         : Alex Biryukov
> >>                          Daniel Dinu
> >>                          Dmitry Khovratovich
> >>                          Simon Josefsson
> >>        Filename        : draft-irtf-cfrg-argon2-02.txt
> >>        Pages           : 26
> >>        Date            : 2017-03-27
> >>
> >>Abstract:
> >>   This document describes the Argon2 memory-hard function for password
> >>   hashing and proof-of-work applications.  We provide an implementer
> >>   oriented description together with sample code and test vectors.  Th=
e
> >>   purpose is to simplify adoption of Argon2 for Internet protocols.
> >>
> >>
> >>The IETF datatracker status page for this draft is:
> >>https://datatracker.ietf.org/doc/draft-irtf-cfrg-argon2/
> >>
> >>There are also htmlized versions available at:
> >>https://tools.ietf.org/html/draft-irtf-cfrg-argon2-02
> >>https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-argon2-02
> >>
> >>A diff from the previous version is available at:
> >>https://www.ietf.org/rfcdiff?url2=3Ddraft-irtf-cfrg-argon2-02
> >>
> >>
> >>Please note that it may take a couple of minutes from the time of
> >>submission
> >>until the htmlized version and diff are available at
> >>tools.ietf.org <http://tools.ietf.org>.
> >>
> >>Internet-Drafts are also available by anonymous FTP at:
> >>ftp://ftp.ietf.org/internet-drafts/
> >>
> >>_______________________________________________
> >>Cfrg mailing list
> >>Cfrg@irtf.org
> >>https://www.irtf.org/mailman/listinfo/cfrg
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >>--
> >>Best regards,
> >>Dmitry Khovratovich
> >>
> >>
> >
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>



--=20
Best regards,
Dmitry Khovratovich

--089e0821eb4095f16f0554490900
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Dear Russ, Stanislav, Jeremiah,<div><br></div><div>thank y=
ou a lot for the efforts! The reviews make the document much better. We are=
 now working on integrating the comments into the draft, hopefully finished=
 next week.</div><div><br></div><div>We&#39;ll publish a document where eve=
ry comment is accompanied with a note.=C2=A0</div><div><br></div><div>Best =
regards,</div><div>Dmitry, Alex</div></div><div class=3D"gmail_extra"><br><=
div class=3D"gmail_quote">On Tue, Jul 4, 2017 at 4:06 PM, Paterson, Kenny <=
span dir=3D"ltr">&lt;<a href=3D"mailto:Kenny.Paterson@rhul.ac.uk" target=3D=
"_blank">Kenny.Paterson@rhul.ac.uk</a>&gt;</span> wrote:<br><blockquote cla=
ss=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;pa=
dding-left:1ex">Dear Argon2 authors,<br>
<br>
<br>
You will have seen the two recent CFRG review panel reviews for<br>
draft-irtf-cfrg-argon2-02.txt:<br>
<br>
<a href=3D"https://www.ietf.org/mail-archive/web/cfrg/current/msg09199.html=
" rel=3D"noreferrer" target=3D"_blank">https://www.ietf.org/mail-<wbr>archi=
ve/web/cfrg/current/<wbr>msg09199.html</a><br>
<br>
<a href=3D"https://www.ietf.org/mail-archive/web/cfrg/current/msg09195.html=
" rel=3D"noreferrer" target=3D"_blank">https://www.ietf.org/mail-<wbr>archi=
ve/web/cfrg/current/<wbr>msg09195.html</a><br>
<br>
<br>
- thanks to Russ Housley and Stanislav Smyshlyaev for preparing these.<br>
<br>
Please would you take these reviews into account when preparing the next<br=
>
version of your draft? It would helpful if you would post a response<br>
explaining how you have addressed the comments when you are ready.<br>
<br>
(Note also that there was a cutoff for new drafts this Monday past because<=
br>
of the upcoming IETF meeting.)<br>
<br>
Regards<br>
<br>
Kenny (for the chairs)<br>
<div class=3D"HOEnZb"><div class=3D"h5"><br>
<br>
On 15/06/2017 15:16, &quot;Paterson, Kenny&quot; &lt;<a href=3D"mailto:Kenn=
y.Paterson@rhul.ac.uk">Kenny.Paterson@rhul.ac.uk</a>&gt; wrote:<br>
<br>
&gt;Dear CFRG,<br>
&gt;<br>
&gt;Dmitry Khovratovich kindly presented the latest draft for Argon2 at the=
<br>
&gt;interim CFRG meeting in Paris. For those of you who could not attend, h=
is<br>
&gt;slides can be found here:<br>
&gt;<br>
&gt;<a href=3D"https://www.ietf.org/proceedings/interim-2017-cfrg-01/slides=
/slides-interi" rel=3D"noreferrer" target=3D"_blank">https://www.ietf.org/<=
wbr>proceedings/interim-2017-cfrg-<wbr>01/slides/slides-interi</a><br>
&gt;m<br>
&gt;-2017-cfrg-01-sessa-argon2-<wbr>00.pdf<br>
&gt;<br>
&gt;<br>
&gt;My sense from the constructive discussion that took place after Dmitry&=
#39;s<br>
&gt;talk in Paris was that there are now no remaining serious objections to=
<br>
&gt;the recommended parameters in the latest version of the draft:<br>
&gt;<br>
&gt;<a href=3D"https://datatracker.ietf.org/doc/draft-irtf-cfrg-argon2/" re=
l=3D"noreferrer" target=3D"_blank">https://datatracker.ietf.org/<wbr>doc/dr=
aft-irtf-cfrg-argon2/</a><br>
&gt;<br>
&gt;<br>
&gt;If there are further substantive technical comments from the CFRG<br>
&gt;membership, the chairs would be grateful if they could be brought to th=
e<br>
&gt;list in the next few days.<br>
&gt;<br>
&gt;Assuming we have indeed reached consensus, then we will be in a positio=
n<br>
&gt;to move to last call for this ID.<br>
&gt;<br>
&gt;Thanks,<br>
&gt;<br>
&gt;Kenny (for the chairs)<br>
&gt;<br>
&gt;<br>
&gt;On 27/03/2017 11:51, &quot;Cfrg on behalf of Dmitry Khovratovich&quot;<=
br>
&gt;&lt;<a href=3D"mailto:cfrg-bounces@irtf.org">cfrg-bounces@irtf.org</a> =
on behalf of <a href=3D"mailto:khovratovich@gmail.com">khovratovich@gmail.c=
om</a>&gt; wrote:<br>
&gt;<br>
&gt;&gt;Some comments on a new draft:VariantsArgon2 fills M bytes of memory=
 in T<br>
&gt;&gt;iterations over<br>
&gt;&gt; it, with M and T being the parameters supplied to Argon2 and deter=
mining<br>
&gt;&gt;its performance. Speed on a typical server is linear in the MT prod=
uct.<br>
&gt;&gt;<br>
&gt;&gt;The Argon2 family has three variants: I, D, and<br>
&gt;&gt; ID, which differ in the way of reusing memory that has been filled=
. The<br>
&gt;&gt;I variant makes queries with predictable addresses, whereas D deter=
mines<br>
&gt;&gt;the addresses on the fly depending on the current state (and thus t=
he<br>
&gt;&gt;password). The ID variant follows I for the<br>
&gt;&gt; first half of the memory used and D for the rest and while overwri=
ting.<br>
&gt;&gt;Side-channelsThe side-channel attacks, which are of still rising<br=
>
&gt;&gt; concern in the security community, are applicable to the D variant=
 as<br>
&gt;&gt;the memory addresses and thus information about the password or oth=
er<br>
&gt;&gt;secret inputs can be determined from the timing leaks. The I varian=
t is<br>
&gt;&gt;completely invulnerable to this attack, and<br>
&gt;&gt; the ID variant provides only a constant factor improvement for the=
<br>
&gt;&gt;attacker.<br>
&gt;&gt;Hardware and tradeoffsThe M and T parameters determine the cost of<=
br>
&gt;&gt;bruteforcing<br>
&gt;&gt; passwords on custom hardware, which is proportional to M2T<br>
&gt;&gt; if we follow the traditional time-area product metric. The time-me=
mory<br>
&gt;&gt;tradeoff analysis [2] shows that the bruteforce cost for the I vari=
ant<br>
&gt;&gt;can be changed to M2T/Q(M,T)<br>
&gt;&gt; for some quality function Q. For instance, Q(230,1)=3D5,<br>
&gt;&gt; Q(230,4)=3D2.5.<br>
&gt;&gt;<br>
&gt;&gt;The D variant is invulnerable to the approach [2],<br>
&gt;&gt; and the savings factor in the ID variant is upper bounded by facto=
r 2<br>
&gt;&gt;for all parameters.<br>
&gt;&gt;Defender tradeoff and ultimate<br>
&gt;&gt; recommendationsIn public and private conversations with security<b=
r>
&gt;&gt; architects in the industry we learned that the bottleneck in a sys=
tem<br>
&gt;&gt;employing the password-hashing function is the function latency rat=
her<br>
&gt;&gt;than memory costs. We then assume that a rational defender would li=
ke to<br>
&gt;&gt;maximize the bruteforce costs for the attacker<br>
&gt;&gt; equipped with a list of hashes, salts, and timing information, for=
 fixed<br>
&gt;&gt;computing time on the<br>
&gt;&gt; defender=E2=80=99s machine.=C2=A0 In this assumption the defender =
keeps the MT<br>
&gt;&gt;product constant and maximizes the losses M/Q(M,T).<br>
&gt;&gt; The authors of [2] provides us with attack cost estimates for cons=
tant<br>
&gt;&gt;MT =3D 228,230,232<br>
&gt;&gt; (measured in iteration-bytes)<br>
&gt;&gt;<br>
&gt;&gt;We ultimately recommend the ID variant with T=3D1 and maximum M as =
a<br>
&gt;&gt;default setting for all environments, which is secure<br>
&gt;&gt; against side-channel attacks and prohibit adversarial advantage on=
<br>
&gt;&gt;dedicated bruteforce hardware.<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;References[1]<br>
&gt;&gt;=E2=80=9CEfficiently Computing Data-Independent<br>
&gt;&gt; Memory-Hard Functions=E2=80=9D &lt;<a href=3D"http://eprint.iacr.o=
rg/2016/115.pdf" rel=3D"noreferrer" target=3D"_blank">http://eprint.iacr.or=
g/2016/<wbr>115.pdf</a>&gt;<br>
&gt;&gt;[2]<br>
&gt;&gt;=E2=80=9CTowards Practical Attacks on<br>
&gt;&gt; Argon2i and Balloon Hashing=E2=80=9D=C2=A0 &lt;<a href=3D"http://e=
print.iacr.org/2016/759.pdf" rel=3D"noreferrer" target=3D"_blank">http://ep=
rint.iacr.org/2016/<wbr>759.pdf</a>&gt;<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;On Mon, Mar 27, 2017 at 12:46 PM, &lt;<a href=3D"mailto:internet-dr=
afts@ietf.org">internet-drafts@ietf.org</a>&gt; wrote:<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;A New Internet-Draft is available from the on-line Internet-Drafts<=
br>
&gt;&gt;directories.<br>
&gt;&gt;This draft is a work item of the Crypto Forum of the IETF.<br>
&gt;&gt;<br>
&gt;&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 Title=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0: The memory-hard Argon2 password hash and<br>
&gt;&gt;proof-of-work function<br>
&gt;&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 Authors=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0: Alex Biryukov<br>
&gt;&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 Daniel Dinu<br>
&gt;&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 Dmitry Khovratovich<br>
&gt;&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 Simon Josefsson<br>
&gt;&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 Filename=C2=A0 =C2=A0 =C2=A0 =C2=A0 : d=
raft-irtf-cfrg-argon2-02.txt<br>
&gt;&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 Pages=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0: 26<br>
&gt;&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 Date=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 : 2017-03-27<br>
&gt;&gt;<br>
&gt;&gt;Abstract:<br>
&gt;&gt;=C2=A0 =C2=A0This document describes the Argon2 memory-hard functio=
n for password<br>
&gt;&gt;=C2=A0 =C2=A0hashing and proof-of-work applications.=C2=A0 We provi=
de an implementer<br>
&gt;&gt;=C2=A0 =C2=A0oriented description together with sample code and tes=
t vectors.=C2=A0 The<br>
&gt;&gt;=C2=A0 =C2=A0purpose is to simplify adoption of Argon2 for Internet=
 protocols.<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;The IETF datatracker status page for this draft is:<br>
&gt;&gt;<a href=3D"https://datatracker.ietf.org/doc/draft-irtf-cfrg-argon2/=
" rel=3D"noreferrer" target=3D"_blank">https://datatracker.ietf.<wbr>org/do=
c/draft-irtf-cfrg-<wbr>argon2/</a><br>
&gt;&gt;<br>
&gt;&gt;There are also htmlized versions available at:<br>
&gt;&gt;<a href=3D"https://tools.ietf.org/html/draft-irtf-cfrg-argon2-02" r=
el=3D"noreferrer" target=3D"_blank">https://tools.ietf.org/html/<wbr>draft-=
irtf-cfrg-argon2-02</a><br>
&gt;&gt;<a href=3D"https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ar=
gon2-02" rel=3D"noreferrer" target=3D"_blank">https://datatracker.ietf.<wbr=
>org/doc/html/draft-irtf-cfrg-<wbr>argon2-02</a><br>
&gt;&gt;<br>
&gt;&gt;A diff from the previous version is available at:<br>
&gt;&gt;<a href=3D"https://www.ietf.org/rfcdiff?url2=3Ddraft-irtf-cfrg-argo=
n2-02" rel=3D"noreferrer" target=3D"_blank">https://www.ietf.org/<wbr>rfcdi=
ff?url2=3Ddraft-irtf-cfrg-<wbr>argon2-02</a><br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;Please note that it may take a couple of minutes from the time of<b=
r>
&gt;&gt;submission<br>
&gt;&gt;until the htmlized version and diff are available at<br>
&gt;&gt;<a href=3D"http://tools.ietf.org" rel=3D"noreferrer" target=3D"_bla=
nk">tools.ietf.org</a> &lt;<a href=3D"http://tools.ietf.org" rel=3D"norefer=
rer" target=3D"_blank">http://tools.ietf.org</a>&gt;.<br>
&gt;&gt;<br>
&gt;&gt;Internet-Drafts are also available by anonymous FTP at:<br>
&gt;&gt;<a href=3D"ftp://ftp.ietf.org/internet-drafts/" rel=3D"noreferrer" =
target=3D"_blank">ftp://ftp.ietf.org/internet-<wbr>drafts/</a><br>
&gt;&gt;<br>
&gt;&gt;____________________________<wbr>___________________<br>
&gt;&gt;Cfrg mailing list<br>
&gt;&gt;<a href=3D"mailto:Cfrg@irtf.org">Cfrg@irtf.org</a><br>
&gt;&gt;<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noref=
errer" target=3D"_blank">https://www.irtf.org/<wbr>mailman/listinfo/cfrg</a=
><br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;&gt;--<br>
&gt;&gt;Best regards,<br>
&gt;&gt;Dmitry Khovratovich<br>
&gt;&gt;<br>
&gt;&gt;<br>
&gt;<br>
<br>
______________________________<wbr>_________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/<wbr>listinfo/cfrg</a><br>
</div></div></blockquote></div><br><br clear=3D"all"><div><br></div>-- <br>=
<div class=3D"gmail_signature" data-smartmail=3D"gmail_signature"><div>Best=
 regards,</div><div>Dmitry Khovratovich</div></div>
</div>

--089e0821eb4095f16f0554490900--


From nobody Fri Jul 14 12:29:18 2017
Return-Path: <francisco@cs.cinvestav.mx>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 5FF4013171B for <cfrg@ietfa.amsl.com>; Fri, 14 Jul 2017 12:29:16 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.903
X-Spam-Level: 
X-Spam-Status: No, score=-1.903 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, RCVD_IN_DNSWL_NONE=-0.0001, RP_MATCHES_RCVD=-0.001, SPF_HELO_PASS=-0.001, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id v73_VuGDZO_g for <cfrg@ietfa.amsl.com>; Fri, 14 Jul 2017 12:29:14 -0700 (PDT)
Received: from delta.cs.cinvestav.mx (delta.cs.cinvestav.mx [148.247.102.21]) (using TLSv1 with cipher DHE-RSA-AES256-SHA (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 2B1FA12EAB0 for <cfrg@irtf.org>; Fri, 14 Jul 2017 12:29:13 -0700 (PDT)
Received: from localhost (localhost [127.0.0.1]) by delta.cs.cinvestav.mx (Postfix) with ESMTP id B654B5C1462; Fri, 14 Jul 2017 14:28:57 -0500 (CDT)
X-Virus-Scanned: amavisd-new at cs.cinvestav.mx
Received: from delta.cs.cinvestav.mx ([127.0.0.1]) by localhost (delta.cs.cinvestav.mx [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id QX-SPrFBaQ-X; Fri, 14 Jul 2017 14:28:56 -0500 (CDT)
Received: by delta.cs.cinvestav.mx (Postfix, from userid 1507) id 38E385C1557; Fri, 14 Jul 2017 14:28:56 -0500 (CDT)
Received: from localhost (localhost [127.0.0.1]) by delta.cs.cinvestav.mx (Postfix) with ESMTP id 299945C1462; Fri, 14 Jul 2017 14:28:56 -0500 (CDT)
Date: Fri, 14 Jul 2017 14:28:56 -0500 (CDT)
From: Francisco Rodriguez- Henriquez <francisco@cs.cinvestav.mx>
To: "cfrg@irtf.org" <cfrg@irtf.org>
cc: Thomaz Oliveira <thomaz.figueiredo@gmail.com>,  =?ISO-8859-15?Q?Julio_C=E9sar_Lopez?= <jlopez@ic.unicamp.br>,  huseyin.hisil@yasar.edu.tr, Armando Faz <armfazh@gmail.com>
In-Reply-To: <alpine.LFD.2.02.1705111858040.25089@delta.cs.cinvestav.mx>
Message-ID: <alpine.LFD.2.02.1707141340500.16576@delta.cs.cinvestav.mx>
References: <CAHOTMVKHA-yJR1oCyPtUp4-aJVc3dTdyxQHNo4xqnJt0hU6jVQ@mail.gmail.com> <CAMm+Lwgm8XzTBarZ1eFePTZGORorBJAeF7brDkhWGQKQVT0LPQ@mail.gmail.com> <CAMm+LwggT_AVv=KjzM1r=6UnkeK+g8zkticXFBDQ0cUXs_PP0A@mail.gmail.com> <CAHOTMVLHPFyi2VWpv85hrZ1MoXqeHYUv52wkMxjj3xp5B4V1cw@mail.gmail.com> <CAMm+Lwgfk1=yEJSbZbaZLvF5k5k66VVSx6MzKLM+DbUV7Ls6Xw@mail.gmail.com> <CAHOTMVK1gYrFiwd8f8zf2zPXYyCorp+jixkcY5FLhfHfv0NkWw@mail.gmail.com> <CAMm+LwjeZdR=ZGX0topN2w6P12jEmR-TQ8M9+anyETj43nbiqg@mail.gmail.com> <CAHOTMVL2e2UjVX6VKgHUbOHrb-gsU8kn_cxY1FdNrnj29cki9g@mail.gmail.com> <alpine.LFD.2.02.1703291804030.8996@delta.cs.cinvestav.mx> <alpine.LFD.2.02.1705111858040.25089@delta.cs.cinvestav.mx>
User-Agent: Alpine 2.02 (LFD 1266 2009-07-14)
MIME-Version: 1.0
Content-Type: MULTIPART/MIXED; BOUNDARY="-141290138-2002586352-1500058027=:16576"
Content-ID: <alpine.LFD.2.02.1707141347280.16576@delta.cs.cinvestav.mx>
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/mZ6apUEEuSnrfoJ5sr2vVbbIzdY>
Subject: Re: [Cfrg] How to (pre-)compute a ladder [full C implementation]
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 14 Jul 2017 19:29:16 -0000

  This message is in MIME format.  The first part should be readable text,
  while the remaining parts are likely unreadable without MIME-aware tools.

---141290138-2002586352-1500058027=:16576
Content-Type: TEXT/PLAIN; CHARSET=ISO-8859-15; format=flowed
Content-Transfer-Encoding: 8BIT
Content-ID: <alpine.LFD.2.02.1707141347281.16576@delta.cs.cinvestav.mx>

Dear CFRG community,

We would like to share with you a full C implementation of the 
ladder procedure described in the IACR pre-print 2017/264:

        "How to (pre-)compute a ladder"

The C code can be downloaded from,
https://github.com/armfazh/rfc7748_precomputed

We are reporting the following benchmarked timings for 64-bit Intel 
architectures (table entries are given in clock cycles),


X25519 				Haswell 	Skylake
proposed Keygen rtl ladder	 90,895 	 72,571
Shared secret 	 		138,962 	107,942
S.Secret/Keygen speedup		  1.529	          1.487
overall D-H speedup               1.209           1.196


X448				Haswell 	Skylake
Proposed Keygen rtl Ladder	401,902 	322,040
Shared Secret 			670,747 	528,470
S.Secret/Keygen speedup           1.668           1.641
overall D-H speedup               1.251           1.243

Notes:

+ The Key generation reported above was computed using the proposed
   right-to-left ladder
+ The Shared secret was computed using the procedure described in the RFC
   7748 memo
+ The D-H speedup is obtained as the ratio,
 		2*shared secret / (shared secret + key generation);
+ In the sense explained in our pre-print, our procedure fully complies
   with the RFC 7748 memo.

With best regards,
Thomaz Oliveira, Julio López, Hüseyin Hisil, Armando Faz-Hernández and 
Francisco Rodríguez-Henríquez


On Thu, 11 May 2017, Francisco Rodriguez- Henriquez wrote:

> Dear CFRG community,
>
> We would like to draw your attention to an improved version of our IACR 
> pre-print 2017/264 now entitled:
>
> 	"How to (pre-)compute a ladder"
>
> In this revised version, we present an improved differential addition formula 
> that uses pre-computation to match the computational cost of the classical 
> Montgomery differential addition.
>
> Accordingly, our estimates suggest that a full implementation of our 
> pre-computable ladder proposal should outperform state-of-the-art software 
> implementations of the X25519 and X448 functions by a 40% speedup when 
> working in the fixed-point scenario.
>
> We would be delighted to receive feedback (including sightings of typos) from 
> the CFRG community.
>
> With best regards,
>
> Thomaz Oliveira, Julio López, Hüseyin Hisil and Francisco Rodríguez-Henríquez
---141290138-2002586352-1500058027=:16576--


From nobody Fri Jul 14 12:34:08 2017
Return-Path: <francisco@cs.cinvestav.mx>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 04FE7129ADD for <cfrg@ietfa.amsl.com>; Fri, 14 Jul 2017 12:34:07 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.903
X-Spam-Level: 
X-Spam-Status: No, score=-1.903 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, RCVD_IN_DNSWL_NONE=-0.0001, RP_MATCHES_RCVD=-0.001, SPF_HELO_PASS=-0.001, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id j87REikMw7Ux for <cfrg@ietfa.amsl.com>; Fri, 14 Jul 2017 12:34:05 -0700 (PDT)
Received: from delta.cs.cinvestav.mx (delta.cs.cinvestav.mx [148.247.102.21]) (using TLSv1 with cipher DHE-RSA-AES256-SHA (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 5BA4B126BFD for <cfrg@irtf.org>; Fri, 14 Jul 2017 12:34:05 -0700 (PDT)
Received: from localhost (localhost [127.0.0.1]) by delta.cs.cinvestav.mx (Postfix) with ESMTP id 4ACDC5C1557; Fri, 14 Jul 2017 14:33:50 -0500 (CDT)
X-Virus-Scanned: amavisd-new at cs.cinvestav.mx
Received: from delta.cs.cinvestav.mx ([127.0.0.1]) by localhost (delta.cs.cinvestav.mx [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id Kf9MbDqbNpJb; Fri, 14 Jul 2017 14:33:48 -0500 (CDT)
Received: by delta.cs.cinvestav.mx (Postfix, from userid 1507) id BD0735C1577; Fri, 14 Jul 2017 14:33:48 -0500 (CDT)
Received: from localhost (localhost [127.0.0.1]) by delta.cs.cinvestav.mx (Postfix) with ESMTP id 93F8C5C1557; Fri, 14 Jul 2017 14:33:48 -0500 (CDT)
Date: Fri, 14 Jul 2017 14:33:48 -0500 (CDT)
From: Francisco Rodriguez- Henriquez <francisco@cs.cinvestav.mx>
To: Peter Dettman <peter.dettman@bouncycastle.org>
cc: "cfrg@irtf.org" <cfrg@irtf.org>,  =?ISO-8859-15?Q?Julio_C=E9sar_Lopez?= <jlopez@ic.unicamp.br>,  Thomaz Oliveira <thomaz.figueiredo@gmail.com>, huseyin.hisil@yasar.edu.tr,  Armando Faz <armfazh@gmail.com>
In-Reply-To: <02899a12-8cf7-c318-32ea-9491ec2a22c2@bouncycastle.org>
Message-ID: <alpine.LFD.2.02.1707141329090.16576@delta.cs.cinvestav.mx>
References: <CAHOTMVKHA-yJR1oCyPtUp4-aJVc3dTdyxQHNo4xqnJt0hU6jVQ@mail.gmail.com> <CAMm+Lwgm8XzTBarZ1eFePTZGORorBJAeF7brDkhWGQKQVT0LPQ@mail.gmail.com> <CAMm+LwggT_AVv=KjzM1r=6UnkeK+g8zkticXFBDQ0cUXs_PP0A@mail.gmail.com> <CAHOTMVLHPFyi2VWpv85hrZ1MoXqeHYUv52wkMxjj3xp5B4V1cw@mail.gmail.com> <CAMm+Lwgfk1=yEJSbZbaZLvF5k5k66VVSx6MzKLM+DbUV7Ls6Xw@mail.gmail.com> <CAHOTMVK1gYrFiwd8f8zf2zPXYyCorp+jixkcY5FLhfHfv0NkWw@mail.gmail.com> <CAMm+LwjeZdR=ZGX0topN2w6P12jEmR-TQ8M9+anyETj43nbiqg@mail.gmail.com> <CAHOTMVL2e2UjVX6VKgHUbOHrb-gsU8kn_cxY1FdNrnj29cki9g@mail.gmail.com> <alpine.LFD.2.02.1703291804030.8996@delta.cs.cinvestav.mx> <alpine.LFD.2.02.1705111858040.25089@delta.cs.cinvestav.mx> <02899a12-8cf7-c318-32ea-9491ec2a22c2@bouncycastle.org>
User-Agent: Alpine 2.02 (LFD 1266 2009-07-14)
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; format=flowed; charset=US-ASCII
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/IvZzpVokzjyvBvOmdUCjAoeK7aU>
Subject: Re: [Cfrg] How to (pre-)compute a ladder [revised version]
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 14 Jul 2017 19:34:07 -0000

Hi Peter,

Please see my reply below.

Cheers,
Francisco
[on behalf of the authors]

On Fri, 16 Jun 2017, Peter Dettman wrote:

> Hi Francisco,
>
> I've updated my (java) implementations of X25519 and X448 in line with
> your revised paper. My rough benchmark results for a complete ECDH are
> -17.7% and -19.5% time required for X25519 and X448 respectively.

Great!
This is roughly in the same ballpark of what we are getting in our C 
implementation, which is available at,

https://github.com/armfazh/rfc7748_precomputed

[please check my previous email to this list]

> These are perhaps slightly more modest than the paper's estimates. Your
> paper already anticipates that (uncounted) field add/sub are significant
> in practice.

Right!

This effect appears to be more significant in the case of X25519 than in 
the case of X448.


> Part of the difference however is that my implementation of Algorithm 3
> handles the final 'q' bits using simple doublings, and removes redundant
> cswaps - just as Algorithm 5 does. Of course Alg. 3 is just as presented
> in RFC 7748, but it might be a fairer comparison to first apply to Alg.
> 3 those of your optimizations that are applicable.
>
> Also, my (32-bit) X448 implementation (Alg. 5) required a carry
> propagation for 'A' (line 10), due to tight bounds on limbs when
> squaring D, E. I did the same for (32-bit) X25519 although I haven't yet
> proved it necessary.

OK!
If you have time please compare against the C implementation mentioned 
above.

> An idea: for fixed-base X25519, why not precompute one doubling? i.e.
> just calculate (k/2) * 2P, needing only 2 final doublings (you even
> already have S of order 4). I am not sure whether this extends to
> precomputing (q-1) doublings.
>
> Another thought that occurred to me is that someone might get the idea
> to use your fixed-base ladder with some other point. Couldn't this go
> awry if that point were already "P + S" or similar? If so, a caution
> somewhere in the paper on preconditions for the fixed point might be
> advised.
>
> Regards,
> Pete Dettman

Thanks for both suggestions. We will carefully analyze both of them.


Cheers,
Francisco


From nobody Fri Jul 14 12:54:46 2017
Return-Path: <francisco@cs.cinvestav.mx>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id A639E131937 for <cfrg@ietfa.amsl.com>; Fri, 14 Jul 2017 12:54:44 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.903
X-Spam-Level: 
X-Spam-Status: No, score=-1.903 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, RCVD_IN_DNSWL_NONE=-0.0001, RP_MATCHES_RCVD=-0.001, SPF_HELO_PASS=-0.001, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id iTnZ2tX1umT2 for <cfrg@ietfa.amsl.com>; Fri, 14 Jul 2017 12:54:43 -0700 (PDT)
Received: from delta.cs.cinvestav.mx (delta.cs.cinvestav.mx [148.247.102.21]) (using TLSv1 with cipher DHE-RSA-AES256-SHA (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 1EE3413193F for <cfrg@irtf.org>; Fri, 14 Jul 2017 12:54:43 -0700 (PDT)
Received: from localhost (localhost [127.0.0.1]) by delta.cs.cinvestav.mx (Postfix) with ESMTP id 144735C13CA; Fri, 14 Jul 2017 14:54:28 -0500 (CDT)
X-Virus-Scanned: amavisd-new at cs.cinvestav.mx
Received: from delta.cs.cinvestav.mx ([127.0.0.1]) by localhost (delta.cs.cinvestav.mx [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id ARCYpgCEAkqt; Fri, 14 Jul 2017 14:54:26 -0500 (CDT)
Received: by delta.cs.cinvestav.mx (Postfix, from userid 1507) id 997265C1526; Fri, 14 Jul 2017 14:54:26 -0500 (CDT)
Received: from localhost (localhost [127.0.0.1]) by delta.cs.cinvestav.mx (Postfix) with ESMTP id 869F75C13CA; Fri, 14 Jul 2017 14:54:26 -0500 (CDT)
Date: Fri, 14 Jul 2017 14:54:26 -0500 (CDT)
From: Francisco Rodriguez- Henriquez <francisco@cs.cinvestav.mx>
To: Mike Hamburg <mike@shiftleft.org>
cc: "cfrg@irtf.org" <cfrg@irtf.org>,  =?ISO-8859-15?Q?Julio_C=E9sar_Lopez?= <jlopez@ic.unicamp.br>,  Thomaz Oliveira <thomaz.figueiredo@gmail.com>, huseyin.hisil@yasar.edu.tr,  Armando Faz <armfazh@gmail.com>
In-Reply-To: <alpine.LFD.2.02.1707141329090.16576@delta.cs.cinvestav.mx>
Message-ID: <alpine.LFD.2.02.1707141441220.17686@delta.cs.cinvestav.mx>
References: <CAHOTMVKHA-yJR1oCyPtUp4-aJVc3dTdyxQHNo4xqnJt0hU6jVQ@mail.gmail.com> <CAMm+Lwgm8XzTBarZ1eFePTZGORorBJAeF7brDkhWGQKQVT0LPQ@mail.gmail.com> <CAMm+LwggT_AVv=KjzM1r=6UnkeK+g8zkticXFBDQ0cUXs_PP0A@mail.gmail.com> <CAHOTMVLHPFyi2VWpv85hrZ1MoXqeHYUv52wkMxjj3xp5B4V1cw@mail.gmail.com> <CAMm+Lwgfk1=yEJSbZbaZLvF5k5k66VVSx6MzKLM+DbUV7Ls6Xw@mail.gmail.com> <CAHOTMVK1gYrFiwd8f8zf2zPXYyCorp+jixkcY5FLhfHfv0NkWw@mail.gmail.com> <CAMm+LwjeZdR=ZGX0topN2w6P12jEmR-TQ8M9+anyETj43nbiqg@mail.gmail.com> <CAHOTMVL2e2UjVX6VKgHUbOHrb-gsU8kn_cxY1FdNrnj29cki9g@mail.gmail.com> <alpine.LFD.2.02.1703291804030.8996@delta.cs.cinvestav.mx> <alpine.LFD.2.02.1705111858040.25089@delta.cs.cinvestav.mx> <02899a12-8cf7-c318-32ea-9491ec2a22c2@bouncycastle.org> <alpine.LFD.2.02.1707141329090.16576@delta.cs.cinvestav.mx>
User-Agent: Alpine 2.02 (LFD 1266 2009-07-14)
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; format=flowed; charset=US-ASCII
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/_1o0eT25xGtQujRdJLuURjZbA9g>
Subject: Re: [Cfrg] How to (pre-)compute a ladder [revised version]
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 14 Jul 2017 19:54:45 -0000

On May 12, 2017, at 2:15 PM, Mike Hamburg <mike@shiftleft.org> wrote:

> Hello Francisco et al,

> This is a clever and useful piece of work.  It's a good intermediate 
> between just using the standard Montgomery ladder for everything, and 
> going to a full Edwards implementation with combs or something.  It 
> especially seems useful where power analysis resistance is required, 
> because other precomputation methods usually aren't suitable.  The RTL 
> Montgomery ladder (or Joye double-add ladder) is already known to be 
> useful in this situation, at least with some modification to prevent 
> coordinates from staying the same between iterations.  Since you're 
> speeding up the RTL Montgomery ladder, your optimization can slot right 
> in to some implementations.

Hi Mike,

Thanks for your comments and sorry for this really slow reply :)

I agree with you about the fact that the RTL Montgomery ladder by Joye was 
already known for performing this feature.

> You should probably compare to existing Edwards precomputation methods 
> in your paper, since they are the likely alternative to your technique. 
> In particular, I noticed that you compared against the EBACS version of 
> Ed448-Goldilocks.  With a fixed base point, your method uses 41% less 
> time for the Montgomery ladder with a 25kiB table.  However, the EBACS 
> version of Ed448-Goldilocks doesn't use the Montgomery ladder for 
> fixed-base scalarmul.  Instead it uses a combs algorithm, which uses a 
> 15kiB table and takes about 70% less time than the Montgomery ladder; 
> see https://bench.cr.yp.to/results-dh.html.  Libdecaf likewise uses 
> precomputed combs for fixed-base scalarmul.  But your new technique is 
> certainly simpler.

I agree with you, there are faster methods to perform pre-computation, 
which offer [some] protection against side-channel attacks.

In our work, we were specifically targeting the RFC 7748 Memo, and hence 
we only meant to compare against ladder procedures for computing the 
scalar multiplication.

I believe that the tradeoffs between the simplicity/elegance/beauty of 
the ladders Vs. the efficiency of regular recoding + other methods of 
pre-computation, was already debated in this list :)

Cheers,
Francisco

> Cheers,
> -- Mike


From nobody Sun Jul 16 19:09:25 2017
Return-Path: <alangley@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id CEAA5129A97 for <cfrg@ietfa.amsl.com>; Sun, 16 Jul 2017 19:09:23 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.399
X-Spam-Level: 
X-Spam-Status: No, score=-2.399 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, FREEMAIL_FORGED_FROMDOMAIN=0.199, FREEMAIL_FROM=0.001, HEADER_FROM_DIFFERENT_DOMAINS=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id f2wIrzMibPYj for <cfrg@ietfa.amsl.com>; Sun, 16 Jul 2017 19:09:21 -0700 (PDT)
Received: from mail-it0-x236.google.com (mail-it0-x236.google.com [IPv6:2607:f8b0:4001:c0b::236]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id AE7F9126C0F for <cfrg@ietf.org>; Sun, 16 Jul 2017 19:09:21 -0700 (PDT)
Received: by mail-it0-x236.google.com with SMTP id l132so6847386ita.1 for <cfrg@ietf.org>; Sun, 16 Jul 2017 19:09:21 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:sender:from:date:message-id:subject:to; bh=d02pySssvugb9fqgIE9nOTK6B5eXiUrJdr72L6hhABQ=; b=ueKWhbBZi8N5WunqaBwoy1RBUJizTCaQanqGmeK+FbjldXQVWaVNwHg49C2tL/x71V Ll5VRkRndIJ+XfNi4LGIaGb4hQOkh7ICBCh7HU3JwMymHRe3trtRRoC9Ob16xGkcRPBa wLArOt+Bhf6QUklzphWxXtzXwe1jhU1u9nGPOjQGaf3umH6mLQQxgsrsw+fYHypmQCTI elWeiEcWXWQ+AdfvgxVGxHV+kIOp+JGNd9q+fWyoIYv0GummgSoZasdlg8s2nXQ6CCy9 M0J6Z7YCzC8JWa4RHO9f5txuyAA4kCOq3D/mMn+pnBF63asZrcDl18ZgkkX7ujggnTh8 16MQ==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:sender:from:date:message-id:subject :to; bh=d02pySssvugb9fqgIE9nOTK6B5eXiUrJdr72L6hhABQ=; b=bH+mc6uGbBJXyAGgq2CEIdehzwzcL0Ylsx2imhNuaEElhQi8ui29udYbznItJUk4yn uh+qhkGuPMEf1BJQaw7r3Ib0wyaa8xFqTGMSxhZa5RT5FkkFWHvm1QAeSNkT0mtot0xN kAVuCf6XKZBm65I9hT8H8H/uFehozEgdneycsn/VZl+8LqgO3cOZnKg+e+Dlx3gOS7CG BqUFQk2Eu7t7CeNPl63jWiZMv5jaJCpuwIakjBcOJbCwps+kAdlvK4Q0ybNdXaZwxXH2 wAPzlR4Z8sFUu9OT5ZxTtSbzJE4Q7j1CjsocolkuZNPHSKbe9fyjsuB3J+TPsJxiIsb8 ioKQ==
X-Gm-Message-State: AIVw112MUxCg+1r/OK+M8XrrJPjYw4AOmYPlz19wInB13mGaT9Gq5A+H kqMQFegE4EPrHSC9NK4Dih9x1Vhe/zKo7us=
X-Received: by 10.36.55.145 with SMTP id r139mr3794391itr.117.1500257360602; Sun, 16 Jul 2017 19:09:20 -0700 (PDT)
MIME-Version: 1.0
Sender: alangley@gmail.com
Received: by 10.79.38.216 with HTTP; Sun, 16 Jul 2017 19:09:20 -0700 (PDT)
From: Adam Langley <agl@imperialviolet.org>
Date: Sun, 16 Jul 2017 19:09:20 -0700
X-Google-Sender-Auth: APp13jiHlf4Tvvw9_IPDABIwWwU
Message-ID: <CAMfhd9UOFNfqoEp31r2moVaEfQZoeppP7h2Anrz0BBP518SeYA@mail.gmail.com>
To: cfrg@ietf.org
Content-Type: text/plain; charset="UTF-8"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/H_nbZXtezA-a4UeRBPDsYdW-N-M>
Subject: [Cfrg] Updated bounds in AES-GCM-SIV paper
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 17 Jul 2017 02:09:24 -0000

Dear CFRG,

We would like to thank Yannick Seurin and Tetsu Iwata for alerting us
to the fact that we had erroneously assumed that one of the terms in
the security bounds of AES-GCM-SIV was negligible when, for
indistinguishability, it was not. Thus, while the security proof was
correct, the example concrete bounds were over optimistic, most
notably for very large messages. This was most evident in Fig 4.

We have updated the paper[1] to correct this mistake and we draw the
group's attention to the revised figure four (now called Table 1). For
typical uses, thankfully, the difference is not material but for we
wish to highlight that one cannot encrypt many messages of
many-gigabytes using AES-GCM-SIV, in contrast to what the figures
previously suggested. However, even in such a case of very long
messages, the overall number of blocks encrypted safely is still
significantly higher than previous schemes.

[1] https://eprint.iacr.org/2017/168


Cheers

AGL

-- 
Adam Langley agl@imperialviolet.org https://www.imperialviolet.org


From nobody Tue Jul 18 11:29:10 2017
Return-Path: <danibrown@blackberry.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id ABEA1128CFF for <cfrg@ietfa.amsl.com>; Tue, 18 Jul 2017 11:29:08 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.601
X-Spam-Level: 
X-Spam-Status: No, score=-2.601 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id wiNbfm0V25tp for <cfrg@ietfa.amsl.com>; Tue, 18 Jul 2017 11:29:05 -0700 (PDT)
Received: from smtp-p02.blackberry.com (smtp-p02.blackberry.com [208.65.78.89]) (using TLSv1.2 with cipher RC4-SHA (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 5C8A6131BAD for <cfrg@irtf.org>; Tue, 18 Jul 2017 11:29:05 -0700 (PDT)
Received: from xct103cnc.rim.net ([10.65.161.203]) by mhs214cnc.rim.net with ESMTP/TLS/DHE-RSA-AES256-SHA; 18 Jul 2017 14:29:03 -0400
Received: from XCT112CNC.rim.net (10.65.161.212) by XCT103CNC.rim.net (10.65.161.203) with Microsoft SMTP Server (TLS) id 14.3.319.2; Tue, 18 Jul 2017 14:29:02 -0400
Received: from XMB116CNC.rim.net ([fe80::45d:f4fe:6277:5d1b]) by XCT112CNC.rim.net ([::1]) with mapi id 14.03.0319.002; Tue, 18 Jul 2017 14:29:02 -0400
From: Dan Brown <danibrown@blackberry.com>
To: Sharon Goldberg <goldbe@cs.bu.edu>, "cfrg@irtf.org" <cfrg@irtf.org>
CC: "jan@ns1.com" <jan@ns1.com>, Dimitrios Papadopoulos <dipapado@umd.edu>, Leonid Reyzin <reyzin@cs.bu.edu>
Thread-Topic: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
Thread-Index: AQHS+vM6+DG9anuMcU+xW6RwdHg7uaJZ5Flg
Date: Tue, 18 Jul 2017 18:29:02 +0000
Message-ID: <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com>
In-Reply-To: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com>
Accept-Language: en-US, en-CA
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
x-originating-ip: [10.65.160.251]
Content-Type: multipart/alternative; boundary="_000_810C31990B57ED40B2062BA10D43FBF501B63B22XMB116CNCrimnet_"
MIME-Version: 1.0
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/V7BJc30FFVMaeV0uNj8VSD7aW1o>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Tue, 18 Jul 2017 18:29:09 -0000

--_000_810C31990B57ED40B2062BA10D43FBF501B63B22XMB116CNCrimnet_
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: base64

SGkgU2hhcm9uIGFuZCBDRlJHLA0KDQpPbiBWUkZzLCBteSB1bmNlcnRhaW4gY29tbWVudHMgdG8g
Y29uc2lkZXIgYXQgeW91ciBsZWlzdXJlOg0KDQpJcyBpdCBmYWlyIHRvIHNheSBWUkZzIGFyZSBy
ZWxhdGl2ZWx5IG5ldz8gIElmIHNvLCB0aGVuIG1heWJlIGEgbGl0dGxlIG1vcmUgY2F1dGlvbiBp
cyBuZWVkZWQgYWJvdXQgdGhlaXIgdXNlLiAgSXQgc2VlbXMgYSB0YWQgaGFzdHkgdGhhdCBpdCBp
cyBiZWluZyB1c2VkIGFscmVhZHkuDQoNClRvIG1lLCBpdCBzZWVtcyB0aGF0IFZSRnMgYXJlIGJh
c2ljYWxseSBzaWduYXR1cmVzLCB3aXRoIGFuIGV4dHJhIGZlYXR1cmUuICBNeSBjb25jZXJuIGlz
IHRoYXQgdGhpcyBleHRyYSBmZWF0dXJlIG1pZ2h0IGdldCBvdmVydXNlZCwgYmVmb3JlIGl0IGlz
IHRob3JvdWdobHkgcmV2aWV3ZWQuDQoNCkl0IGlzIHVuc3VycHJpc2luZyB0byBtZSB0aGF0IHJh
bmRvbSBvcmFjbGUgbW9kZWwgcHJvb2YgY2FuIHByb3ZlIHRoZSBvdXRwdXQgb2YgYSBoYXNoIHRv
IGJlIHJhbmRvbS4gIE15IGludHVpdGl2ZSBjb25jZXJuIGlzIHRoYXQgYXQgbGVhc3QgaW5mb3Jt
YWxseSwgdGhpcyBpcyBraW5kIG9mIGNpcmN1bGFyLiAgSGFzaGVzIG9mdGVuIGhhdmUgc29tZSBu
b24tcmFuZG9tLWlzaCBwcm9wZXJ0aWVzIHRoYXQgbWlnaHQgYWZmZWN0IHRoZSBleHRyYSBzZWN1
cml0eSAob3ZlciBzaWduYXR1cmVzKSB0aGF0IFZSRnMgYXJlIGFpbWluZyBmb3IuICBJIGd1ZXNz
IEkgd291bGQgbXVjaCBwcmVmZXIgYSBwcm9vZiBzYXlpbmcgaWYgdGhlIGhhc2ggaGFzICh3ZWxs
LXN0dWRpZWQpIHByb3BlcnRpZXMgWFlaLCB0aGVuIHlvdXIgY29uc3RydWN0aW9uIGFyZSBWUkZz
LiAgKE1heWJlIHlvdSBoYXZlIHRoaXMgYWxyZWFkeT8gIElmIHNvLCB0aGVuIHRlbGwgbWUgc28u
KQ0KDQpTaW5jZSwgVlJGcyByZXF1aXJlIHNlbmRpbmcgdGhlIOKAnHByb29mc+KAnSBvbiB0aGUg
d2lyZSwgSSBmaW5kIGl0IGhhcmQgdG8gc2VlIGhvdyBpdCBjb3VsZCBiZSB1c2VkIHRvIHByZXZl
bnQgZGljdGlvbmFyeSBhdHRhY2tzLiAgSSBhc3N1bWUgdGhhdCB5b3UgYXJlIHNheWluZyB0aGUg
cHJvb2ZzIG11c3QgYmUgZW5jcnlwdGVkIHdoZW4gb25lIG5lZWRzIHRvIGF2b2lkIGRpY3Rpb25h
cnkgbW9kZWxzPyAgSSBzdXBwb3NlIGFsbCB0aGUgZGV0YWlscyBhcmUgdGhlcmUgaW4gSS1EIGFu
ZCBwYXBlcnMsIGJ1dCBmb3Igbm93LCBJIGFtIGNvbmZ1c2VkIGFib3V0IHRoZSB0aHJlYXQgbW9k
ZWwgKHdoaWNoIHBhcnRpZXMgaGF2ZSBrZXlzLCBldGMuLCBpZiB0aGV5IHJlcXVpcmUgYSBzZWN1
cmUgY2hhbm5lbCBhbmQgbXV0dWFsIHRydXN0LCB3aHkganVzdCB1c2UgcGxhaW4gb2xkIGhhc2gs
4oCmKS4gVG8gcmVzaXN0IGRpY3Rpb25hcnkgYXR0YWNrcywgd2VyZSBhbHJlYWR5IGhhdmUgUEFL
RXMgYW5kIFBCSGFzaGluZy4gIE5vdyB0aGlzPw0KDQpGaW5hbGx5LCBvbiBhIGJpa2VzaGVkLWNv
bG9yaW5nIG5vdGUsIEkgb2JqZWN0IHRvIHRoZSBuYW1lIOKAnHZlcmlmaWFibGUgcmFuZG9tIGZ1
bmN0aW9u4oCdLCBvbiBzZXZlcmFsIGdyb3VuZHMuDQoNCg0KICAxLiAgSXQgaXMgbm90IGEgZnVu
Y3Rpb24uICBJdCBpcyBhdCBsZWFzdCBmb3VyIGZ1bmN0aW9ucywga2V5Z2VuLCBzaWduLCB2ZXJp
ZnksIGFuZCBoYXNoaWZ5Lg0KICAyLiAgSWYgeW91IG1ha2UgaXQgaW50byBhIGtleWVkIGZ1bmN0
aW9uIEZfc2sobSksIGFzIGluIHByb29mdG9oYXNoKHNpZ25fc2sobSkpLCBpdCBpcyBub3QgdmVy
aWZpYWJsZS4NCiAgMy4gIFZlcmlmaWNhdGlvbiByZXF1aXJlcyB0aGUgaW50ZXJtZWRpYXRlIHBy
b29mLCB3aGljaCBpcyBjZXJ0YWlubHkgbm90IGV2ZW4gcHNldWRvcmFuZG9tIChpdCBpcyBlYXN5
IHRvIGRpc3Rpbmd1aXNoIHZhbGlkIHNpZ25hdHVyZXMgZnJvbSByYW5kb20pLg0KICA0LiAgSXQg
aXMgcHNldWRvcmFuZG9tLCBub3QgcmFuZG9tLiAgKFRoZSBrZXlzIGFyZSByYW5kb20sIGJ1dCBt
YW55IGNyeXB0byBoYXMga2V5cywgd2l0aG91dCBoYXZpbmcg4oCccmFuZG9t4oCdIGluIGl0cyBu
YW1lOiBlbmNyeXB0aW9uLCBNQUMsIHNpZ25hdHVyZXMsIGtleSBleGNoYW5nZSwg4oCmLCB0aGV5
IGFsc28gZG9u4oCZdCB2ZXJpZmlhYmxlIG9yIHJhbmRvbSBpbiB0aGVpciBuYW1lcyBlaXRoZXIu
KQ0KICA1LiAgVGhlIHNpbWlsYXIgcGhyYXNlIOKAnHZlcmlmaWFibHkgcmFuZG9t4oCdLCBhbGJl
aXQgYXMgYSBtaXNub21lciwgaGFzIHBhc3QgcHJlY2VkZW50cywgc2VlIE5JU1QgUC0yNTYgYW5k
IEJyYWlucG9vbCwgZXRjLiAgV2hlbiBJIHNlZSBWUkYsIEkgdGhpbmsgYSBmdW5jdGlvbiwgdGhh
dCBhaW1zIHRvIFZSIGluIHRoYXQgc2Vuc2UsIGFuZCBncmVhdCwgbm93IHdlIGNhbiBpbXByb3Zl
IG9uIEJyYWlucG9vbCwgZXRjLg0KICA2LiAg4oCcUmFuZG9tIGZ1bmN0aW9u4oCdIHNob3VsZCBi
ZSByZXNlcnZlZCBmb3IgdGhlIGlkZWFsIHJhbmRvbSBtYXBwaW5nIGNvbmNlcHQsIGZvciBleGFt
cGxlLCBhcyBzdHVkaWVkIGJ5IEZsYWpvbGV0LU9kbHl6a28gKG9rIHRoZXkgb25seSBzdHVkaWVk
IHRoZSBjYXNlIG9mIGVxdWFsIHNpemUgZG9tYWluIGFuZCByYW5nZSkuICBUaGUgcmFuZG9tIG9y
YWNsZSBtb2RlbCwgaXMgdGhlIGlkZWEgb2YgYXBwcm94aW1hdGluZyB0aGlzIGlkZWFsLCBldGMu
ICBBbiBhY3R1YWwgYXBwcm94aW1hdGlvbiBzaG91bGQgbm90IGJlIG5hbWUgYXMgdGhlIGlkZWFs
IChzb3JyeSwgSeKAmW0ga2luZCBvZiByZXBlYXRpbmcgbXkgcG9pbnQgNCkuDQoNClBsZWFzZSBm
b3JnaXZlIHRoZSBmYWN0IHRoYXQgbXkgY29tbWVudHMgYWJvdmUgYXJlIG5vdCB2ZXJ5IGNvbnN0
cnVjdGl2ZSAob3IgaWYgdGhlIHRvbmUgaXMgd3JvbmcpLiAgVGhpcyBpcyBhIG5ldyB0b3BpYyBm
b3IgbWUsIHNvIEkgYW0gcmVsdWN0YW50IHRvbyBtYW55IHN1Z2dlc3Rpb25zLiAgTm9uZXRoZWxl
c3MsIEkgc3VnZ2VzdCAoMCkgd2FpdGluZyBhIGxpdHRsZSwgKDEpIGEgbm9uLXJhbmRvbS1vcmFj
bGUgc2VjdXJpdHkgcHJvb2YgKGlmIHlvdSBkb27igJl0IGhhdmUgaXQgeWV0KSwgKDIpIHJlLW5h
bWluZyB0aGUgc2NoZW1lIHRvIHNvbWV0aGluZyBsaWtlIHJlLWhhc2hhYmxlIChvciBkaWdlc3Rp
YmxlKSBzaWduYXR1cmVzIChhbmQgcmUtbmFtZSB0aGUgdmFyaW91cyBwYXJ0cywgaS5lLiBwcm9v
ZiAtPiBzaWduYXR1cmUsIGV0Yy4pLg0KDQpCZXN0IHJlZ2FyZHMsDQoNCkRhbg0KDQoNCkZyb206
IENmcmcgW21haWx0bzpjZnJnLWJvdW5jZXNAaXJ0Zi5vcmddIE9uIEJlaGFsZiBPZiBTaGFyb24g
R29sZGJlcmcNClNlbnQ6IFdlZG5lc2RheSwgSnVseSAxMiwgMjAxNyA1OjQyIEFNDQpUbzogY2Zy
Z0BpcnRmLm9yZw0KQ2M6IGphbkBuczEuY29tOyBEaW1pdHJpb3MgUGFwYWRvcG91bG9zIDxkaXBh
cGFkb0B1bWQuZWR1PjsgTGVvbmlkIFJleXppbiA8cmV5emluQGNzLmJ1LmVkdT4NClN1YmplY3Q6
IFtDZnJnXSBkcmFmdC1nb2xkYmUtdnJmOiBWZXJpZmlhYmxlIFJhbmRvbSBGdW5jdGlvbnMNCg0K
RGVhciBDRlJHLA0KDQpJJ20gcHJlc2VudGluZyBhdCBuZXh0IHdlZWsncyBtZWV0aW5nIG9uIFZl
cmlmaWFibGUgUmFuZG9tIEZ1bmN0aW9ucy4gQSBWUkYgaXMgdGhlIHB1YmxpYy1rZXkgdmVyc2lv
biBvZiBrZXllZCBjcnlwdG9ncmFwaGljIGhhc2guIE9ubHkgdGhlIGhvbGRlciBvZiB0aGUgVlJG
IHNlY3JldCBrZXkgY2FuIGNvbXB1dGUgdGhlIGhhc2gsIGJ1dCBhbnlvbmUgd2l0aCB0aGUgcHVi
bGljIGtleSBjYW4gdmVyaWZ5IGl0LiAgVlJGcyBjYW4gYmUgdXNlZCB0byBwcmV2ZW50IGRpY3Rp
b25hcnkgYXR0YWNrcyBvbiBoYXNoLWJhc2VkIGRhdGEgc3RydWN0dXJlcywgYW5kIGhhdmUgYXBw
bGljYXRpb25zIHRvIGtleSB0cmFuc3BhcmVuY3kgKENPTklLUyksIEROU1NFQyAoTlNFQzUpLCBh
bmQgY3J5cHRvY3VycmVuY2llcyAoQWxnb3JhbmQpLg0KDQpJbiBhZHZhbmNlIG9mIHRoZSBtZWV0
aW5nLCBwbGVhc2Ugc2VlOg0KDQoxKSBPdXIgc3Vic3RhbnRpYWxseSB1cGRhdGVkIC0wMSBkcmFm
dDoNCmh0dHBzOi8vZGF0YXRyYWNrZXIuaWV0Zi5vcmcvZG9jL2RyYWZ0LWdvbGRiZS12cmYvDQoN
CjIpIE91ciBwcm9qZWN0IHBhZ2UsIHdpdGggbGlua3MgdG8gdmFyaW91cyBWUkYgaW1wbGVtZW50
YXRpb25zOg0KaHR0cHM6Ly93d3cuY3MuYnUuZWR1L35nb2xkYmUvcHJvamVjdHMvdnJmDQoNCkNv
bW1lbnRzIHdlbGNvbWUuICBUaGFua3MsDQoNClNoYXJvbg0KDQotLQ0KU2hhcm9uIEdvbGRiZXJn
DQpDb21wdXRlciBTY2llbmNlLCBCb3N0b24gVW5pdmVyc2l0eQ0KaHR0cDovL3d3dy5jcy5idS5l
ZHUvfmdvbGRiZQ0K

--_000_810C31990B57ED40B2062BA10D43FBF501B63B22XMB116CNCrimnet_
Content-Type: text/html; charset="utf-8"
Content-Transfer-Encoding: base64
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--_000_810C31990B57ED40B2062BA10D43FBF501B63B22XMB116CNCrimnet_--


From nobody Tue Jul 18 11:37:33 2017
Return-Path: <bascule@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 9034812F299 for <cfrg@ietfa.amsl.com>; Tue, 18 Jul 2017 11:37:32 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.699
X-Spam-Level: 
X-Spam-Status: No, score=-2.699 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id Sv0bLX6Ml5xX for <cfrg@ietfa.amsl.com>; Tue, 18 Jul 2017 11:37:31 -0700 (PDT)
Received: from mail-yw0-x235.google.com (mail-yw0-x235.google.com [IPv6:2607:f8b0:4002:c05::235]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 2D54B129B35 for <cfrg@irtf.org>; Tue, 18 Jul 2017 11:37:31 -0700 (PDT)
Received: by mail-yw0-x235.google.com with SMTP id y186so9761096ywc.1 for <cfrg@irtf.org>; Tue, 18 Jul 2017 11:37:31 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=fIs9mRoCp8OXtZODjnmYDZSNZw3pca2UN+mVwQpCZGA=; b=a/T3qJvSYyoSNS5TSNvnGQBU/NJtknaSzHs6RDaoZ7tDDhKv9YQ5YzW+ph2bKxxkmq 0LKwDI9DMWa+a4O0N8cfGl4gDGfej43m9Si17BNc7A7b9DIOzD6/erm430XkL+i2P8B4 MAGbXyiNXWxrnMuVsbzK9iO/zuNIoUvkfGFnNHF+owWRF+A26nF+om33FRCHxHK+xdCd 4eNKxErnm/sLcWHT3Rb6fA0qg0akuGvf5tTdQro/GdAakuy8vknvmEmxN9vicO0M1Iqy ygLlay4CD54It9ShYMy2uGJt8axjgmuT/QZpPrN/N02/pHScRsQjMs/mH3dh8B2u9E+A UMuA==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=fIs9mRoCp8OXtZODjnmYDZSNZw3pca2UN+mVwQpCZGA=; b=sEvOSIU4gWqhDIwPtOtDBV/rJ5EW9fp2ZvKNvjXFprnvy9C//8DpCDCLecsvn4hb2n Iw8E4ahpe0oQ1wwGGq415daK5qXYvpnmlqioHfJOsqa19+UhssFSwdR//OrJOk+xVAOv 2GIc5Y0UVKXUT8tROQRLv431PAfuvWe7m+NqvnPJKCoAoJgzirV7YPQmsNRny/JLnS3D SE5BGQz/kARyy9fwjvkIEbyHRs2PzVdjuqmUEpxKCdZiCND+8yqQ48JsQAwgh57DClem B9qqoowRHkYvRvQ5qgk/wGKYqL0a9uhXy1ju6WFfV6AJlxYGqxPiEXUoGJgvlRnfjdk8 XXwA==
X-Gm-Message-State: AIVw113P35aJEJ8sxrAIAH4IG4Y37Zuibv0vrCsMfbRpjW3DEchDCEgX WT6l8CjxCGB+Urx4zLaucavILEJRjg==
X-Received: by 10.129.53.205 with SMTP id c196mr2311279ywa.38.1500403050190; Tue, 18 Jul 2017 11:37:30 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.37.170.132 with HTTP; Tue, 18 Jul 2017 11:37:09 -0700 (PDT)
In-Reply-To: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com>
From: Tony Arcieri <bascule@gmail.com>
Date: Tue, 18 Jul 2017 11:37:09 -0700
Message-ID: <CAHOTMVJ3v1xUm0fDXq6gy7hgUv1hLYO7ny=mwC4FskW6s68q3Q@mail.gmail.com>
To: Sharon Goldberg <goldbe@cs.bu.edu>
Cc: "cfrg@irtf.org" <cfrg@irtf.org>, jan@ns1.com, Dimitrios Papadopoulos <dipapado@umd.edu>,  Leonid Reyzin <reyzin@cs.bu.edu>
Content-Type: multipart/alternative; boundary="001a114224c6d3b48005549bce86"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/yp1n19igcohM8hQsEOP2wXVdc2w>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Tue, 18 Jul 2017 18:37:32 -0000

--001a114224c6d3b48005549bce86
Content-Type: text/plain; charset="UTF-8"

Just a quick note on section 5.4.1, and perhaps a question to the chairs:

Would it be worth it for the CFRG to specify standard schemes for hashing
to elliptic curve points? This draft talks about both the "hash and pray"
method (5.4.1.1) then also the Icart method as well as Elligator (5.4.1.2).

This seems like a common enough problem it'd be nice to have off-the-shelf
solutions for it, rather than every higher level protocol having to specify
their own.

--
Tony Arcieri

--001a114224c6d3b48005549bce86
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Just a quick note on section 5.4.1, and perhaps a question=
 to the chairs:<div><br></div>Would it be worth it for the CFRG to specify =
standard schemes for hashing to elliptic curve points? This draft talks abo=
ut both the &quot;hash and pray&quot; method (5.4.1.1) then also the Icart =
method as well as Elligator (5.4.1.2).<div><br></div><div>This seems like a=
 common enough problem it&#39;d be nice to have off-the-shelf solutions for=
 it, rather than every higher level protocol having to specify their own.<b=
r><br>--<br>Tony Arcieri</div></div>

--001a114224c6d3b48005549bce86--


From nobody Tue Jul 18 11:51:23 2017
Return-Path: <internet-drafts@ietf.org>
X-Original-To: cfrg@ietf.org
Delivered-To: cfrg@ietfa.amsl.com
Received: from ietfa.amsl.com (localhost [IPv6:::1]) by ietfa.amsl.com (Postfix) with ESMTP id B3D8612EC11; Tue, 18 Jul 2017 11:51:21 -0700 (PDT)
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: 7bit
From: internet-drafts@ietf.org
To: <i-d-announce@ietf.org>
Cc: cfrg@ietf.org
X-Test-IDTracker: no
X-IETF-IDTracker: 6.56.0
Auto-Submitted: auto-generated
Precedence: bulk
Message-ID: <150040388169.11304.11188669832144366187@ietfa.amsl.com>
Date: Tue, 18 Jul 2017 11:51:21 -0700
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/S0qjrTh3aqcSOm2pnBSDl9Qof9w>
Subject: [Cfrg] I-D Action: draft-irtf-cfrg-augpake-08.txt
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Tue, 18 Jul 2017 18:51:22 -0000

A New Internet-Draft is available from the on-line Internet-Drafts directories.
This draft is a work item of the Crypto Forum of the IETF.

        Title           : Augmented Password-Authenticated Key Exchange (AugPAKE)
        Authors         : SeongHan Shin
                          Kazukuni Kobara
	Filename        : draft-irtf-cfrg-augpake-08.txt
	Pages           : 20
	Date            : 2017-07-18

Abstract:
   This document describes a secure and highly-efficient augmented
   password-authenticated key exchange (AugPAKE) protocol where a user
   remembers a low-entropy password and its verifier is registered in
   the intended server.  In general, the user's password is chosen from
   a small set of dictionary, making the password susceptible to offline
   dictionary attacks.  The AugPAKE protocol described here is secure
   against passive attacks, active attacks and offline dictionary
   attacks (on the obtained messages with passive/active attacks).
   Also, this protocol provides resistance to server compromise in the
   context that an attacker, who obtained the password verifier from the
   server, must at least perform offline dictionary attacks to gain any
   advantage in impersonating the user.  The AugPAKE protocol is not
   only provably secure in the random oracle model but also the most
   efficient over the previous augmented PAKE protocols (SRP and AMP).


The IETF datatracker status page for this draft is:
https://datatracker.ietf.org/doc/draft-irtf-cfrg-augpake/

There are also htmlized versions available at:
https://tools.ietf.org/html/draft-irtf-cfrg-augpake-08
https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-augpake-08

A diff from the previous version is available at:
https://www.ietf.org/rfcdiff?url2=draft-irtf-cfrg-augpake-08


Please note that it may take a couple of minutes from the time of submission
until the htmlized version and diff are available at tools.ietf.org.

Internet-Drafts are also available by anonymous FTP at:
ftp://ftp.ietf.org/internet-drafts/


From nobody Wed Jul 19 00:55:16 2017
Return-Path: <Kenny.Paterson@rhul.ac.uk>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id AA4EE131C07 for <cfrg@ietfa.amsl.com>; Wed, 19 Jul 2017 00:55:14 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -4.7
X-Spam-Level: 
X-Spam-Status: No, score=-4.7 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, RCVD_IN_DNSWL_NONE=-0.0001, RCVD_IN_MSPIKE_H2=-2.8, SPF_HELO_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=rhul.onmicrosoft.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id HFi7jjedysTp for <cfrg@ietfa.amsl.com>; Wed, 19 Jul 2017 00:55:12 -0700 (PDT)
Received: from EUR03-DB5-obe.outbound.protection.outlook.com (mail-eopbgr40081.outbound.protection.outlook.com [40.107.4.81]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id F3F10131C08 for <cfrg@irtf.org>; Wed, 19 Jul 2017 00:55:09 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=rhul.onmicrosoft.com;  s=selector1-rhul-ac-uk; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version; bh=nL8B6a2ZAvY7/D9HcncXGt0qXXcd2PY1oY5Dr9cceWE=; b=gt+z+B0C4bvoSB7g9+qeaA1k/d0KbvubHJrsiIO654CKeykNsSCiZYrCEX1rxjAqjwEuYFcd4c4Pm1Fx4E3uz1e0W13GxlQDrbFqTI6DVQbvEFDxdXro0xGa1oOumlpxBtWiY8vO5TQsz22SMzqDWi4TtL7o8YewEptAu1spDj4=
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com (10.168.2.156) by AM4PR0301MB1905.eurprd03.prod.outlook.com (10.168.2.155) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256) id 15.1.1261.13; Wed, 19 Jul 2017 07:55:07 +0000
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a]) by AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a%14]) with mapi id 15.01.1261.024; Wed, 19 Jul 2017 07:55:07 +0000
From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: Tony Arcieri <bascule@gmail.com>, Sharon Goldberg <goldbe@cs.bu.edu>
CC: "jan@ns1.com" <jan@ns1.com>, "cfrg@irtf.org" <cfrg@irtf.org>, "Leonid Reyzin" <reyzin@cs.bu.edu>, Dimitrios Papadopoulos <dipapado@umd.edu>
Thread-Topic: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
Thread-Index: AQHS+vNBkrUviGJWskGoaUVUdJgq0aJZ89OAgADv0YA=
Date: Wed, 19 Jul 2017 07:55:07 +0000
Message-ID: <D594CE8F.98ED1%kenny.paterson@rhul.ac.uk>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com> <CAHOTMVJ3v1xUm0fDXq6gy7hgUv1hLYO7ny=mwC4FskW6s68q3Q@mail.gmail.com>
In-Reply-To: <CAHOTMVJ3v1xUm0fDXq6gy7hgUv1hLYO7ny=mwC4FskW6s68q3Q@mail.gmail.com>
Accept-Language: en-GB, en-US
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
user-agent: Microsoft-MacOutlook/14.7.1.161129
authentication-results: gmail.com; dkim=none (message not signed) header.d=none;gmail.com; dmarc=none action=none header.from=rhul.ac.uk;
x-originating-ip: [31.133.132.244]
x-ms-publictraffictype: Email
x-microsoft-exchange-diagnostics: 1; AM4PR0301MB1905; 7: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
x-forefront-antispam-report: SFV:SKI; SCL:-1SFV:NSPM; SFS:(10009020)(6009001)(39400400002)(39850400002)(39450400003)(39410400002)(39840400002)(24454002)(230783001)(72206003)(36756003)(74482002)(4326008)(25786009)(6246003)(5250100002)(83506001)(38730400002)(6512007)(99286003)(54906002)(53936002)(2171002)(39060400002)(86362001)(3846002)(102836003)(6116002)(8676002)(14454004)(478600001)(7736002)(305945005)(2950100002)(66066001)(2906002)(42882006)(189998001)(54356999)(81166006)(50986999)(76176999)(8936002)(6486002)(5660300001)(229853002)(6506006)(53546010)(6436002)(4001350100001)(3660700001)(3280700002)(2900100001); DIR:OUT; SFP:1101; SCL:1; SRVR:AM4PR0301MB1905; H:AM4PR0301MB1906.eurprd03.prod.outlook.com; FPR:; SPF:None; MLV:ovrnspm; PTR:InfoNoRecords; LANG:en; 
x-ms-office365-filtering-correlation-id: 3d06a190-b11a-4c9e-cddd-08d4ce7b78e7
x-microsoft-antispam: UriScan:; BCL:0; PCL:0; RULEID:(300000500095)(300135000095)(300000501095)(300135300095)(22001)(300000502095)(300135100095)(2017030254075)(300000503095)(300135400095)(2017052603031)(201703131423075)(201703031133081)(300000504095)(300135200095)(300000505095)(300135600095)(300000506095)(300135500095); SRVR:AM4PR0301MB1905; 
x-ms-traffictypediagnostic: AM4PR0301MB1905:
x-exchange-antispam-report-test: UriScan:(236129657087228);
x-microsoft-antispam-prvs: <AM4PR0301MB1905E34CAE9710532786E68DBCA60@AM4PR0301MB1905.eurprd03.prod.outlook.com>
x-exchange-antispam-report-cfa-test: BCL:0; PCL:0; RULEID:(100000700101)(100105000095)(100000701101)(100105300095)(100000702101)(100105100095)(6040450)(601004)(2401047)(8121501046)(5005006)(2017060910075)(10201501046)(100000703101)(100105400095)(3002001)(93006095)(93001095)(6041248)(20161123555025)(201703131423075)(201702281529075)(201702281528075)(201703061421075)(201703061406153)(20161123560025)(20161123562025)(20161123564025)(20161123558100)(6072148)(100000704101)(100105200095)(100000705101)(100105500095); SRVR:AM4PR0301MB1905; BCL:0; PCL:0; RULEID:(100000800101)(100110000095)(100000801101)(100110300095)(100000802101)(100110100095)(100000803101)(100110400095)(100000804101)(100110200095)(100000805101)(100110500095); SRVR:AM4PR0301MB1905; 
x-forefront-prvs: 0373D94D15
spamdiagnosticoutput: 1:99
spamdiagnosticmetadata: NSPM
Content-Type: text/plain; charset="utf-8"
Content-ID: <0783D249EF8D224A8152ED75FDD4CAD3@eurprd03.prod.outlook.com>
Content-Transfer-Encoding: base64
MIME-Version: 1.0
X-OriginatorOrg: rhul.ac.uk
X-MS-Exchange-CrossTenant-originalarrivaltime: 19 Jul 2017 07:55:07.0214 (UTC)
X-MS-Exchange-CrossTenant-fromentityheader: Hosted
X-MS-Exchange-CrossTenant-id: 2efd699a-1922-4e69-b601-108008d28a2e
X-MS-Exchange-Transport-CrossTenantHeadersStamped: AM4PR0301MB1905
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/kq6ikDA4gSmQPWkQGmgfsZstLeg>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 19 Jul 2017 07:55:15 -0000
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From nobody Wed Jul 19 01:34:55 2017
Return-Path: <jezhu@nvidia.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 3755C131C3B for <cfrg@ietfa.amsl.com>; Wed, 19 Jul 2017 01:34:52 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.9
X-Spam-Level: 
X-Spam-Status: No, score=-1.9 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, HTML_MESSAGE=0.001, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id zS9ohKXeuXRs for <cfrg@ietfa.amsl.com>; Wed, 19 Jul 2017 01:34:50 -0700 (PDT)
Received: from nat-hk.nvidia.com (nat-hk.nvidia.com [203.18.50.4]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 4B73F131C35 for <cfrg@irtf.org>; Wed, 19 Jul 2017 01:34:50 -0700 (PDT)
Received: from hkpgpgate102.nvidia.com (Not Verified[10.18.92.9]) by nat-hk.nvidia.com id <B596f15ec0001>; Wed, 19 Jul 2017 16:18:52 +0800
Received: from HKMAIL102.nvidia.com ([10.18.16.11]) by hkpgpgate102.nvidia.com (PGP Universal service); Wed, 19 Jul 2017 01:34:47 -0700
X-PGP-Universal: processed; by hkpgpgate102.nvidia.com on Wed, 19 Jul 2017 01:34:47 -0700
Received: from HKMAIL103.nvidia.com (10.18.16.12) by HKMAIL102.nvidia.com (10.18.16.11) with Microsoft SMTP Server (TLS) id 15.0.1263.5; Wed, 19 Jul 2017 08:34:46 +0000
Received: from HKMAIL103.nvidia.com ([fe80::f5ae:f43f:ff37:8c85]) by HKMAIL103.nvidia.com ([fe80::f5ae:f43f:ff37:8c85%19]) with mapi id 15.00.1263.000; Wed, 19 Jul 2017 08:34:46 +0000
From: Jerry Zhu <jezhu@nvidia.com>
To: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: RFC 8032: Question on Side-Channel Leaks
Thread-Index: AdMAahSpyutm7k8jSgmJRdRK3qusBg==
Date: Wed, 19 Jul 2017 08:34:46 +0000
Message-ID: <6fa65bd5e4ce454ba871ddec56a87d9c@HKMAIL103.nvidia.com>
Accept-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
x-ms-exchange-transport-fromentityheader: Hosted
x-originating-ip: [10.19.219.23]
MIME-Version: 1.0
Content-Language: en-US
Content-Type: multipart/alternative; boundary="_000_6fa65bd5e4ce454ba871ddec56a87d9cHKMAIL103nvidiacom_"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/-5QI56d6ULOPYDCsLOm6BKefaf0>
Subject: [Cfrg] RFC 8032: Question on Side-Channel Leaks
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 19 Jul 2017 08:34:52 -0000

--_000_6fa65bd5e4ce454ba871ddec56a87d9cHKMAIL103nvidiacom_
Content-Type: text/plain; charset="us-ascii"
Content-Transfer-Encoding: quoted-printable

Dear RFC experts,

I am an engineer in Nvidia. When reading below statement in https://tools=
.ietf.org/html/rfc8032#section-8.1

"To make an implementation side-channel silent in this way, the modulo p =
arithmetic must not use any data-dependent branches, e.g., related to car=
ry propagation."

Does the 'modulo p' refer to a generic prime number, or the prime number =
defining GF(p) e.g. 2^255-19 for Ed25519?
I am asking this because some modulo arithmetic in  Ed25519 Sign is again=
st  L, not p.


"5.  Compute S =3D (r + k * s) mod L.  For efficiency, again reduce k mod=
ulo L first."
I think this computation shall also be side channel silent to keep confid=
entiality of k.

Could you please clarify?


Thanks
-Jerry Zhu (Ext. 41218)


-------------------------------------------------------------------------=
----------
This email message is for the sole use of the intended recipient(s) and m=
ay contain
confidential information.  Any unauthorized review, use, disclosure or di=
stribution
is prohibited.  If you are not the intended recipient, please contact the=
=20sender by
reply email and destroy all copies of the original message.
-------------------------------------------------------------------------=
----------

--_000_6fa65bd5e4ce454ba871ddec56a87d9cHKMAIL103nvidiacom_
Content-Type: text/html; charset="us-ascii"
Content-Transfer-Encoding: quoted-printable

<html xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-mi=
crosoft-com:office:office" xmlns:w=3D"urn:schemas-microsoft-com:office:wo=
rd" xmlns:m=3D"http://schemas.microsoft.com/office/2004/12/omml" xmlns=3D=
"http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3Dus-asci=
i">
<meta name=3D"Generator" content=3D"Microsoft Word 15 (filtered medium)">=

<style><!--
/* Font Definitions */
@font-face
=09{font-family:"Cambria Math";
=09panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
=09{font-family:\7B49\7EBF;
=09panose-1:2 1 6 0 3 1 1 1 1 1;}
@font-face
=09{font-family:Calibri;
=09panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
=09{font-family:"\@\7B49\7EBF";
=09panose-1:2 1 6 0 3 1 1 1 1 1;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
=09{margin:0in;
=09margin-bottom:.0001pt;
=09font-size:11.0pt;
=09font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
=09{mso-style-priority:99;
=09color:#0563C1;
=09text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
=09{mso-style-priority:99;
=09color:#954F72;
=09text-decoration:underline;}
pre
=09{mso-style-priority:99;
=09mso-style-link:"HTML Preformatted Char";
=09margin:0in;
=09margin-bottom:.0001pt;
=09font-size:10.0pt;
=09font-family:"Courier New";}
span.EmailStyle17
=09{mso-style-type:personal-compose;
=09font-family:"Calibri",sans-serif;
=09color:windowtext;}
span.HTMLPreformattedChar
=09{mso-style-name:"HTML Preformatted Char";
=09mso-style-priority:99;
=09mso-style-link:"HTML Preformatted";
=09font-family:"Courier New";}
.MsoChpDefault
=09{mso-style-type:export-only;
=09font-family:"Calibri",sans-serif;}
@page WordSection1
=09{size:8.5in 11.0in;
=09margin:1.0in 1.25in 1.0in 1.25in;}
div.WordSection1
=09{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext=3D"edit" spidmax=3D"1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext=3D"edit">
<o:idmap v:ext=3D"edit" data=3D"1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang=3D"EN-US" link=3D"#0563C1" vlink=3D"#954F72">
<div class=3D"WordSection1">
<p class=3D"MsoNormal">Dear RFC experts,<o:p></o:p></p>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
<p class=3D"MsoNormal">I am an engineer in Nvidia. When reading below sta=
tement in <a href=3D"https://tools.ietf.org/html/rfc8032#section-8.1">
https://tools.ietf.org/html/rfc8032#section-8.1</a><o:p></o:p></p>
<pre>&#8220;<span style=3D"color:black">To make an implementation side-ch=
annel silent in this way, the <span style=3D"background:yellow;mso-highli=
ght:yellow">modulo p</span> arithmetic must not use any data-dependent br=
anches, e.g., related to carry propagation.&#8221;<o:p></o:p></span></pre=
>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
<p class=3D"MsoNormal">Does the &#8216;modulo p&#8217; refer to a generic=
=20prime number, or the prime number defining GF(p) e.g. 2^255-19 for Ed2=
5519?<o:p></o:p></p>
<p class=3D"MsoNormal">I am asking this because some modulo arithmetic in=
=20&nbsp;Ed25519 Sign is against&nbsp; L, not p.<o:p></o:p></p>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
<pre>&#8220;<span style=3D"color:black">5.&nbsp; Compute S =3D (r &#43; k=
=20* s) mod L.&nbsp; For efficiency, again reduce k modulo L first.&#8221=
;<o:p></o:p></span></pre>
<p class=3D"MsoNormal">I think this computation shall also be side channe=
l silent to keep confidentiality of k.<o:p></o:p></p>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
<p class=3D"MsoNormal">Could you please clarify?<o:p></o:p></p>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
<p class=3D"MsoNormal"><span style=3D"font-size:12.0pt;color:#1F497D">Tha=
nks<o:p></o:p></span></p>
<p class=3D"MsoNormal"><b><span style=3D"font-size:12.0pt;color:#1F497D">=
-Jerry Zhu (Ext. 41218)<o:p></o:p></span></b></p>
<p class=3D"MsoNormal"><o:p>&nbsp;</o:p></p>
</div>

<DIV>
<HR>
</DIV>
<DIV>This email message is for the sole use of the intended recipient(s) =
and may=20
contain confidential information.&nbsp; Any unauthorized review, use, dis=
closure=20
or distribution is prohibited.&nbsp; If you are not the intended recipien=
t,=20
please contact the sender by reply email and destroy all copies of the or=
iginal=20
message. </DIV>
<DIV>
<HR>
</DIV>
</body>
</html>

--_000_6fa65bd5e4ce454ba871ddec56a87d9cHKMAIL103nvidiacom_--


From nobody Wed Jul 19 03:02:41 2017
Return-Path: <ilariliusvaara@welho.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 4810C131C78 for <cfrg@ietfa.amsl.com>; Wed, 19 Jul 2017 03:02:36 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.9
X-Spam-Level: 
X-Spam-Status: No, score=-1.9 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, RCVD_IN_DNSWL_NONE=-0.0001, RP_MATCHES_RCVD=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id yxlaTUDKLbpJ for <cfrg@ietfa.amsl.com>; Wed, 19 Jul 2017 03:02:31 -0700 (PDT)
Received: from welho-filter3.welho.com (welho-filter3.welho.com [83.102.41.25]) by ietfa.amsl.com (Postfix) with ESMTP id C93A112F24E for <cfrg@irtf.org>; Wed, 19 Jul 2017 03:02:30 -0700 (PDT)
Received: from localhost (localhost [127.0.0.1]) by welho-filter3.welho.com (Postfix) with ESMTP id 79EEF223D1; Wed, 19 Jul 2017 13:02:28 +0300 (EEST)
X-Virus-Scanned: Debian amavisd-new at pp.htv.fi
Received: from welho-smtp1.welho.com ([IPv6:::ffff:83.102.41.84]) by localhost (welho-filter3.welho.com [::ffff:83.102.41.25]) (amavisd-new, port 10024) with ESMTP id dRm-me5nixsy; Wed, 19 Jul 2017 13:02:27 +0300 (EEST)
Received: from LK-Perkele-VII (87-92-19-27.bb.dnainternet.fi [87.92.19.27]) (using TLSv1 with cipher ECDHE-RSA-AES256-SHA (256/256 bits)) (No client certificate requested) by welho-smtp1.welho.com (Postfix) with ESMTPSA id 8794A286; Wed, 19 Jul 2017 13:02:25 +0300 (EEST)
Date: Wed, 19 Jul 2017 13:02:25 +0300
From: Ilari Liusvaara <ilariliusvaara@welho.com>
To: Jerry Zhu <jezhu@nvidia.com>
Cc: "cfrg@irtf.org" <cfrg@irtf.org>
Message-ID: <20170719100225.wwaazm7f3mxz3aca@LK-Perkele-VII>
References: <6fa65bd5e4ce454ba871ddec56a87d9c@HKMAIL103.nvidia.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Disposition: inline
In-Reply-To: <6fa65bd5e4ce454ba871ddec56a87d9c@HKMAIL103.nvidia.com>
User-Agent: NeoMutt/20170609 (1.8.3)
Sender: ilariliusvaara@welho.com
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/DuALG8BcFG7Lki7NHWkCgIJbs-0>
Subject: Re: [Cfrg] RFC 8032: Question on Side-Channel Leaks
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 19 Jul 2017 10:02:36 -0000

On Wed, Jul 19, 2017 at 08:34:46AM +0000, Jerry Zhu wrote:
> Dear RFC experts,
> 
> I am an engineer in Nvidia. When reading below statement in https://tools.ietf.org/html/rfc8032#section-8.1
> 
> "To make an implementation side-channel silent in this way, the modulo p arithmetic must not use any data-dependent branches, e.g., related to carry propagation."
> 
> Does the 'modulo p' refer to a generic prime number, or the prime number defining GF(p) e.g. 2^255-19 for Ed25519?
> I am asking this because some modulo arithmetic in  Ed25519 Sign is against  L, not p.

> 
> "5.  Compute S = (r + k * s) mod L.  For efficiency, again reduce k modulo L first."
> I think this computation shall also be side channel silent to keep confidentiality of k.
> 
> Could you please clarify?
> 

Looks like the section concentrates on elliptic curves and forgets
the scalar (mod L) computations.

However, there are much less computations modulo L than mod p. So even
relatively dumb implemenantion does not affect speed very much.

k is AFAIK not secret.



The way I coded the mod L calculations was:

- The multiplication and addition are ordinary integer operations, done
  on constant number of words for being constant-time.
- There are specialized routines for partially reducing from "double
  width" (e.g., 512 bits for 25519) to "single width" (e.g., 255 bits).
- Then there is specialized full reduction routine (e.g., from 256 bits
  to ~252 bits).

The ladder the code uses to reduce numbers uses the following:

Let L = 2^252 + k.

Let r1 = h1 * 2^252 + l1

Then r1 = l1 - k * h1 = x1*L + l1 - k * h1 (mod L).

Choose x1 to be big enough so that the expression is always positive.

Let r2 = h2 * 2^256 + l2

Then r2 = l2 - 16k * h2 = x2*L + l2 - 16k * h2 (mod L).

Choose x2 to be big enough so that the expression is always positive.



Let L = 2^446 - k.

Let r3 = h3 * 2^446 + l3

Then r3 = l3 + k * h3 (mod L).

Let r4 = h4 * 2^448 + l4

Then r4 = l4 + 4k * h4 (mod L).


These formulas rather rapidly can reduce the numbers, eliminating
half of the bits in about three rounds, with the last round having
single-word multiplication.

For full reductions, one needs one round followed by conditional
substraction (which takes some care to do in constant time).



-Ilari


From nobody Wed Jul 19 23:28:31 2017
Return-Path: <jezhu@nvidia.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 6F88B129B34 for <cfrg@ietfa.amsl.com>; Wed, 19 Jul 2017 23:28:24 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.902
X-Spam-Level: 
X-Spam-Status: No, score=-1.902 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id WeviSIB3we22 for <cfrg@ietfa.amsl.com>; Wed, 19 Jul 2017 23:28:20 -0700 (PDT)
Received: from nat-hk.nvidia.com (nat-hk.nvidia.com [203.18.50.4]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 6E6891289B0 for <cfrg@irtf.org>; Wed, 19 Jul 2017 23:28:20 -0700 (PDT)
Received: from hkpgpgate102.nvidia.com (Not Verified[10.18.92.9]) by nat-hk.nvidia.com id <B59704d7f0000>; Thu, 20 Jul 2017 14:28:15 +0800
Received: from HKMAIL104.nvidia.com ([10.18.16.13]) by hkpgpgate102.nvidia.com (PGP Universal service); Wed, 19 Jul 2017 23:28:18 -0700
X-PGP-Universal: processed; by hkpgpgate102.nvidia.com on Wed, 19 Jul 2017 23:28:18 -0700
Received: from HKMAIL103.nvidia.com (10.18.16.12) by HKMAIL104.nvidia.com (10.18.16.13) with Microsoft SMTP Server (TLS) id 15.0.1263.5; Thu, 20 Jul 2017 06:28:16 +0000
Received: from HKMAIL103.nvidia.com ([fe80::f5ae:f43f:ff37:8c85]) by HKMAIL103.nvidia.com ([fe80::f5ae:f43f:ff37:8c85%19]) with mapi id 15.00.1263.000; Thu, 20 Jul 2017 06:28:16 +0000
From: Jerry Zhu <jezhu@nvidia.com>
To: "ilariliusvaara@welho.com" <ilariliusvaara@welho.com>
CC: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] RFC 8032: Question on Side-Channel Leaks
Thread-Index: AdMAahSpyutm7k8jSgmJRdRK3qusBgADApWAACrHtzA=
Date: Thu, 20 Jul 2017 06:28:16 +0000
Message-ID: <ef5c39e7ac904c0f806eb2a3be1f0384@HKMAIL103.nvidia.com>
References: <6fa65bd5e4ce454ba871ddec56a87d9c@HKMAIL103.nvidia.com> <20170719100225.wwaazm7f3mxz3aca@LK-Perkele-VII>
In-Reply-To: <20170719100225.wwaazm7f3mxz3aca@LK-Perkele-VII>
Accept-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
x-ms-exchange-transport-fromentityheader: Hosted
x-originating-ip: [10.18.19.222]
MIME-Version: 1.0
Content-Language: en-US
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: base64
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/gNmBtmV4blX1VbOlw6W-BSI6fmw>
Subject: Re: [Cfrg] RFC 8032: Question on Side-Channel Leaks
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Thu, 20 Jul 2017 06:28:24 -0000
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From nobody Thu Jul 20 01:08:05 2017
Return-Path: <ilariliusvaara@welho.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 25D12126B72 for <cfrg@ietfa.amsl.com>; Thu, 20 Jul 2017 01:08:05 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.901
X-Spam-Level: 
X-Spam-Status: No, score=-1.901 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, RCVD_IN_DNSWL_NONE=-0.0001, RP_MATCHES_RCVD=-0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id tSuA9sez4FhY for <cfrg@ietfa.amsl.com>; Thu, 20 Jul 2017 01:08:03 -0700 (PDT)
Received: from welho-filter1.welho.com (welho-filter1.welho.com [83.102.41.23]) by ietfa.amsl.com (Postfix) with ESMTP id 23840126557 for <cfrg@irtf.org>; Thu, 20 Jul 2017 01:08:03 -0700 (PDT)
Received: from localhost (localhost [127.0.0.1]) by welho-filter1.welho.com (Postfix) with ESMTP id 57FE06586C; Thu, 20 Jul 2017 11:08:01 +0300 (EEST)
X-Virus-Scanned: Debian amavisd-new at pp.htv.fi
Received: from welho-smtp3.welho.com ([IPv6:::ffff:83.102.41.86]) by localhost (welho-filter1.welho.com [::ffff:83.102.41.23]) (amavisd-new, port 10024) with ESMTP id IYS2Q51SsDxJ; Thu, 20 Jul 2017 11:08:01 +0300 (EEST)
Received: from LK-Perkele-VII (87-92-19-27.bb.dnainternet.fi [87.92.19.27]) (using TLSv1 with cipher ECDHE-RSA-AES256-SHA (256/256 bits)) (No client certificate requested) by welho-smtp3.welho.com (Postfix) with ESMTPSA id 1341A2313; Thu, 20 Jul 2017 11:07:59 +0300 (EEST)
Date: Thu, 20 Jul 2017 11:07:58 +0300
From: Ilari Liusvaara <ilariliusvaara@welho.com>
To: Jerry Zhu <jezhu@nvidia.com>
Cc: "cfrg@irtf.org" <cfrg@irtf.org>
Message-ID: <20170720080758.hp6mps4q5u2m54e7@LK-Perkele-VII>
References: <6fa65bd5e4ce454ba871ddec56a87d9c@HKMAIL103.nvidia.com> <20170719100225.wwaazm7f3mxz3aca@LK-Perkele-VII> <ef5c39e7ac904c0f806eb2a3be1f0384@HKMAIL103.nvidia.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Disposition: inline
In-Reply-To: <ef5c39e7ac904c0f806eb2a3be1f0384@HKMAIL103.nvidia.com>
User-Agent: NeoMutt/20170609 (1.8.3)
Sender: ilariliusvaara@welho.com
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/Og1RVCQYiFXrMNfZPXhsOegemBc>
Subject: Re: [Cfrg] RFC 8032: Question on Side-Channel Leaks
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Thu, 20 Jul 2017 08:08:05 -0000

On Thu, Jul 20, 2017 at 06:28:16AM +0000, Jerry Zhu wrote:
> Hi Ilari,
> 
> Appreciate your response and sample implementation. 
> Isn't there repudiation risk if k is leaked to adversary?

k is computable from context[1], message, signature and the public
key. And in fact, k is reconstructed in signature verification.


[1] Contexts turn out to be pretty much useless except for generating
time-wasting discussion...


-Ilari


From nobody Thu Jul 20 01:34:18 2017
Return-Path: <jezhu@nvidia.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 0C208131B09 for <cfrg@ietfa.amsl.com>; Thu, 20 Jul 2017 01:34:17 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.902
X-Spam-Level: 
X-Spam-Status: No, score=-1.902 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id Yt2zS_bEzmSf for <cfrg@ietfa.amsl.com>; Thu, 20 Jul 2017 01:34:15 -0700 (PDT)
Received: from nat-hk.nvidia.com (nat-hk.nvidia.com [203.18.50.4]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 7FA4213157A for <cfrg@irtf.org>; Thu, 20 Jul 2017 01:34:15 -0700 (PDT)
Received: from hkpgpgate101.nvidia.com (Not Verified[10.18.92.9]) by nat-hk.nvidia.com id <B59706b020000>; Thu, 20 Jul 2017 16:34:10 +0800
Received: from HKMAIL101.nvidia.com ([10.18.16.10]) by hkpgpgate101.nvidia.com (PGP Universal service); Thu, 20 Jul 2017 01:34:13 -0700
X-PGP-Universal: processed; by hkpgpgate101.nvidia.com on Thu, 20 Jul 2017 01:34:13 -0700
Received: from HKMAIL103.nvidia.com (10.18.16.12) by HKMAIL101.nvidia.com (10.18.16.10) with Microsoft SMTP Server (TLS) id 15.0.1263.5; Thu, 20 Jul 2017 08:34:11 +0000
Received: from HKMAIL103.nvidia.com ([fe80::f5ae:f43f:ff37:8c85]) by HKMAIL103.nvidia.com ([fe80::f5ae:f43f:ff37:8c85%19]) with mapi id 15.00.1263.000; Thu, 20 Jul 2017 08:34:11 +0000
From: Jerry Zhu <jezhu@nvidia.com>
To: "ilariliusvaara@welho.com" <ilariliusvaara@welho.com>
CC: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] RFC 8032: Question on Side-Channel Leaks
Thread-Index: AdMAahSpyutm7k8jSgmJRdRK3qusBgADApWAACrHtzAAA4OgAAAA9BDg
Date: Thu, 20 Jul 2017 08:34:11 +0000
Message-ID: <b3b7e6ee153f4ece822e17140a36878d@HKMAIL103.nvidia.com>
References: <6fa65bd5e4ce454ba871ddec56a87d9c@HKMAIL103.nvidia.com> <20170719100225.wwaazm7f3mxz3aca@LK-Perkele-VII> <ef5c39e7ac904c0f806eb2a3be1f0384@HKMAIL103.nvidia.com> <20170720080758.hp6mps4q5u2m54e7@LK-Perkele-VII>
In-Reply-To: <20170720080758.hp6mps4q5u2m54e7@LK-Perkele-VII>
Accept-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
x-ms-exchange-transport-fromentityheader: Hosted
x-originating-ip: [10.18.19.222]
MIME-Version: 1.0
Content-Language: en-US
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: base64
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/03AYe9CtFAve0DPBEcdY18wYcWc>
Subject: Re: [Cfrg] RFC 8032: Question on Side-Channel Leaks
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Thu, 20 Jul 2017 08:34:17 -0000
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From nobody Thu Jul 20 03:20:15 2017
Return-Path: <Kenny.Paterson@rhul.ac.uk>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 0799B131BFA for <cfrg@ietfa.amsl.com>; Thu, 20 Jul 2017 03:20:08 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.921
X-Spam-Level: 
X-Spam-Status: No, score=-1.921 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, RCVD_IN_DNSWL_NONE=-0.0001, RCVD_IN_MSPIKE_H3=-0.01, RCVD_IN_MSPIKE_WL=-0.01, SPF_HELO_PASS=-0.001] autolearn=unavailable autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=rhul.onmicrosoft.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id XYoWXCUVtNwW for <cfrg@ietfa.amsl.com>; Thu, 20 Jul 2017 03:20:05 -0700 (PDT)
Received: from EUR02-HE1-obe.outbound.protection.outlook.com (mail-eopbgr10057.outbound.protection.outlook.com [40.107.1.57]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 16AD6131C03 for <cfrg@irtf.org>; Thu, 20 Jul 2017 03:20:05 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=rhul.onmicrosoft.com;  s=selector1-rhul-ac-uk; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version; bh=SFuwu/H/XaZ/Kkoowjhbtof1vUvJ0xbmcaiwhb3xlMA=; b=Ne3k1J6BkJQcDWK9hu6QUxFHOhesbPexPCETU+kwTIlEbgKi1e4P0Ruj4LA94cokkDR/4JbctXONNQQeWdpoh5CvdkgNPaosctwJW76jHccbobeEh6wzLEryeUfw99VafnR5qSDBG1E6j3A6M50Nxn6M7RD1Ond/qpHMjL9RW40=
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com (10.168.2.156) by AM4PR0301MB1907.eurprd03.prod.outlook.com (10.168.3.7) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256) id 15.1.1261.13; Thu, 20 Jul 2017 10:20:01 +0000
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a]) by AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::482:61a:3f1b:be7a%14]) with mapi id 15.01.1261.024; Thu, 20 Jul 2017 10:20:01 +0000
From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: saag <saag@ietf.org>
CC: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: CFRG report from IETF99
Thread-Index: AQHTAUG/nrwJR++nlEmj0kW0KhMR2g==
Date: Thu, 20 Jul 2017 10:20:01 +0000
Message-ID: <D5964219.99079%kenny.paterson@rhul.ac.uk>
Accept-Language: en-GB, en-US
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
user-agent: Microsoft-MacOutlook/14.7.1.161129
authentication-results: ietf.org; dkim=none (message not signed) header.d=none;ietf.org; dmarc=none action=none header.from=rhul.ac.uk;
x-originating-ip: [31.133.147.39]
x-ms-publictraffictype: Email
x-microsoft-exchange-diagnostics: 1; AM4PR0301MB1907; 7: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
x-forefront-antispam-report: SFV:SKI; SCL:-1SFV:NSPM; SFS:(10009020)(979002)(6009001)(39450400003)(39840400002)(39850400002)(39400400002)(39410400002)(6436002)(7736002)(305945005)(25786009)(4001350100001)(14454004)(110136004)(38730400002)(6512007)(99286003)(8936002)(8676002)(81166006)(102836003)(6116002)(4326008)(36756003)(74482002)(3280700002)(5660300001)(2900100001)(2906002)(3660700001)(114624004)(83506001)(478600001)(6506006)(86362001)(6916009)(50986999)(3846002)(189998001)(6486002)(54356999)(53936002)(5250100002)(66066001)(72206003)(42882006)(969003)(989001)(999001)(1009001)(1019001); DIR:OUT; SFP:1101; SCL:1; SRVR:AM4PR0301MB1907; H:AM4PR0301MB1906.eurprd03.prod.outlook.com; FPR:; SPF:None; MLV:ovrnspm; PTR:InfoNoRecords; LANG:en; 
x-ms-office365-filtering-correlation-id: 3d7b4287-e68f-4c56-8cfa-08d4cf58e1e3
x-microsoft-antispam: UriScan:; BCL:0; PCL:0; RULEID:(300000500095)(300135000095)(300000501095)(300135300095)(22001)(300000502095)(300135100095)(2017030254075)(300000503095)(300135400095)(2017052603031)(201703131423075)(201703031133081)(201702281549075)(300000504095)(300135200095)(300000505095)(300135600095)(300000506095)(300135500095); SRVR:AM4PR0301MB1907; 
x-ms-traffictypediagnostic: AM4PR0301MB1907:
x-exchange-antispam-report-test: UriScan:(278178393323532)(133145235818549)(236129657087228)(148574349560750)(167848164394848);
x-microsoft-antispam-prvs: <AM4PR0301MB19079CD777E5202A13BCD70EBCA70@AM4PR0301MB1907.eurprd03.prod.outlook.com>
x-exchange-antispam-report-cfa-test: BCL:0; PCL:0; RULEID:(100000700101)(100105000095)(100000701101)(100105300095)(100000702101)(100105100095)(6040450)(601004)(2401047)(5005006)(8121501046)(2017060910075)(93006095)(93001095)(100000703101)(100105400095)(3002001)(10201501046)(6041248)(201703131423075)(201702281529075)(201702281528075)(201703061421075)(201703061406153)(20161123558100)(20161123562025)(20161123560025)(20161123564025)(20161123555025)(6072148)(100000704101)(100105200095)(100000705101)(100105500095); SRVR:AM4PR0301MB1907; BCL:0; PCL:0; RULEID:(100000800101)(100110000095)(100000801101)(100110300095)(100000802101)(100110100095)(100000803101)(100110400095)(100000804101)(100110200095)(100000805101)(100110500095); SRVR:AM4PR0301MB1907; 
x-forefront-prvs: 0374433C81
spamdiagnosticoutput: 1:99
spamdiagnosticmetadata: NSPM
Content-Type: text/plain; charset="utf-8"
Content-ID: <7D356937BBD20C4EAFDAE108E38FCAD6@eurprd03.prod.outlook.com>
Content-Transfer-Encoding: base64
MIME-Version: 1.0
X-OriginatorOrg: rhul.ac.uk
X-MS-Exchange-CrossTenant-originalarrivaltime: 20 Jul 2017 10:20:01.9159 (UTC)
X-MS-Exchange-CrossTenant-fromentityheader: Hosted
X-MS-Exchange-CrossTenant-id: 2efd699a-1922-4e69-b601-108008d28a2e
X-MS-Exchange-Transport-CrossTenantHeadersStamped: AM4PR0301MB1907
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/uafUboODJ-5-EreQpIjqOQOEdEQ>
Subject: [Cfrg] CFRG report from IETF99
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Thu, 20 Jul 2017 10:20:08 -0000
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From nobody Thu Jul 20 14:19:01 2017
Return-Path: <ietf-secretariat-reply@ietf.org>
X-Original-To: cfrg@ietf.org
Delivered-To: cfrg@ietfa.amsl.com
Received: from ietfa.amsl.com (localhost [IPv6:::1]) by ietfa.amsl.com (Postfix) with ESMTP id 67A82126DC2 for <cfrg@ietf.org>; Thu, 20 Jul 2017 14:19:00 -0700 (PDT)
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: 7bit
To: <cfrg@ietf.org>
X-Test-IDTracker: no
X-IETF-IDTracker: 6.57.0
Auto-Submitted: auto-generated
Precedence: bulk
Message-ID: <150058554042.22410.15964670819190795015.idtracker@ietfa.amsl.com>
Date: Thu, 20 Jul 2017 14:19:00 -0700
From: IETF Secretariat <ietf-secretariat-reply@ietf.org>
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/ganqiE_O10QP2gfRSsyJU2_Pw9Q>
Subject: [Cfrg] Milestones changed for cfrg RG
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Thu, 20 Jul 2017 21:19:00 -0000

Changed milestone "Submit "Hash-Based Signatures" to IRSG", set state to
active from review, accepting new milestone.

URL: https://datatracker.ietf.org/rg/cfrg/about/


From nobody Fri Jul 21 03:18:06 2017
Return-Path: <alexey.melnikov@isode.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 6FAA0129B3A for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 03:18:05 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.001
X-Spam-Level: 
X-Spam-Status: No, score=-2.001 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=isode.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id d9IJ88eV0kjE for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 03:18:04 -0700 (PDT)
Received: from waldorf.isode.com (waldorf.isode.com [62.232.206.188]) by ietfa.amsl.com (Postfix) with ESMTP id 1DD03127ABE for <cfrg@irtf.org>; Fri, 21 Jul 2017 03:18:04 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; t=1500632283; d=isode.com; s=june2016; i=@isode.com; bh=TV/OO4/R4Ns5iyJ2nuUNmHeIVTwdT/PwBB53jf6aLwY=; h=From:Sender:Reply-To:Subject:Date:Message-ID:To:Cc:MIME-Version: In-Reply-To:References:Content-Type:Content-Transfer-Encoding: Content-ID:Content-Description; b=AJd650ZKCFNowRm5MFytzvluquUJkOrjPu3FW22R7lQh0efwPhYwyu5ruBvGJSZ/r1B7jJ lHHGCh5RGZWYOliISfYxCiY8tFBB17Tm+pa8+Z/xi33PmBxat21KBX5YZY1ybXT5oXXxZG mYqfyYRdPItg4hnnRHsB6JMX3Xek5k0=;
Received: from [31.133.129.198] (dhcp-81c6.meeting.ietf.org [31.133.129.198])  by waldorf.isode.com (submission channel) via TCP with ESMTPSA  id <WXHU2gBtVZoj@waldorf.isode.com>; Fri, 21 Jul 2017 11:18:03 +0100
To: "cfrg@irtf.org" <cfrg@irtf.org>
From: Alexey Melnikov <alexey.melnikov@isode.com>
Message-ID: <5971D4DD.9030005@isode.com>
Date: Fri, 21 Jul 2017 11:18:05 +0100
User-Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:38.0) Gecko/20100101 Thunderbird/38.5.0
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-transfer-encoding: quoted-printable
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/-U81Hdjf4k11iyYZV_RAgT4pkxg>
Subject: [Cfrg] Adoption call for "Verifiable Random Functions": draft-goldbe-vrf-01
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 21 Jul 2017 10:18:05 -0000

Dear CFRG,

Based on interest in the face-to-face CFRG meeting in Prague, chairs are
starting adoption call for "Verifiable Random Functions"
<https://datatracker.ietf.org/doc/draft-goldbe-vrf/>.

Unless chairs hear some objections to taking this document as a CFRG
deliverable, the default is to work on this document in CFRG.

The adoption call will last for 3 weeks (finishing on August 11th).

Thank you,
Kenny and Alexey


From nobody Fri Jul 21 04:15:03 2017
Return-Path: <alexey.melnikov@isode.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 7923612EE45 for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 04:15:01 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.001
X-Spam-Level: 
X-Spam-Status: No, score=-2.001 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=isode.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id sJjkG0v4vkjp for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 04:15:00 -0700 (PDT)
Received: from waldorf.isode.com (waldorf.isode.com [62.232.206.188]) by ietfa.amsl.com (Postfix) with ESMTP id 05154129B7F for <cfrg@irtf.org>; Fri, 21 Jul 2017 04:15:00 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; t=1500635699; d=isode.com; s=june2016; i=@isode.com; bh=Dcgz/WEhrfr3cYUA8UTEOIFY46HxruYkiRzI2V0Sv7I=; h=From:Sender:Reply-To:Subject:Date:Message-ID:To:Cc:MIME-Version: In-Reply-To:References:Content-Type:Content-Transfer-Encoding: Content-ID:Content-Description; b=BOQX+BvrFt5LQ0R2EnMG4wTvpsZZh4sekBgfx6wyz/HgT6ao54lFx7ujUCoEG7qA7lNyVe JHsQO+wUC9wXkhgx4AxYvmNpJoS+h9LZBV2OIN0awnob+AJhTXSpWPIjkOIzOgyQYiRB+M EWN3Ezo1OPiJIxhT+GzD66vedIReEVg=;
Received: from [31.133.129.198] (dhcp-81c6.meeting.ietf.org [31.133.129.198])  by waldorf.isode.com (submission channel) via TCP with ESMTPSA  id <WXHiMgBtVaPI@waldorf.isode.com>; Fri, 21 Jul 2017 12:14:59 +0100
From: Alexey Melnikov <alexey.melnikov@isode.com>
To: "cfrg@irtf.org" <cfrg@irtf.org>
Message-ID: <5971E235.9060703@isode.com>
Date: Fri, 21 Jul 2017 12:15:01 +0100
User-Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:38.0) Gecko/20100101 Thunderbird/38.5.0
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 7bit
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/jJtodsk7GBzSaA16CvDIw9ine14>
Subject: [Cfrg] RGLC on "Hash-Based Signatures": draft-mcgrew-hash-sigs-07
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 21 Jul 2017 11:15:01 -0000

Dear CFRG participants,

This message is starting 4 weeks CFRG Last Call on "Hash-Based
Signatures" <https://datatracker.ietf.org/doc/draft-mcgrew-hash-sigs/>.
The LC is going to finish on August 18th.

Please send your comments in a reply to this message or directly to
chairs (cfrg-chairs@ietf.org). Statement of support (or not) for this
draft being submitted to IRSG for review and publication are also welcomed.

Thank you,
Kenny and Alexey



From nobody Fri Jul 21 04:26:02 2017
Return-Path: <housley@vigilsec.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 5AC2D131483 for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 04:26:01 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.899
X-Spam-Level: 
X-Spam-Status: No, score=-1.899 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id gsjppkzhS23c for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 04:25:59 -0700 (PDT)
Received: from mail.smeinc.net (mail.smeinc.net [209.135.209.11]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 880F7129B7F for <cfrg@irtf.org>; Fri, 21 Jul 2017 04:25:59 -0700 (PDT)
Received: from localhost (localhost [127.0.0.1]) by mail.smeinc.net (Postfix) with ESMTP id F35B43004FE for <cfrg@irtf.org>; Fri, 21 Jul 2017 07:25:58 -0400 (EDT)
X-Virus-Scanned: amavisd-new at mail.smeinc.net
Received: from mail.smeinc.net ([127.0.0.1]) by localhost (mail.smeinc.net [127.0.0.1]) (amavisd-new, port 10026) with ESMTP id QB7YfetS05ZQ for <cfrg@irtf.org>; Fri, 21 Jul 2017 07:25:57 -0400 (EDT)
Received: from [5.5.33.183] (vpn.snozzages.com [204.42.252.17]) by mail.smeinc.net (Postfix) with ESMTPSA id 66817300429; Fri, 21 Jul 2017 07:25:57 -0400 (EDT)
Content-Type: text/plain; charset=us-ascii
Mime-Version: 1.0 (Mac OS X Mail 10.3 \(3273\))
From: Russ Housley <housley@vigilsec.com>
In-Reply-To: <5971E235.9060703@isode.com>
Date: Fri, 21 Jul 2017 07:25:55 -0400
Cc: IRTF CFRG <cfrg@irtf.org>
Content-Transfer-Encoding: quoted-printable
Message-Id: <8EE92C2B-F484-42D4-B799-993C024DA559@vigilsec.com>
References: <5971E235.9060703@isode.com>
To: Alexey Melnikov <alexey.melnikov@isode.com>
X-Mailer: Apple Mail (2.3273)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/5OIISPvrvxD3WCmqMlgwqzEQjLs>
Subject: Re: [Cfrg] RGLC on "Hash-Based Signatures": draft-mcgrew-hash-sigs-07
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 21 Jul 2017 11:26:01 -0000

I have read the document, and I have an individual draft that depends on =
it.  I think it is ready.

Russ



> On Jul 21, 2017, at 7:15 AM, Alexey Melnikov =
<alexey.melnikov@isode.com> wrote:
>=20
> Dear CFRG participants,
>=20
> This message is starting 4 weeks CFRG Last Call on "Hash-Based
> Signatures" =
<https://datatracker.ietf.org/doc/draft-mcgrew-hash-sigs/>.
> The LC is going to finish on August 18th.
>=20
> Please send your comments in a reply to this message or directly to
> chairs (cfrg-chairs@ietf.org). Statement of support (or not) for this
> draft being submitted to IRSG for review and publication are also =
welcomed.
>=20
> Thank you,
> Kenny and Alexey


From nobody Fri Jul 21 05:01:28 2017
Return-Path: <philip.lafrance92@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 1B4F6131BB0 for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 05:01:27 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.448
X-Spam-Level: 
X-Spam-Status: No, score=-2.448 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_ENVFROM_END_DIGIT=0.25, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id pFJBpKQs-aLD for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 05:01:20 -0700 (PDT)
Received: from mail-it0-x22f.google.com (mail-it0-x22f.google.com [IPv6:2607:f8b0:4001:c0b::22f]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 4210B131A87 for <cfrg@irtf.org>; Fri, 21 Jul 2017 05:01:20 -0700 (PDT)
Received: by mail-it0-x22f.google.com with SMTP id h199so6349040ith.0 for <cfrg@irtf.org>; Fri, 21 Jul 2017 05:01:20 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:from:date:message-id:subject:to; bh=wyjmdf8Y/Qp7+LZy95p1hSu+naNUecsxStSjOQUDWOQ=; b=azGtoZr2ws5wMeGqOXZ8E7KljrU5nUkMYNoRE8crON1N6UbGhay1RTozZ7P74d8AwN ZaWyLpRX6eEnLDLTBAHQjfpmB36tggAkWmYoAAATTlSaDbEF6shvwETs67KJD/Bdrtba f7v7sptMTYItn+EVMt4zgGjltQAUk8bg8Xd04GMRxxVtGyyeK+6VbwZY/9LSu0Ni0t8O dlxQYSXr+uNjOaNY7vUcvAYQixAa+XBIXJNg20a7PqjNPvuZEpKFVXILGG4NHEpHQRQy fORq7UMRJ9cCPOwayDbyFK45sJ7vwfcx2YgaW+dMsWqBszP8PsEMhX5yZGJlWQjOAL5R CpLA==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:from:date:message-id:subject:to; bh=wyjmdf8Y/Qp7+LZy95p1hSu+naNUecsxStSjOQUDWOQ=; b=M21SN6NWihQ8FPEC2t0/lXrykMOKZ3tWB9J5AI7YPKPkyqYP+UQIMZEKo3LS/lozaJ 4iqiv9641O39ZkMmaswEk/+0Hcb/+3V47vu5Yw9feLWWe4wtqQrbfitlMv/48f7SNh31 Tordv3GUigDf9qTpP6K1ocC/aDv0vQ7D2QAIl4jnU1wHLYSV3x5uR+sXit52t8UDjUZt xLzztSAAUsGUTZ3viEp/IoF+Md4ODNws4ztz12Un/M1iTj+YcejUuUD7vj+SZ3dm7U2c G7OkWgNSNE/LIbbdGaXaCSV5xkEGWxaNJyckhmrlE8Pwm+xgbenY4GFes8wMK4/RHVOh cKNg==
X-Gm-Message-State: AIVw111YCgMOdc9Xmguo6XWYEFU606LToq+tG6ah8pfLlP4A5kN3GYgY 3P2gpIJOQ1Mz76LQFtuvLA3lGRwcgZjg
X-Received: by 10.36.4.139 with SMTP id 133mr6925607itb.142.1500638479037; Fri, 21 Jul 2017 05:01:19 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.107.189.194 with HTTP; Fri, 21 Jul 2017 05:01:18 -0700 (PDT)
From: Philip Lafrance <philip.lafrance92@gmail.com>
Date: Fri, 21 Jul 2017 08:01:18 -0400
Message-ID: <CALwqbuyti95Tvx43vvWHhnfdrHo+yNVc8GQ0B-utk+C==3-h-A@mail.gmail.com>
To: cfrg@irtf.org
Content-Type: multipart/alternative; boundary="001a113fe1e27abc4a0554d29f23"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/U1ZlyJcxeiFjjAr2tn3jEcfVu7I>
Subject: [Cfrg] Comments on draft-hoffman-c2pq-01
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 21 Jul 2017 12:01:27 -0000

--001a113fe1e27abc4a0554d29f23
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Hello all,

So I can't express enough how much I support this document.

I gave it a cursory read and prepared some remarks (see below).

Since I was up at 3am today (IPSECME meeting was at 5:50 am my time) I kind
of want to go home and sleep. So, I'll give a more detailed review sometime
next week (hopefully with some input from my quantum crypto colleagues).

Comments:

Section 1.3

            -The definition given for =E2=80=9Cpost-quantum cryptography=E2=
=80=9D is pretty
limited and kind of inaccurate. The definition as given would suggest that
ECC is post-quantum as it does not rely on factoring large numbers or
determine the discrete log of a large composite number.


Maybe something like:


 "The term "post-quantum cryptography" refers to the invention and study of
cryptographic techniques (including encryption, signature and key exchange
algorithms) that are implementable on a classical computer and are based on
problems that are believed to be difficult for a quantum computer to solve.
In particular, this includes algorithms based on lattices, isogenies,
hash-functions, multivariate polynomial systems, and coding theory. It
excludes systems whose security relies on factoring numbers, or the
difficulty of determining the discrete log of one group element with
respect to another."



Section 1.6

            -The good folks at the Institute for Quantum Computing have a
good textbook which would be a nice reference (here is a link
http://hep.fcfm.buap.mx/cursos/2014/MCI/An_Intro_to_Quantum.pdf)



Section 2.1

            -This section seems to only be concerned with using quantum
algorithms to recover secret key. Why not also mention for example using
Grover to find collisions to forge signatures?



            -We should maybe consider replacing =E2=80=9Clarge-scale=E2=80=
=9D quantum
computer with =E2=80=9Cuniversal=E2=80=9D quantum computer.



-Maybe some discussion about the differences between quantum annealing and
a universal quantum computer. This would be useful because, for example
D-Wave is a quantum annealer, not a universal quantum computer, but the
difference is lost on most people. Understanding the difference is
important if we=E2=80=99re talking about when to transition.


That's all for now.


All the best folks! Safe travels home from Prague!


-Philip Lafrance

--001a113fe1e27abc4a0554d29f23
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Hello all,<div><br></div><div>So I can&#39;t express enoug=
h how much I support this document.</div><div><br></div><div>I gave it a cu=
rsory read and prepared some remarks (see below).</div><div><br></div><div>=
Since I was up at 3am today (IPSECME meeting was at 5:50 am my time) I kind=
 of want to go home and sleep. So, I&#39;ll give a more detailed review som=
etime next week (hopefully with some input from my quantum crypto colleague=
s).</div><div><br></div><div>Comments:</div><div><br></div><div>
















<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;">Section 1.3<span></span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;">=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0=C2=A0=C2=A0 -The
definition given for =E2=80=9Cpost-quantum cryptography=E2=80=9D is pretty =
limited and kind of
inaccurate. The definition as given would suggest that ECC is post-quantum =
as
it does not rely on factoring large numbers or determine the discrete log o=
f a
large composite number.=C2=A0</span></p><p class=3D"MsoNormal" style=3D"lin=
e-height:16pt"><span style=3D"font-family:&quot;Helvetica Neue&quot;"><br><=
/span></p><p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"=
font-family:&quot;Helvetica Neue&quot;">Maybe something like:</span></p><p =
class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-family:&=
quot;Helvetica Neue&quot;"><br></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;">=C2=A0&quot;The term &quot;post-quantum crypt=
ography&quot; refers
to the invention and study of cryptographic techniques (including encryptio=
n,
signature and key exchange algorithms) that are implementable on a classica=
l
computer and are based on problems that are believed to be difficult for a
quantum computer to solve. In particular, this includes algorithms based on
lattices, isogenies, hash-functions, multivariate polynomial systems, and
coding theory. It excludes systems whose security relies on factoring numbe=
rs, or
the difficulty of determining the discrete log of one group element with
respect to another.&quot;<span></span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;"><span>=C2=A0</span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;">Section 1.6<span></span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;">=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0=C2=A0=C2=A0 -The good
folks at the Institute for Quantum Computing have a good textbook which wou=
ld
be a nice reference (here is a link <a href=3D"http://hep.fcfm.buap.mx/curs=
os/2014/MCI/An_Intro_to_Quantum.pdf">http://hep.fcfm.buap.mx/cursos/2014/MC=
I/An_Intro_to_Quantum.pdf</a>)<span></span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;"><span>=C2=A0</span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;">Section 2.1<span></span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;">=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0=C2=A0=C2=A0 -This
section seems to only be concerned with using quantum algorithms to recover
secret key. Why not also mention for example using Grover to find collision=
s to
forge signatures?<span></span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;"><span>=C2=A0</span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;">=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=
=A0=C2=A0=C2=A0=C2=A0 -We should
maybe consider replacing =E2=80=9Clarge-scale=E2=80=9D quantum computer wit=
h =E2=80=9Cuniversal=E2=80=9D
quantum computer.<span></span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;"><span>=C2=A0</span></span></p>

<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;">-Maybe some discussion about the differences =
between quantum
annealing and a universal quantum computer. This would be useful because, f=
or
example D-Wave is a quantum annealer, not a universal quantum computer, but=
 the
difference is lost on most people. Understanding the difference is importan=
t if
we=E2=80=99re talking about when to transition.<span></span></span></p><p c=
lass=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-family:&q=
uot;Helvetica Neue&quot;"><br></span></p><p class=3D"MsoNormal" style=3D"li=
ne-height:16pt"><span style=3D"font-family:&quot;Helvetica Neue&quot;">That=
&#39;s all for now.</span></p><p class=3D"MsoNormal" style=3D"line-height:1=
6pt"><span style=3D"font-family:&quot;Helvetica Neue&quot;"><br></span></p>=
<p class=3D"MsoNormal" style=3D"line-height:16pt"><span style=3D"font-famil=
y:&quot;Helvetica Neue&quot;">All the best folks! Safe travels home from Pr=
ague!</span></p><p class=3D"MsoNormal" style=3D"line-height:16pt"><span sty=
le=3D"font-family:&quot;Helvetica Neue&quot;"><br></span></p><p class=3D"Ms=
oNormal" style=3D"line-height:16pt"><span style=3D"font-family:&quot;Helvet=
ica Neue&quot;">-Philip Lafrance</span></p>

</div></div>

--001a113fe1e27abc4a0554d29f23--


From nobody Fri Jul 21 09:27:09 2017
Return-Path: <paul.hoffman@vpnc.org>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 5533C131B29 for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 09:27:07 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.899
X-Spam-Level: 
X-Spam-Status: No, score=-1.899 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id MpbJDsrBqGyc for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 09:27:05 -0700 (PDT)
Received: from mail.proper.com (Opus1.Proper.COM [207.182.41.91]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id A3EFF131891 for <cfrg@irtf.org>; Fri, 21 Jul 2017 09:27:05 -0700 (PDT)
Received: from [10.47.60.62] ([62.168.35.66]) (authenticated bits=0) by mail.proper.com (8.15.2/8.14.9) with ESMTPSA id v6LGQ8Vf051406 (version=TLSv1.2 cipher=ECDHE-RSA-AES256-GCM-SHA384 bits=256 verify=NO); Fri, 21 Jul 2017 09:26:11 -0700 (MST) (envelope-from paul.hoffman@vpnc.org)
X-Authentication-Warning: mail.proper.com: Host [62.168.35.66] claimed to be [10.47.60.62]
From: "Paul Hoffman" <paul.hoffman@vpnc.org>
To: "Philip Lafrance" <philip.lafrance92@gmail.com>
Cc: cfrg@irtf.org
Date: Fri, 21 Jul 2017 18:26:56 +0200
Message-ID: <001D22D7-2A0C-4DA1-A980-89C78C95A17A@vpnc.org>
In-Reply-To: <CALwqbuyti95Tvx43vvWHhnfdrHo+yNVc8GQ0B-utk+C==3-h-A@mail.gmail.com>
References: <CALwqbuyti95Tvx43vvWHhnfdrHo+yNVc8GQ0B-utk+C==3-h-A@mail.gmail.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
X-Mailer: MailMate (1.9.6r5347)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/pI8BEdmUSK6Mfl1vemrL_WcpeZQ>
Subject: Re: [Cfrg] Comments on draft-hoffman-c2pq-01
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 21 Jul 2017 16:27:07 -0000

On 21 Jul 2017, at 14:01, Philip Lafrance wrote:

> So I can't express enough how much I support this document.

Thanks!

> Comments:
>
> Section 1.3
>
>             -The definition given for “post-quantum cryptography” 
> is pretty
> limited and kind of inaccurate. The definition as given would suggest 
> that
> ECC is post-quantum as it does not rely on factoring large numbers or
> determine the discrete log of a large composite number.
>
>
> Maybe something like:
>
>
>  "The term "post-quantum cryptography" refers to the invention and 
> study of
> cryptographic techniques (including encryption, signature and key 
> exchange
> algorithms) that are implementable on a classical computer and are 
> based on
> problems that are believed to be difficult for a quantum computer to 
> solve.
> In particular, this includes algorithms based on lattices, isogenies,
> hash-functions, multivariate polynomial systems, and coding theory. It
> excludes systems whose security relies on factoring numbers, or the
> difficulty of determining the discrete log of one group element with
> respect to another."

Yes, great.

> Section 1.6
>
>             -The good folks at the Institute for Quantum Computing 
> have a
> good textbook which would be a nice reference (here is a link
> http://hep.fcfm.buap.mx/cursos/2014/MCI/An_Intro_to_Quantum.pdf)

That book is more limited (and, to my eye, harder to read) than the more 
popular Nielsen and Chuang. (Side-note: posting URLs to ripped copies of 
books is a bit tacky...)

> Section 2.1
>
>             -This section seems to only be concerned with using 
> quantum
> algorithms to recover secret key. Why not also mention for example 
> using
> Grover to find collisions to forge signatures?

Finding collisions in greater than 2^128 quantum steps doesn't seem like 
an interesting threat (assuming that you are using a hash like SHA256 or 
better).

>             -We should maybe consider replacing “large-scale” 
> quantum
> computer with “universal” quantum computer.

I definitely need to work on the terminology here. I'll send out 
separate messages after I have incorporated some other off-list 
suggestions in this area that I have received.

> -Maybe some discussion about the differences between quantum annealing 
> and
> a universal quantum computer. This would be useful because, for 
> example
> D-Wave is a quantum annealer, not a universal quantum computer, but 
> the
> difference is lost on most people. Understanding the difference is
> important if we’re talking about when to transition.

This sounds great. Suggestions of text are welcome!

--Paul Hoffman


From nobody Fri Jul 21 09:32:16 2017
Return-Path: <danibrown@blackberry.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id B6082131B71 for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 09:32:14 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -5.4
X-Spam-Level: 
X-Spam-Status: No, score=-5.4 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, RCVD_IN_MSPIKE_H2=-2.8, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id DKiWEN4s00w8 for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 09:32:11 -0700 (PDT)
Received: from smtp-p01.blackberry.com (smtp-p01.blackberry.com [208.65.78.88]) (using TLSv1.2 with cipher RC4-SHA (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 7B82E131B29 for <cfrg@irtf.org>; Fri, 21 Jul 2017 09:32:11 -0700 (PDT)
Received: from xct103cnc.rim.net ([10.65.161.203]) by mhs211cnc.rim.net with ESMTP/TLS/DHE-RSA-AES256-SHA; 21 Jul 2017 12:32:08 -0400
Received: from XCT116CNC.rim.net (10.65.161.216) by XCT103CNC.rim.net (10.65.161.203) with Microsoft SMTP Server (TLS) id 14.3.319.2; Fri, 21 Jul 2017 12:32:09 -0400
Received: from XMB116CNC.rim.net ([fe80::45d:f4fe:6277:5d1b]) by XCT116CNC.rim.net ([::1]) with mapi id 14.03.0319.002; Fri, 21 Jul 2017 12:32:09 -0400
From: Dan Brown <danibrown@blackberry.com>
To: Sharon Goldberg <goldbe@cs.bu.edu>, "cfrg@irtf.org" <cfrg@irtf.org>
CC: "jan@ns1.com" <jan@ns1.com>, Leonid Reyzin <reyzin@cs.bu.edu>, "Dimitrios Papadopoulos" <dipapado@umd.edu>
Thread-Topic: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
Thread-Index: AQHS+vM6+DG9anuMcU+xW6RwdHg7uaJZ5FlggASji3c=
Date: Fri, 21 Jul 2017 16:32:08 +0000
Message-ID: <20170721163204.8573013.1016.15939@blackberry.com>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com>,  <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net>
In-Reply-To: <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net>
Accept-Language: en-US, en-CA
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
Content-Type: multipart/alternative; boundary="_000_201707211632048573013101615939blackberrycom_"
MIME-Version: 1.0
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/ImNk05DFmX7HdUflklvtpaBr-Mc>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Fri, 21 Jul 2017 16:32:15 -0000

--_000_201707211632048573013101615939blackberrycom_
Content-Type: text/plain; charset="windows-1256"
Content-Transfer-Encoding: quoted-printable

Answering myself below: VRFs have been around since 1999, so are not so new=
.  =FDStill don't like the name, and still have trouble seeing the value.

From: Dan Brown
Sent: Tuesday, July 18, 2017 2:29 PM
To: Sharon Goldberg; cfrg@irtf.org
Cc: jan@ns1.com; Leonid Reyzin; Dimitrios Papadopoulos
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions


Hi Sharon and CFRG,

On VRFs, my uncertain comments to consider at your leisure:

Is it fair to say VRFs are relatively new?  If so, then maybe a little more=
 caution is needed about their use.  It seems a tad hasty that it is being =
used already.

To me, it seems that VRFs are basically signatures, with an extra feature. =
 My concern is that this extra feature might get overused, before it is tho=
roughly reviewed.

It is unsurprising to me that random oracle model proof can prove the outpu=
t of a hash to be random.  My intuitive concern is that at least informally=
, this is kind of circular.  Hashes often have some non-random-ish properti=
es that might affect the extra security (over signatures) that VRFs are aim=
ing for.  I guess I would much prefer a proof saying if the hash has (well-=
studied) properties XYZ, then your construction are VRFs.  (Maybe you have =
this already?  If so, then tell me so.)

Since, VRFs require sending the =93proofs=94 on the wire, I find it hard to=
 see how it could be used to prevent dictionary attacks.  I assume that you=
 are saying the proofs must be encrypted when one needs to avoid dictionary=
 models?  I suppose all the details are there in I-D and papers, but for no=
w, I am confused about the threat model (which parties have keys, etc., if =
they require a secure channel and mutual trust, why just use plain old hash=
,=85). To resist dictionary attacks, were already have PAKEs and PBHashing.=
  Now this?

Finally, on a bikeshed-coloring note, I object to the name =93verifiable ra=
ndom function=94, on several grounds.


  1.  It is not a function.  It is at least four functions, keygen, sign, v=
erify, and hashify.
  2.  If you make it into a keyed function F_sk(m), as in prooftohash(sign_=
sk(m)), it is not verifiable.
  3.  Verification requires the intermediate proof, which is certainly not =
even pseudorandom (it is easy to distinguish valid signatures from random).
  4.  It is pseudorandom, not random.  (The keys are random, but many crypt=
o has keys, without having =93random=94 in its name: encryption, MAC, signa=
tures, key exchange, =85, they also don=92t verifiable or random in their n=
ames either.)
  5.  The similar phrase =93verifiably random=94, albeit as a misnomer, has=
 past precedents, see NIST P-256 and Brainpool, etc.  When I see VRF, I thi=
nk a function, that aims to VR in that sense, and great, now we can improve=
 on Brainpool, etc.
  6.  =93Random function=94 should be reserved for the ideal random mapping=
 concept, for example, as studied by Flajolet-Odlyzko (ok they only studied=
 the case of equal size domain and range).  The random oracle model, is the=
 idea of approximating this ideal, etc.  An actual approximation should not=
 be name as the ideal (sorry, I=92m kind of repeating my point 4).

Please forgive the fact that my comments above are not very constructive (o=
r if the tone is wrong).  This is a new topic for me, so I am reluctant too=
 many suggestions.  Nonetheless, I suggest (0) waiting a little, (1) a non-=
random-oracle security proof (if you don=92t have it yet), (2) re-naming th=
e scheme to something like re-hashable (or digestible) signatures (and re-n=
ame the various parts, i.e. proof -> signature, etc.).

Best regards,

Dan


From: Cfrg [mailto:cfrg-bounces@irtf.org] On Behalf Of Sharon Goldberg
Sent: Wednesday, July 12, 2017 5:42 AM
To: cfrg@irtf.org
Cc: jan@ns1.com; Dimitrios Papadopoulos <dipapado@umd.edu>; Leonid Reyzin <=
reyzin@cs.bu.edu>
Subject: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions

Dear CFRG,

I'm presenting at next week's meeting on Verifiable Random Functions. A VRF=
 is the public-key version of keyed cryptographic hash. Only the holder of =
the VRF secret key can compute the hash, but anyone with the public key can=
 verify it.  VRFs can be used to prevent dictionary attacks on hash-based d=
ata structures, and have applications to key transparency (CONIKS), DNSSEC =
(NSEC5), and cryptocurrencies (Algorand).

In advance of the meeting, please see:

1) Our substantially updated -01 draft:
https://datatracker.ietf.org/doc/draft-goldbe-vrf/

2) Our project page, with links to various VRF implementations:
https://www.cs.bu.edu/~goldbe/projects/vrf

Comments welcome.  Thanks,

Sharon

--
Sharon Goldberg
Computer Science, Boston University
http://www.cs.bu.edu/~goldbe

--_000_201707211632048573013101615939blackberrycom_
Content-Type: text/html; charset="windows-1256"
Content-Transfer-Encoding: quoted-printable

<html>
<head>
<meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3Dwindows-1=
256">
<style>
<!--
@font-face
	{font-family:"Cambria Math"}
@font-face
	{font-family:Calibri}
p.MsoNormal, li.MsoNormal, div.MsoNormal
	{margin:0in;
	margin-bottom:.0001pt;
	font-size:12.0pt;
	font-family:"Times New Roman",serif}
a:link, span.MsoHyperlink
	{color:blue;
	text-decoration:underline}
a:visited, span.MsoHyperlinkFollowed
	{color:purple;
	text-decoration:underline}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
	{margin-top:0in;
	margin-right:0in;
	margin-bottom:0in;
	margin-left:.5in;
	margin-bottom:.0001pt;
	font-size:12.0pt;
	font-family:"Times New Roman",serif}
p.msonormal0, li.msonormal0, div.msonormal0
	{margin-right:0in;
	margin-left:0in;
	font-size:12.0pt;
	font-family:"Times New Roman",serif}
span.EmailStyle18
	{font-family:"Calibri",sans-serif;
	color:windowtext}
.MsoChpDefault
	{font-size:10.0pt;
	font-family:"Calibri",sans-serif}
@page WordSection1
	{margin:1.0in 1.0in 1.0in 1.0in}
div.WordSection1
	{}
ol
	{margin-bottom:0in}
ul
	{margin-bottom:0in}
-->
</style>
</head>
<body lang=3D"EN-US" link=3D"blue" vlink=3D"purple">
<div style=3D"width:100%; font-size:initial; font-family:Calibri,'Slate Pro=
',sans-serif,sans-serif; color:rgb(31,73,125); text-align:initial; backgrou=
nd-color:rgb(255,255,255)">
Answering myself below: VRFs have been around since 1999, so are not so new=
. &nbsp;=FDStill don't like the name, and still have trouble seeing the val=
ue.</div>
<div style=3D"width:100%; font-size:initial; font-family:Calibri,'Slate Pro=
',sans-serif,sans-serif; color:rgb(31,73,125); text-align:initial; backgrou=
nd-color:rgb(255,255,255)">
<span style=3D"font-family:Calibri,'Slate Pro',sans-serif,sans-serif; font-=
size:initial; line-height:initial; text-align:initial"><br>
</span></div>
<table width=3D"100%" style=3D"background-color:white; border-spacing:0px">
<tbody>
<tr>
<td colspan=3D"2" style=3D"font-size:initial; text-align:initial; backgroun=
d-color:rgb(255,255,255)">
<div style=3D"border-style:solid none none; border-top-color:rgb(181,196,22=
3); border-top-width:1pt; padding:3pt 0in 0in; font-family:Tahoma,'BB Alpha=
 Sans','Slate Pro'; font-size:10pt">
<div><b>From: </b>Dan Brown</div>
<div><b>Sent: </b>Tuesday, July 18, 2017 2:29 PM</div>
<div><b>To: </b>Sharon Goldberg; cfrg@irtf.org</div>
<div><b>Cc: </b>jan@ns1.com; Leonid Reyzin; Dimitrios Papadopoulos</div>
<div><b>Subject: </b>Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functio=
ns</div>
</div>
</td>
</tr>
</tbody>
</table>
<div style=3D"border-style:solid none none; border-top-color:rgb(186,188,20=
9); border-top-width:1pt; font-size:initial; text-align:initial; background=
-color:rgb(255,255,255)">
</div>
<br>
<div>
<div class=3D"WordSection1">
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">Hi Sharon and CFRG,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">On VRFs, my uncertain comments to consider at your=
 leisure:</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">Is it fair to say VRFs are relatively new?&nbsp; I=
f so, then maybe a little more caution is needed about their use.&nbsp; It =
seems a tad hasty that it is being used already.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">To me, it seems that VRFs are basically signatures=
, with an extra feature.&nbsp; My concern is that this extra feature might =
get overused, before it is thoroughly reviewed.&nbsp;
</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">It is unsurprising to me that random oracle model =
proof can prove the output of a hash to be random.&nbsp; My intuitive conce=
rn is that at least informally, this is kind of circular.&nbsp;
 Hashes often have some non-random-ish properties that might affect the ext=
ra security (over signatures) that VRFs are aiming for.&nbsp; I guess I wou=
ld much prefer a proof saying if the hash has (well-studied) properties XYZ=
, then your construction are VRFs.&nbsp; (Maybe
 you have this already?&nbsp; If so, then tell me so.)</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">Since, VRFs require sending the =93proofs=94 on th=
e wire, I find it hard to see how it could be used to prevent dictionary at=
tacks.&nbsp; I assume that you are saying the proofs must
 be encrypted when one needs to avoid dictionary models?&nbsp; I suppose al=
l the details are there in I-D and papers, but for now, I am confused about=
 the threat model (which parties have keys, etc., if they require a secure =
channel and mutual trust, why just use
 plain old hash,=85). To resist dictionary attacks, were already have PAKEs=
 and PBHashing.&nbsp; Now this?</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">Finally, on a bikeshed-coloring note, I object to =
the name =93verifiable random function=94, on several grounds.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<ol start=3D"1" type=3D"1" style=3D"margin-top:0in">
<li class=3D"MsoListParagraph" style=3D"margin-left:0in"><span style=3D"fon=
t-size:11.0pt; font-family:&quot;Calibri&quot;,sans-serif">It is not a func=
tion.&nbsp; It is at least four functions, keygen, sign, verify, and hashif=
y.</span></li><li class=3D"MsoListParagraph" style=3D"margin-left:0in"><spa=
n style=3D"font-size:11.0pt; font-family:&quot;Calibri&quot;,sans-serif">If=
 you make it into a keyed function F_sk(m), as in prooftohash(sign_sk(m)), =
it is not verifiable.&nbsp;
</span></li><li class=3D"MsoListParagraph" style=3D"margin-left:0in"><span =
style=3D"font-size:11.0pt; font-family:&quot;Calibri&quot;,sans-serif">Veri=
fication requires the intermediate proof, which is certainly not even pseud=
orandom (it is easy to distinguish valid signatures from random).</span></l=
i><li class=3D"MsoListParagraph" style=3D"margin-left:0in"><span style=3D"f=
ont-size:11.0pt; font-family:&quot;Calibri&quot;,sans-serif">It is pseudora=
ndom, not random.&nbsp; (The keys are random, but many crypto has keys, wit=
hout having =93random=94 in its name: encryption, MAC, signatures,
 key exchange, =85, they also don=92t verifiable or random in their names e=
ither.)</span></li><li class=3D"MsoListParagraph" style=3D"margin-left:0in"=
><span style=3D"font-size:11.0pt; font-family:&quot;Calibri&quot;,sans-seri=
f">The similar phrase =93verifiably random=94, albeit as a misnomer, has pa=
st precedents, see NIST P-256 and Brainpool, etc.&nbsp; When I see VRF, I t=
hink
 a function, that aims to VR in that sense, and great, now we can improve o=
n Brainpool, etc.</span></li><li class=3D"MsoListParagraph" style=3D"margin=
-left:0in"><span style=3D"font-size:11.0pt; font-family:&quot;Calibri&quot;=
,sans-serif">=93Random function=94 should be reserved for the ideal random =
mapping concept, for example, as studied by Flajolet-Odlyzko (ok they only =
studied
 the case of equal size domain and range).&nbsp; The random oracle model, i=
s the idea of approximating this ideal, etc.&nbsp; An actual approximation =
should not be name as the ideal (sorry, I=92m kind of repeating my point 4)=
.</span></li></ol>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">Please forgive the fact that my comments above are=
 not very constructive (or if the tone is wrong).&nbsp; This is a new topic=
 for me, so I am reluctant too many suggestions.&nbsp; Nonetheless,
 I suggest (0) waiting a little, (1) a non-random-oracle security proof (if=
 you don=92t have it yet), (2) re-naming the scheme to something like re-ha=
shable (or digestible) signatures (and re-name the various parts, i.e. proo=
f -&gt; signature, etc.).</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">Best regards,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">Dan</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt; font-family:&quot;C=
alibri&quot;,sans-serif">&nbsp;</span></p>
<p class=3D"MsoNormal"><b><span style=3D"font-size:11.0pt; font-family:&quo=
t;Calibri&quot;,sans-serif">From:</span></b><span style=3D"font-size:11.0pt=
; font-family:&quot;Calibri&quot;,sans-serif"> Cfrg [mailto:cfrg-bounces@ir=
tf.org]
<b>On Behalf Of </b>Sharon Goldberg<br>
<b>Sent:</b> Wednesday, July 12, 2017 5:42 AM<br>
<b>To:</b> cfrg@irtf.org<br>
<b>Cc:</b> jan@ns1.com; Dimitrios Papadopoulos &lt;dipapado@umd.edu&gt;; Le=
onid Reyzin &lt;reyzin@cs.bu.edu&gt;<br>
<b>Subject:</b> [Cfrg] draft-goldbe-vrf: Verifiable Random Functions</span>=
</p>
<p class=3D"MsoNormal">&nbsp;</p>
<div>
<p class=3D"MsoNormal">Dear CFRG,<br>
<br>
I'm presenting at next week's meeting on Verifiable Random Functions. A VRF=
 is the public-key version of keyed cryptographic hash. Only the holder of =
the VRF secret key can compute the hash, but anyone with the public key can=
 verify it.&nbsp; VRFs can be used to
 prevent dictionary attacks on hash-based data structures, and have applica=
tions to key transparency (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (A=
lgorand).<br>
<br>
In advance of the meeting, please see:<br>
<br>
1) Our substantially updated -01 draft:<br>
<a href=3D"https://datatracker.ietf.org/doc/draft-goldbe-vrf/" target=3D"_b=
lank">https://datatracker.ietf.org/doc/draft-goldbe-vrf/</a><br>
<br>
2) Our project page, with links to various VRF implementations:<br>
<a href=3D"https://www.cs.bu.edu/~goldbe/projects/vrf" target=3D"_blank">ht=
tps://www.cs.bu.edu/~goldbe/projects/vrf</a><br>
<br>
Comments welcome.&nbsp; Thanks,<br>
<br>
Sharon<br>
<br>
--<br>
Sharon Goldberg<br>
Computer Science, Boston University<br>
<a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu=
.edu/~goldbe</a></p>
</div>
</div>
</div>
</body>
</html>

--_000_201707211632048573013101615939blackberrycom_--


From nobody Fri Jul 21 19:37:39 2017
Return-Path: <watsonbladd@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 8446A1270A3 for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 19:37:37 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.999
X-Spam-Level: 
X-Spam-Status: No, score=-1.999 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id i1J4YakoAB7r for <cfrg@ietfa.amsl.com>; Fri, 21 Jul 2017 19:37:34 -0700 (PDT)
Received: from mail-pg0-x236.google.com (mail-pg0-x236.google.com [IPv6:2607:f8b0:400e:c05::236]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id BD5AA126BF3 for <cfrg@irtf.org>; Fri, 21 Jul 2017 19:37:34 -0700 (PDT)
Received: by mail-pg0-x236.google.com with SMTP id k14so35446115pgr.0 for <cfrg@irtf.org>; Fri, 21 Jul 2017 19:37:34 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=QRrNbnMg2WA4qPmCsK0eW2zbNf+wbFAep7Rg666aVck=; b=DZHkBcz6PSbsiZVab8N22loSp/Em4Ym9L0/VEmuFhT3HnTZLnewWpM1pM/WyxK+cLT cXygwCRTwCblqmzuoXp6FRPg9ZMSGockvTfoBaWgql3xq2gVBbE+ZGc+eMTC0JeXBfRp NAhX0a9OCeJDa+Qlr6neh6XO08fRt5re97OJFZoXgpK91iC4qxdfNcnss4eCbvOMeSoB d5UPYw2UN3Fd8zOuSiZ3lpfneAwgnqbdGn3VjrRMn4ynQXKVXQ+CvfzW+VhcPVK1dItD Cnzifx7jaGqTbDAPCb3NG23rAedlyepqsoPlhu+3QiMksn3FVe3k0LILvuQnL/P0eolh lRTg==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=QRrNbnMg2WA4qPmCsK0eW2zbNf+wbFAep7Rg666aVck=; b=hAWPboya4FtQwCUanPnv4LKD5X0Dd29+rHPrfE47VJX0Gu4E3CX2RqXugEWrB7hE/Q ae7709Zt1XPo2Wj+MTawstRExNh6O7LtaIErempTqmrJ1NhDHp4/1yC9yiZ6zvuHNjho x7Kf7oOKdz0hD6uSvJ+WBb2wBkNHRZ6/V3YqviVTvCZHwAYMVtQZoGBJq7N46IAsHl1H yka4bVIaQo5x/sXKt6s3iDCuvnb8F+KPJAaYUsKFue335DElaBg2Htnwi8xvjpZ48I+k Di64mxy+9NsKw9+Wz6Oxc9Fr+z6NGXNxjGiaACVBtpNPOxqI7JjZ25IkFyh320sC7IQO C9Aw==
X-Gm-Message-State: AIVw112kUKyT8ql3+yAZtwHrTWlRKTRZYeYy4cPiZU5TWGdYZtJMeI9c UmevaZrII1g59LqBAwtA47rFjH6Prw==
X-Received: by 10.98.38.68 with SMTP id m65mr9280308pfm.47.1500691054342; Fri, 21 Jul 2017 19:37:34 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.100.187.77 with HTTP; Fri, 21 Jul 2017 19:37:33 -0700 (PDT)
In-Reply-To: <20170721163204.8573013.1016.15939@blackberry.com>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com> <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net> <20170721163204.8573013.1016.15939@blackberry.com>
From: Watson Ladd <watsonbladd@gmail.com>
Date: Fri, 21 Jul 2017 19:37:33 -0700
Message-ID: <CACsn0cm3QCiT9jFYp=EKfK8n6GdyW4TpyddG5NS5+zRFjLJoJg@mail.gmail.com>
To: Dan Brown <danibrown@blackberry.com>
Cc: Sharon Goldberg <goldbe@cs.bu.edu>, "cfrg@irtf.org" <cfrg@irtf.org>, "jan@ns1.com" <jan@ns1.com>,  Dimitrios Papadopoulos <dipapado@umd.edu>, Leonid Reyzin <reyzin@cs.bu.edu>
Content-Type: multipart/alternative; boundary="94eb2c0ca0003643b00554deddb2"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/zVGPGuKAsJooLxl2P3W6iauPSnw>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Sat, 22 Jul 2017 02:37:37 -0000

--94eb2c0ca0003643b00554deddb2
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Two applications:
-NSEC5 uses VRFs to use online signing for zonewalking prevention and
offline signing for authenticity.
- Cloudflare uses OPRFs, a slightly different construction, to improve the
experience of Tor users



On Fri, Jul 21, 2017 at 9:32 AM, Dan Brown <danibrown@blackberry.com> wrote=
:

> Answering myself below: VRFs have been around since 1999, so are not so
> new.  =E2=80=8EStill don't like the name, and still have trouble seeing t=
he value.
>
> *From: *Dan Brown
> *Sent: *Tuesday, July 18, 2017 2:29 PM
> *To: *Sharon Goldberg; cfrg@irtf.org
> *Cc: *jan@ns1.com; Leonid Reyzin; Dimitrios Papadopoulos
> *Subject: *Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>
> Hi Sharon and CFRG,
>
>
>
> On VRFs, my uncertain comments to consider at your leisure:
>
>
>
> Is it fair to say VRFs are relatively new?  If so, then maybe a little
> more caution is needed about their use.  It seems a tad hasty that it is
> being used already.
>
>
>
> To me, it seems that VRFs are basically signatures, with an extra
> feature.  My concern is that this extra feature might get overused, befor=
e
> it is thoroughly reviewed.
>
>
>
> It is unsurprising to me that random oracle model proof can prove the
> output of a hash to be random.  My intuitive concern is that at least
> informally, this is kind of circular.  Hashes often have some
> non-random-ish properties that might affect the extra security (over
> signatures) that VRFs are aiming for.  I guess I would much prefer a proo=
f
> saying if the hash has (well-studied) properties XYZ, then your
> construction are VRFs.  (Maybe you have this already?  If so, then tell m=
e
> so.)
>
>
>
> Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the wire, I f=
ind it hard to
> see how it could be used to prevent dictionary attacks.  I assume that yo=
u
> are saying the proofs must be encrypted when one needs to avoid dictionar=
y
> models?  I suppose all the details are there in I-D and papers, but for
> now, I am confused about the threat model (which parties have keys, etc.,
> if they require a secure channel and mutual trust, why just use plain old
> hash,=E2=80=A6). To resist dictionary attacks, were already have PAKEs an=
d
> PBHashing.  Now this?
>
>
>
> Finally, on a bikeshed-coloring note, I object to the name =E2=80=9Cverif=
iable
> random function=E2=80=9D, on several grounds.
>
>
>
>    1. It is not a function.  It is at least four functions, keygen, sign,
>    verify, and hashify.
>    2. If you make it into a keyed function F_sk(m), as in
>    prooftohash(sign_sk(m)), it is not verifiable.
>    3. Verification requires the intermediate proof, which is certainly
>    not even pseudorandom (it is easy to distinguish valid signatures from
>    random).
>    4. It is pseudorandom, not random.  (The keys are random, but many
>    crypto has keys, without having =E2=80=9Crandom=E2=80=9D in its name: =
encryption, MAC,
>    signatures, key exchange, =E2=80=A6, they also don=E2=80=99t verifiabl=
e or random in their
>    names either.)
>    5. The similar phrase =E2=80=9Cverifiably random=E2=80=9D, albeit as a=
 misnomer, has
>    past precedents, see NIST P-256 and Brainpool, etc.  When I see VRF, I
>    think a function, that aims to VR in that sense, and great, now we can
>    improve on Brainpool, etc.
>    6. =E2=80=9CRandom function=E2=80=9D should be reserved for the ideal =
random mapping
>    concept, for example, as studied by Flajolet-Odlyzko (ok they only stu=
died
>    the case of equal size domain and range).  The random oracle model, is=
 the
>    idea of approximating this ideal, etc.  An actual approximation should=
 not
>    be name as the ideal (sorry, I=E2=80=99m kind of repeating my point 4)=
.
>
>
>
> Please forgive the fact that my comments above are not very constructive
> (or if the tone is wrong).  This is a new topic for me, so I am reluctant
> too many suggestions.  Nonetheless, I suggest (0) waiting a little, (1) a
> non-random-oracle security proof (if you don=E2=80=99t have it yet), (2) =
re-naming
> the scheme to something like re-hashable (or digestible) signatures (and
> re-name the various parts, i.e. proof -> signature, etc.).
>
>
>
> Best regards,
>
>
>
> Dan
>
>
>
>
>
> *From:* Cfrg [mailto:cfrg-bounces@irtf.org] *On Behalf Of *Sharon Goldber=
g
> *Sent:* Wednesday, July 12, 2017 5:42 AM
> *To:* cfrg@irtf.org
> *Cc:* jan@ns1.com; Dimitrios Papadopoulos <dipapado@umd.edu>; Leonid
> Reyzin <reyzin@cs.bu.edu>
> *Subject:* [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>
>
>
> Dear CFRG,
>
> I'm presenting at next week's meeting on Verifiable Random Functions. A
> VRF is the public-key version of keyed cryptographic hash. Only the holde=
r
> of the VRF secret key can compute the hash, but anyone with the public ke=
y
> can verify it.  VRFs can be used to prevent dictionary attacks on
> hash-based data structures, and have applications to key transparency
> (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (Algorand).
>
> In advance of the meeting, please see:
>
> 1) Our substantially updated -01 draft:
> https://datatracker.ietf.org/doc/draft-goldbe-vrf/
>
> 2) Our project page, with links to various VRF implementations:
> https://www.cs.bu.edu/~goldbe/projects/vrf
>
> Comments welcome.  Thanks,
>
> Sharon
>
> --
> Sharon Goldberg
> Computer Science, Boston University
> http://www.cs.bu.edu/~goldbe
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>
>


--=20
"Man is born free, but everywhere he is in chains".
--Rousseau.

--94eb2c0ca0003643b00554deddb2
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div>Two applications:</div>-NSEC5 uses VRFs to use online=
 signing for zonewalking prevention and offline signing for authenticity.<d=
iv>- Cloudflare uses OPRFs, a slightly different construction, to improve t=
he experience of Tor users</div><div><br></div><div><br></div></div><div cl=
ass=3D"gmail_extra"><br><div class=3D"gmail_quote">On Fri, Jul 21, 2017 at =
9:32 AM, Dan Brown <span dir=3D"ltr">&lt;<a href=3D"mailto:danibrown@blackb=
erry.com" target=3D"_blank">danibrown@blackberry.com</a>&gt;</span> wrote:<=
br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left=
:1px #ccc solid;padding-left:1ex">




<div lang=3D"EN-US" link=3D"blue" vlink=3D"purple">
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&#39;Slate P=
ro&#39;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;backg=
round-color:rgb(255,255,255)">
Answering myself below: VRFs have been around since 1999, so are not so new=
. =C2=A0=E2=80=8EStill don&#39;t like the name, and still have trouble seei=
ng the value.</div>
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&#39;Slate P=
ro&#39;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;backg=
round-color:rgb(255,255,255)">
<span style=3D"font-family:Calibri,&#39;Slate Pro&#39;,sans-serif,sans-seri=
f;font-size:initial;line-height:initial;text-align:initial"><br>
</span></div>
<table width=3D"100%" style=3D"background-color:white;border-spacing:0px">
<tbody>
<tr>
<td colspan=3D"2" style=3D"font-size:initial;text-align:initial;background-=
color:rgb(255,255,255)">
<div style=3D"border-style:solid none none;border-top-color:rgb(181,196,223=
);border-top-width:1pt;padding:3pt 0in 0in;font-family:Tahoma,&#39;BB Alpha=
 Sans&#39;,&#39;Slate Pro&#39;;font-size:10pt">
<div><b>From: </b>Dan Brown</div>
<div><b>Sent: </b>Tuesday, July 18, 2017 2:29 PM</div>
<div><b>To: </b>Sharon Goldberg; <a href=3D"mailto:cfrg@irtf.org" target=3D=
"_blank">cfrg@irtf.org</a></div>
<div><b>Cc: </b><a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.co=
m</a>; Leonid Reyzin; Dimitrios Papadopoulos</div>
<div><b>Subject: </b>Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functio=
ns</div>
</div>
</td>
</tr>
</tbody>
</table><div><div class=3D"h5">
<div style=3D"border-style:solid none none;border-top-color:rgb(186,188,209=
);border-top-width:1pt;font-size:initial;text-align:initial;background-colo=
r:rgb(255,255,255)">
</div>
<br>
<div>
<div class=3D"m_8579908292832695881WordSection1">
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">Hi Sharon and CFRG,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">On VRFs, my uncertain comments to consider at your =
leisure:</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">Is it fair to say VRFs are relatively new?=C2=A0 If=
 so, then maybe a little more caution is needed about their use.=C2=A0 It s=
eems a tad hasty that it is being used already.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">To me, it seems that VRFs are basically signatures,=
 with an extra feature.=C2=A0 My concern is that this extra feature might g=
et overused, before it is thoroughly reviewed.=C2=A0
</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">It is unsurprising to me that random oracle model p=
roof can prove the output of a hash to be random.=C2=A0 My intuitive concer=
n is that at least informally, this is kind of circular.=C2=A0
 Hashes often have some non-random-ish properties that might affect the ext=
ra security (over signatures) that VRFs are aiming for.=C2=A0 I guess I wou=
ld much prefer a proof saying if the hash has (well-studied) properties XYZ=
, then your construction are VRFs.=C2=A0 (Maybe
 you have this already?=C2=A0 If so, then tell me so.)</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">Since, VRFs require sending the =E2=80=9Cproofs=E2=
=80=9D on the wire, I find it hard to see how it could be used to prevent d=
ictionary attacks.=C2=A0 I assume that you are saying the proofs must
 be encrypted when one needs to avoid dictionary models?=C2=A0 I suppose al=
l the details are there in I-D and papers, but for now, I am confused about=
 the threat model (which parties have keys, etc., if they require a secure =
channel and mutual trust, why just use
 plain old hash,=E2=80=A6). To resist dictionary attacks, were already have=
 PAKEs and PBHashing.=C2=A0 Now this?</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">Finally, on a bikeshed-coloring note, I object to t=
he name =E2=80=9Cverifiable random function=E2=80=9D, on several grounds.</=
span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<ol start=3D"1" type=3D"1" style=3D"margin-top:0in">
<li class=3D"m_8579908292832695881MsoListParagraph" style=3D"margin-left:0i=
n"><span style=3D"font-size:11.0pt;font-family:&quot;Calibri&quot;,sans-ser=
if">It is not a function.=C2=A0 It is at least four functions, keygen, sign=
, verify, and hashify.</span></li><li class=3D"m_8579908292832695881MsoList=
Paragraph" style=3D"margin-left:0in"><span style=3D"font-size:11.0pt;font-f=
amily:&quot;Calibri&quot;,sans-serif">If you make it into a keyed function =
F_sk(m), as in prooftohash(sign_sk(m)), it is not verifiable.=C2=A0
</span></li><li class=3D"m_8579908292832695881MsoListParagraph" style=3D"ma=
rgin-left:0in"><span style=3D"font-size:11.0pt;font-family:&quot;Calibri&qu=
ot;,sans-serif">Verification requires the intermediate proof, which is cert=
ainly not even pseudorandom (it is easy to distinguish valid signatures fro=
m random).</span></li><li class=3D"m_8579908292832695881MsoListParagraph" s=
tyle=3D"margin-left:0in"><span style=3D"font-size:11.0pt;font-family:&quot;=
Calibri&quot;,sans-serif">It is pseudorandom, not random.=C2=A0 (The keys a=
re random, but many crypto has keys, without having =E2=80=9Crandom=E2=80=
=9D in its name: encryption, MAC, signatures,
 key exchange, =E2=80=A6, they also don=E2=80=99t verifiable or random in t=
heir names either.)</span></li><li class=3D"m_8579908292832695881MsoListPar=
agraph" style=3D"margin-left:0in"><span style=3D"font-size:11.0pt;font-fami=
ly:&quot;Calibri&quot;,sans-serif">The similar phrase =E2=80=9Cverifiably r=
andom=E2=80=9D, albeit as a misnomer, has past precedents, see NIST P-256 a=
nd Brainpool, etc.=C2=A0 When I see VRF, I think
 a function, that aims to VR in that sense, and great, now we can improve o=
n Brainpool, etc.</span></li><li class=3D"m_8579908292832695881MsoListParag=
raph" style=3D"margin-left:0in"><span style=3D"font-size:11.0pt;font-family=
:&quot;Calibri&quot;,sans-serif">=E2=80=9CRandom function=E2=80=9D should b=
e reserved for the ideal random mapping concept, for example, as studied by=
 Flajolet-Odlyzko (ok they only studied
 the case of equal size domain and range).=C2=A0 The random oracle model, i=
s the idea of approximating this ideal, etc.=C2=A0 An actual approximation =
should not be name as the ideal (sorry, I=E2=80=99m kind of repeating my po=
int 4).</span></li></ol>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">Please forgive the fact that my comments above are =
not very constructive (or if the tone is wrong).=C2=A0 This is a new topic =
for me, so I am reluctant too many suggestions.=C2=A0 Nonetheless,
 I suggest (0) waiting a little, (1) a non-random-oracle security proof (if=
 you don=E2=80=99t have it yet), (2) re-naming the scheme to something like=
 re-hashable (or digestible) signatures (and re-name the various parts, i.e=
. proof -&gt; signature, etc.).</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">Best regards,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">Dan</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11.0pt;font-family:&quot;Ca=
libri&quot;,sans-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><b><span style=3D"font-size:11.0pt;font-family:&quot=
;Calibri&quot;,sans-serif">From:</span></b><span style=3D"font-size:11.0pt;=
font-family:&quot;Calibri&quot;,sans-serif"> Cfrg [mailto:<a href=3D"mailto=
:cfrg-bounces@irtf.org" target=3D"_blank">cfrg-bounces@irtf.org</a>]
<b>On Behalf Of </b>Sharon Goldberg<br>
<b>Sent:</b> Wednesday, July 12, 2017 5:42 AM<br>
<b>To:</b> <a href=3D"mailto:cfrg@irtf.org" target=3D"_blank">cfrg@irtf.org=
</a><br>
<b>Cc:</b> <a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.com</a>=
; Dimitrios Papadopoulos &lt;<a href=3D"mailto:dipapado@umd.edu" target=3D"=
_blank">dipapado@umd.edu</a>&gt;; Leonid Reyzin &lt;<a href=3D"mailto:reyzi=
n@cs.bu.edu" target=3D"_blank">reyzin@cs.bu.edu</a>&gt;<br>
<b>Subject:</b> [Cfrg] draft-goldbe-vrf: Verifiable Random Functions</span>=
</p>
<p class=3D"MsoNormal">=C2=A0</p>
<div>
<p class=3D"MsoNormal">Dear CFRG,<br>
<br>
I&#39;m presenting at next week&#39;s meeting on Verifiable Random Function=
s. A VRF is the public-key version of keyed cryptographic hash. Only the ho=
lder of the VRF secret key can compute the hash, but anyone with the public=
 key can verify it.=C2=A0 VRFs can be used to
 prevent dictionary attacks on hash-based data structures, and have applica=
tions to key transparency (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (A=
lgorand).<br>
<br>
In advance of the meeting, please see:<br>
<br>
1) Our substantially updated -01 draft:<br>
<a href=3D"https://datatracker.ietf.org/doc/draft-goldbe-vrf/" target=3D"_b=
lank">https://datatracker.ietf.org/<wbr>doc/draft-goldbe-vrf/</a><br>
<br>
2) Our project page, with links to various VRF implementations:<br>
<a href=3D"https://www.cs.bu.edu/~goldbe/projects/vrf" target=3D"_blank">ht=
tps://www.cs.bu.edu/~goldbe/<wbr>projects/vrf</a><br>
<br>
Comments welcome.=C2=A0 Thanks,<br>
<br>
Sharon<br>
<br>
--<br>
Sharon Goldberg<br>
Computer Science, Boston University<br>
<a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu=
.edu/~goldbe</a></p>
</div>
</div>
</div>
</div></div></div>

<br>______________________________<wbr>_________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/<wbr>listinfo/cfrg</a><br>
<br></blockquote></div><br><br clear=3D"all"><div><br></div>-- <br><div cla=
ss=3D"gmail_signature" data-smartmail=3D"gmail_signature">&quot;Man is born=
 free, but everywhere he is in chains&quot;.<br>--Rousseau.</div>
</div>

--94eb2c0ca0003643b00554deddb2--


From nobody Sat Jul 22 09:08:47 2017
Return-Path: <bascule@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 97DE3126CD8 for <cfrg@ietfa.amsl.com>; Sat, 22 Jul 2017 09:08:46 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.689
X-Spam-Level: 
X-Spam-Status: No, score=-2.689 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, T_FILL_THIS_FORM_SHORT=0.01] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 8xZpf0oN0Rhi for <cfrg@ietfa.amsl.com>; Sat, 22 Jul 2017 09:08:45 -0700 (PDT)
Received: from mail-yw0-x231.google.com (mail-yw0-x231.google.com [IPv6:2607:f8b0:4002:c05::231]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 4FD59120725 for <cfrg@irtf.org>; Sat, 22 Jul 2017 09:08:45 -0700 (PDT)
Received: by mail-yw0-x231.google.com with SMTP id v128so7445096ywb.1 for <cfrg@irtf.org>; Sat, 22 Jul 2017 09:08:45 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=7Ksn7Ujf3gvETzc+xUApNC3fyAL6E7sMfYUlWLUS1EA=; b=DLfXUiblCXgl2OE6q7hV4vv4rZOruRd7KtMXNMFlt16/gWih+Ef+QJ0tQt+s5CSFFl k5/2MP/OYQ00lzGdNdaQIHDzQUd5ow6fNKOYc2GIen+eg2b1gf7Sz2Xp3QCfULB+uQCV SY1GWIitFq6J1VayO9xCzRdj95vJko7B9N14mI/HxD8nY58QSe4kbQbOj7VIEYCbbcpZ ooNZGyuxx3Yh4v06aKDoNNm4iThHWyqzWbp3Box3Qnn3Y3Hrd1UegQ+a/RLLD+/1ckWi Y6VLkEqduabBmO9KGMT3FDuZDFAbIELujJv7i/4IBGCPSojFoUlbvhk1YeoMY0i/K7uj AuEQ==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=7Ksn7Ujf3gvETzc+xUApNC3fyAL6E7sMfYUlWLUS1EA=; b=gwQjUlfnCeyeZRhSX3dzA/DPIerwqmndUYOXZtys9C47wsP5xtqIzWZa89Qfk8VvJS TvbXiNS/YdNG0IHOX9uOE7q+Ww8HINdQ2gU/k9+c6P6IXZG3pVsZTkygPvNnUnC6b6Cz F6pqEq4SrMlntC3KmJpUHXa51tyoxeRWqZ029YfSeezfz1dGI/r9T03lc5wqEU0GNLlM Vulm8jlwspeJSf4o/3nrnF1NqbfownNPjBa2hfRrnKBI6dHlJPdZurLRoW7iwpCyNYbd 1VzV5kGLQNUe7KoE5v1xMpft/yXY+W49HndEHfl75eS7w1pghqQZ9U5tX4ArER897E2Y Qyfg==
X-Gm-Message-State: AIVw110KTmGA6NP0XXyfX6vhiRTEbG1sTq7RHNXT35hkKw0NU4zYX6ny D5lIMnyk2Ok6z5Tpslc6uyq1af/exw==
X-Received: by 10.13.229.132 with SMTP id o126mr10695402ywe.186.1500739724414;  Sat, 22 Jul 2017 09:08:44 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.37.170.132 with HTTP; Sat, 22 Jul 2017 09:08:23 -0700 (PDT)
In-Reply-To: <20170721163204.8573013.1016.15939@blackberry.com>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com> <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net> <20170721163204.8573013.1016.15939@blackberry.com>
From: Tony Arcieri <bascule@gmail.com>
Date: Sat, 22 Jul 2017 09:08:23 -0700
Message-ID: <CAHOTMVLNZhX9LreywH0usurTHiULCJTbF2WNYeKZcrjMZJsC7w@mail.gmail.com>
To: Dan Brown <danibrown@blackberry.com>
Cc: Sharon Goldberg <goldbe@cs.bu.edu>, "cfrg@irtf.org" <cfrg@irtf.org>, "jan@ns1.com" <jan@ns1.com>,  Dimitrios Papadopoulos <dipapado@umd.edu>, Leonid Reyzin <reyzin@cs.bu.edu>
Content-Type: multipart/alternative; boundary="94eb2c07f9f02cadf50554ea321a"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/fM9z6H8qJjHc2i_yGE1ZkP2GfAw>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Sat, 22 Jul 2017 16:08:46 -0000

--94eb2c07f9f02cadf50554ea321a
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

On Fri, Jul 21, 2017 at 9:32 AM, Dan Brown <danibrown@blackberry.com> wrote=
:

> Answering myself below: VRFs have been around since 1999, so are not so
> new.  =E2=80=8EStill don't like the name, and still have trouble seeing t=
he value.
>

VRFs provide deterministic precommitments you can reveal at a later time.
This is useful if you want to maintain a 1:1 mapping of low entropy inputs
(e.g. names, email addresses, phone numbers) to some random values you can
commit to in advance, e.g. through a timestamping service/transparency log.

Using a VRF means you can make these random outputs effectively public
without them being subject to a preimage attack (so long as the VRF private
key is not leaked). This way a key transparency server can prove a given
user's keys were included in a transparency log without enabling spammers
to obtain all of the names in the directory.

--=20
Tony Arcieri

--94eb2c07f9f02cadf50554ea321a
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_extra"><div class=3D"gmail_quote">On F=
ri, Jul 21, 2017 at 9:32 AM, Dan Brown <span dir=3D"ltr">&lt;<a href=3D"mai=
lto:danibrown@blackberry.com" target=3D"_blank">danibrown@blackberry.com</a=
>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 =
0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">




<div lang=3D"EN-US" link=3D"blue" vlink=3D"purple">
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&#39;Slate P=
ro&#39;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;backg=
round-color:rgb(255,255,255)">
Answering myself below: VRFs have been around since 1999, so are not so new=
. =C2=A0=E2=80=8EStill don&#39;t like the name, and still have trouble seei=
ng the value.</div></div></blockquote><div><br></div><div>VRFs provide dete=
rministic precommitments you can reveal at a later time. This is useful if =
you want to maintain a 1:1 mapping of low entropy inputs (e.g. names, email=
 addresses, phone numbers) to some random values you can commit to in advan=
ce, e.g. through a timestamping service/transparency log.</div><div><br></d=
iv><div>Using a VRF means you can make these random outputs effectively pub=
lic without them being subject to a preimage attack (so long as the VRF pri=
vate key is not leaked). This way a key transparency server can prove a giv=
en user&#39;s keys were included in a transparency log without enabling spa=
mmers to obtain all of the names in the directory.</div><div><br></div></di=
v>-- <br><div class=3D"gmail_signature" data-smartmail=3D"gmail_signature">=
Tony Arcieri<br></div>
</div></div>

--94eb2c07f9f02cadf50554ea321a--


From nobody Sat Jul 22 19:26:02 2017
Return-Path: <prvs=8377653b91=uri@ll.mit.edu>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 57351131A4C for <cfrg@ietfa.amsl.com>; Sat, 22 Jul 2017 19:26:00 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -4.188
X-Spam-Level: 
X-Spam-Status: No, score=-4.188 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_MED=-2.3, RP_MATCHES_RCVD=-0.001, T_FILL_THIS_FORM_SHORT=0.01, UNPARSEABLE_RELAY=0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id llV5wYgfi0Ox for <cfrg@ietfa.amsl.com>; Sat, 22 Jul 2017 19:25:58 -0700 (PDT)
Received: from llmx2.ll.mit.edu (LLMX2.LL.MIT.EDU [129.55.12.48]) by ietfa.amsl.com (Postfix) with ESMTP id 718ED127B73 for <cfrg@irtf.org>; Sat, 22 Jul 2017 19:25:58 -0700 (PDT)
Received: from LLE2K10-HUB01.mitll.ad.local (LLE2K10-HUB01.mitll.ad.local) by llmx2.ll.mit.edu (unknown) with ESMTP id v6N2Pt7m005041; Sat, 22 Jul 2017 22:25:55 -0400
From: "Blumenthal, Uri - 0553 - MITLL" <uri@ll.mit.edu>
To: Tony Arcieri <bascule@gmail.com>, "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
Thread-Index: AQHS+vNP80F0E1pfY0yQXqh5796h7KJaNJwAgASWVQCAAYuygIAArIiA
Date: Sun, 23 Jul 2017 02:25:54 +0000
Message-ID: <D21D0C23-B4C8-460A-88A4-9832A65421A5@ll.mit.edu>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com> <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net> <20170721163204.8573013.1016.15939@blackberry.com> <CAHOTMVLNZhX9LreywH0usurTHiULCJTbF2WNYeKZcrjMZJsC7w@mail.gmail.com>
In-Reply-To: <CAHOTMVLNZhX9LreywH0usurTHiULCJTbF2WNYeKZcrjMZJsC7w@mail.gmail.com>
Accept-Language: en-US
Content-Language: en-US
X-MS-Has-Attach: yes
X-MS-TNEF-Correlator: 
Content-Type: multipart/signed; boundary="Apple-Mail-A25145B9-9C9B-4A83-986C-FAF07A1A5B34"; protocol="application/pkcs7-signature"; micalg=sha1
MIME-Version: 1.0
X-Proofpoint-Virus-Version: vendor=fsecure engine=2.50.10432:, , definitions=2017-07-22_19:, , signatures=0
X-Proofpoint-Spam-Details: rule=notspam policy=default score=0 spamscore=0 suspectscore=0 malwarescore=0 phishscore=0 adultscore=0 bulkscore=0 classifier=spam adjust=0 reason=mlx scancount=1 engine=8.0.1-1706020000 definitions=main-1707230037
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/5hZCZ0rcHU7HMFpJIY3mtTJghpQ>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Sun, 23 Jul 2017 02:26:00 -0000

--Apple-Mail-A25145B9-9C9B-4A83-986C-FAF07A1A5B34
Content-Type: multipart/alternative;
	boundary=Apple-Mail-076A17C2-D9F3-4AF2-A400-4213207B7FF3
Content-Transfer-Encoding: 7bit


--Apple-Mail-076A17C2-D9F3-4AF2-A400-4213207B7FF3
Content-Type: text/plain;
	charset=utf-8
Content-Transfer-Encoding: base64
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--Apple-Mail-076A17C2-D9F3-4AF2-A400-4213207B7FF3
Content-Type: text/html;
	charset=utf-8
Content-Transfer-Encoding: base64
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--Apple-Mail-076A17C2-D9F3-4AF2-A400-4213207B7FF3--

--Apple-Mail-A25145B9-9C9B-4A83-986C-FAF07A1A5B34
Content-Type: application/pkcs7-signature; name="smime.p7s"
Content-Disposition: attachment; filename="smime.p7s"
Content-Transfer-Encoding: base64
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--Apple-Mail-A25145B9-9C9B-4A83-986C-FAF07A1A5B34--


From nobody Sat Jul 22 22:11:25 2017
Return-Path: <sharon.goldbe@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 20E52127B73 for <cfrg@ietfa.amsl.com>; Sat, 22 Jul 2017 22:11:24 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.698
X-Spam-Level: 
X-Spam-Status: No, score=-2.698 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id zuxxYiHAQr1S for <cfrg@ietfa.amsl.com>; Sat, 22 Jul 2017 22:11:21 -0700 (PDT)
Received: from mail-it0-x234.google.com (mail-it0-x234.google.com [IPv6:2607:f8b0:4001:c0b::234]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 6822E1201F2 for <cfrg@irtf.org>; Sat, 22 Jul 2017 22:11:21 -0700 (PDT)
Received: by mail-it0-x234.google.com with SMTP id v205so6783371itf.1 for <cfrg@irtf.org>; Sat, 22 Jul 2017 22:11:21 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=rduRgvu4H1BNBRfLEkk7f2Jz2cc0Q0PApjzVm4jfQiw=; b=jEOltisDFAarvGjAkF3/vQ9MgLuiEHsCs+Ip5O78EruEVG5bjosWb5+3zZUR0QFfHM JHZot05+HurHc+RpydA0k4xACKJVyW+FVI4oU8+U2SQ6dfyJ7GkOcu9EINoVmJHyaQT6 FcHdZhXp0FVi8XSmiNdDgE6ojrYocIH7Nar5Bce6xubPTDRRKS4cAppx619CiXI9kgjQ cXsNEy0FtQRP/z83zwXsx9nz5xkruMSoxMr3rxsFAJ4o3NggEiVnjdA559zpObkkrXNj LRs6CzKaRTLg1pcqUytss+ZrYfx4orJ7yBymcmIjB/smIZ8I7Gkm02TiPz/bxPtferJL c+2g==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=rduRgvu4H1BNBRfLEkk7f2Jz2cc0Q0PApjzVm4jfQiw=; b=DrrXIZE8LYy4Jv+7pyk7orzE4+lA0j3CcJHHnZFJY5+XLWImXknsE+8jnozeU4aMZ+ sk6sYk5mfuHrCUIaRV0VR3K8DowAyYDfetqJF817rSOJxCQMSjRQUAdkVuafgucgpIgw 4EDskV1deiDPAoD2PEBzRfre5aDAGS7WIwKu13T3TgppJTZrh5t578y5kKlvzPdW+ZrP sTQb59m8BMFOoT2VOFUQdjfi6zBwltSAsnigEGBiwoe92Al6eiVRKXJ9ZmYSNRQrkBQl ztLkFfQqIoKaHqrpFVzCYmwTS1PGLaQ8sxMGym7SsIU94joTc70/YCaXdxQ9TIsiYdL3 B8EA==
X-Gm-Message-State: AIVw113jAKdeTAZSpm1bEi+b9MljNoHXHeT8g30qpHCPRREzpQV2Q/eT Yolg/5x0Sa0J+X6rQP3oxCPQs+jfigBn
X-Received: by 10.36.103.65 with SMTP id u62mr3572624itc.27.1500786680626; Sat, 22 Jul 2017 22:11:20 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.107.39.83 with HTTP; Sat, 22 Jul 2017 22:10:40 -0700 (PDT)
In-Reply-To: <20170721163204.8573013.1016.15939@blackberry.com>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com> <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net> <20170721163204.8573013.1016.15939@blackberry.com>
From: Sharon Goldberg <sharon.goldbe@gmail.com>
Date: Sun, 23 Jul 2017 08:10:40 +0300
Message-ID: <CAJHGrrTbjL3rd_XU9tx28g3QcBe9tJBOxs2t1OebfvZR_c7epA@mail.gmail.com>
To: Dan Brown <danibrown@blackberry.com>
Cc: "cfrg@irtf.org" <cfrg@irtf.org>, "jan@ns1.com" <jan@ns1.com>, Leonid Reyzin <reyzin@cs.bu.edu>,  Dimitrios Papadopoulos <dipapado@umd.edu>
Content-Type: multipart/alternative; boundary="001a114ac81cfb80fa0554f520d4"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/-AH2J0DQ7pPUcVtMauOWpwAp9lM>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Sun, 23 Jul 2017 05:11:24 -0000

--001a114ac81cfb80fa0554f520d4
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Hi Dan,

Thank you for your comments. Indeed, VRFs have been around since 1999. They
are really "verifiable PRFs" but the name is by now standard in the crypto
literature, and changing it will cause more confusion than keeping it.

In terms of the VRF's security properties, there are three:  uniqueness,
collision resistance, and pseudorandomness. These are defined in our draft =
(
https://tools.ietf.org/html/draft-goldbe-vrf-01#section-3).

How VRFs prevent dictionary attacks: a public hash is subject to a
dictionary attack because, given the output, an adversary can evaluate the
hash on different inputs and see what hits the outputs. In a VRF, the
adversary can't evaluate the hash on different inputs.

You say it's not surprising that "random oracle model proof can prove the
output of a hash to be random". But actually, the output of a hash is NOT
random if the input and the hash function are known. This is because the
output of a hash is deterministic (every input maps to a unique output).
That's exactly what enables dictionary attacks. This is in contrast to a
VRF, where the output is (pseudo)random even given knowledge of the input.
Only once the VRF proof is given, does the VRF output stop looking random.
Note that random oracles are not essential for VRFs, and non-random-oracles
constructions exist (but are less efficient than what we propose to
standardize).

As far as use cases, here are a few:

In the NSEC5 use case for DNSSEC, you have sensitive data (domain names)
and you sign consecutive pairs of hashes of domain names in order to be
able to prove absence of a name. If you just use standard hashing, whenever
signed hash values are disclosed, your sensitive data is subject to
dictionary attacks. VRFs solve that problem, and sensitive names don't have
to be disclosed at all. More details are in https://eprint.iacr.org/201
7/099.pdf

In CONIKS (also Google Key Transparency, Signal secure messaging, Yahoo!
Coname) you also have some sensitive data (user names) that are put into a
Merkle-like authenticated data structure. If you just use standard hashing,
whenever hash values are disclosed, sensitive data is subject to dictionary
attacks. If you use VRFs, sensitive data again can be disclosed only on an
as-needed basis. More details are in  https://eprint.iacr.org/2014/1004.pdf=
.

In a cryptocurrency use case, you wish perform a coin flip that is
deterministic and provably correct, but cannot be done by just anyone.
More details are in https://people.csail.mit.ed
u/nickolai/papers/gilad-algorand-eprint.pdf and possibly other
cryptocurrency papers.

Bryan Ford mentioned an additional usecase at the mic on Tuesday:
distributed password protection protocols

Many of these use case are already putting VRFs into production use (esp.
the CONIKS one).  You can see a list of the various implementations we have
found in the "implementation status" section of our draft.  One of the
reasons we think this spec is so important is that we found flaws in
several of the implementations that can be used to trivially break
uniqueness.  (See eg: https://github.com/google/keytransparency/issues/567)

Thanks,
Sharon

On Fri, Jul 21, 2017 at 7:32 PM, Dan Brown <danibrown@blackberry.com> wrote=
:

> Answering myself below: VRFs have been around since 1999, so are not so
> new.  =E2=80=8EStill don't like the name, and still have trouble seeing t=
he value.
>
> *From: *Dan Brown
> *Sent: *Tuesday, July 18, 2017 2:29 PM
> *To: *Sharon Goldberg; cfrg@irtf.org
> *Cc: *jan@ns1.com; Leonid Reyzin; Dimitrios Papadopoulos
> *Subject: *Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>
> Hi Sharon and CFRG,
>
>
>
> On VRFs, my uncertain comments to consider at your leisure:
>
>
>
> Is it fair to say VRFs are relatively new?  If so, then maybe a little
> more caution is needed about their use.  It seems a tad hasty that it is
> being used already.
>
>
>
> To me, it seems that VRFs are basically signatures, with an extra
> feature.  My concern is that this extra feature might get overused, befor=
e
> it is thoroughly reviewed.
>
>
>
> It is unsurprising to me that random oracle model proof can prove the
> output of a hash to be random.  My intuitive concern is that at least
> informally, this is kind of circular.  Hashes often have some
> non-random-ish properties that might affect the extra security (over
> signatures) that VRFs are aiming for.  I guess I would much prefer a proo=
f
> saying if the hash has (well-studied) properties XYZ, then your
> construction are VRFs.  (Maybe you have this already?  If so, then tell m=
e
> so.)
>
>
>
> Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the wire, I f=
ind it hard to
> see how it could be used to prevent dictionary attacks.  I assume that yo=
u
> are saying the proofs must be encrypted when one needs to avoid dictionar=
y
> models?  I suppose all the details are there in I-D and papers, but for
> now, I am confused about the threat model (which parties have keys, etc.,
> if they require a secure channel and mutual trust, why just use plain old
> hash,=E2=80=A6). To resist dictionary attacks, were already have PAKEs an=
d
> PBHashing.  Now this?
>
>
>
> Finally, on a bikeshed-coloring note, I object to the name =E2=80=9Cverif=
iable
> random function=E2=80=9D, on several grounds.
>
>
>
>    1. It is not a function.  It is at least four functions, keygen, sign,
>    verify, and hashify.
>    2. If you make it into a keyed function F_sk(m), as in
>    prooftohash(sign_sk(m)), it is not verifiable.
>    3. Verification requires the intermediate proof, which is certainly
>    not even pseudorandom (it is easy to distinguish valid signatures from
>    random).
>    4. It is pseudorandom, not random.  (The keys are random, but many
>    crypto has keys, without having =E2=80=9Crandom=E2=80=9D in its name: =
encryption, MAC,
>    signatures, key exchange, =E2=80=A6, they also don=E2=80=99t verifiabl=
e or random in their
>    names either.)
>    5. The similar phrase =E2=80=9Cverifiably random=E2=80=9D, albeit as a=
 misnomer, has
>    past precedents, see NIST P-256 and Brainpool, etc.  When I see VRF, I
>    think a function, that aims to VR in that sense, and great, now we can
>    improve on Brainpool, etc.
>    6. =E2=80=9CRandom function=E2=80=9D should be reserved for the ideal =
random mapping
>    concept, for example, as studied by Flajolet-Odlyzko (ok they only stu=
died
>    the case of equal size domain and range).  The random oracle model, is=
 the
>    idea of approximating this ideal, etc.  An actual approximation should=
 not
>    be name as the ideal (sorry, I=E2=80=99m kind of repeating my point 4)=
.
>
>
>
> Please forgive the fact that my comments above are not very constructive
> (or if the tone is wrong).  This is a new topic for me, so I am reluctant
> too many suggestions.  Nonetheless, I suggest (0) waiting a little, (1) a
> non-random-oracle security proof (if you don=E2=80=99t have it yet), (2) =
re-naming
> the scheme to something like re-hashable (or digestible) signatures (and
> re-name the various parts, i.e. proof -> signature, etc.).
>
>
>
> Best regards,
>
>
>
> Dan
>
>
>
>
>
> *From:* Cfrg [mailto:cfrg-bounces@irtf.org] *On Behalf Of *Sharon Goldber=
g
> *Sent:* Wednesday, July 12, 2017 5:42 AM
> *To:* cfrg@irtf.org
> *Cc:* jan@ns1.com; Dimitrios Papadopoulos <dipapado@umd.edu>; Leonid
> Reyzin <reyzin@cs.bu.edu>
> *Subject:* [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>
>
>
> Dear CFRG,
>
> I'm presenting at next week's meeting on Verifiable Random Functions. A
> VRF is the public-key version of keyed cryptographic hash. Only the holde=
r
> of the VRF secret key can compute the hash, but anyone with the public ke=
y
> can verify it.  VRFs can be used to prevent dictionary attacks on
> hash-based data structures, and have applications to key transparency
> (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (Algorand).
>
> In advance of the meeting, please see:
>
> 1) Our substantially updated -01 draft:
> https://datatracker.ietf.org/doc/draft-goldbe-vrf/
>
> 2) Our project page, with links to various VRF implementations:
> https://www.cs.bu.edu/~goldbe/projects/vrf
>
> Comments welcome.  Thanks,
>
> Sharon
>
> --
> Sharon Goldberg
> Computer Science, Boston University
> http://www.cs.bu.edu/~goldbe
>



--=20
---
Sharon Goldberg
Computer Science, Boston University
http://www.cs.bu.edu/~goldbe

--001a114ac81cfb80fa0554f520d4
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div style=3D"font-size:12.8px">Hi Dan,</div><div style=3D=
"font-size:12.8px"><br></div><div style=3D"font-size:12.8px">Thank you for =
your comments. Indeed, VRFs have been around since 1999. They are really &q=
uot;verifiable PRFs&quot; but the name is by now standard in the crypto lit=
erature, and changing it will cause more confusion than keeping it.</div><d=
iv style=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8px">In =
terms of the VRF&#39;s security properties, there are three: =C2=A0uniquene=
ss, collision resistance, and pseudorandomness. These are defined in our dr=
aft (<span style=3D"font-size:12.8px"><a href=3D"https://tools.ietf.org/htm=
l/draft-goldbe-vrf-01#section-3" target=3D"_blank">https://tools.ietf.org/h=
tml/<wbr>draft-goldbe-vrf-01#section-3</a></span><span style=3D"font-size:1=
2.8px">)<wbr>.=C2=A0</span></div><div style=3D"font-size:12.8px"><br></div>=
<div style=3D"font-size:12.8px">How VRFs prevent dictionary attacks: a publ=
ic hash is subject to a dictionary attack because, given the output, an adv=
ersary can evaluate the hash on different inputs and see what hits the outp=
uts. In a VRF, the adversary can&#39;t evaluate the hash on different input=
s.=C2=A0</div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-=
size:12.8px">You say it&#39;s not surprising that &quot;random oracle model=
 proof can prove the output of a hash to be random&quot;. But actually, the=
 output of a hash is NOT random if the input and the hash function are know=
n. This is because the output of a hash is deterministic (every input maps =
to a unique output). That&#39;s exactly what enables dictionary attacks. Th=
is is in contrast to a VRF, where the output is (pseudo)random even given k=
nowledge of the input. Only once the VRF proof is given, does the VRF outpu=
t stop looking random. Note that random oracles are not essential for VRFs,=
 and non-random-oracles constructions exist (but are less efficient than wh=
at we propose to standardize).</div><div style=3D"font-size:12.8px"><br></d=
iv><div style=3D"font-size:12.8px">As far as use cases, here are a few:=C2=
=A0</div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-size:=
12.8px">In the NSEC5 use case for DNSSEC, you have sensitive data (domain n=
ames) and you sign consecutive pairs of hashes of domain names in order to =
be able to prove absence of a name. If you just use standard hashing, whene=
ver signed hash values are disclosed, your sensitive data is subject to dic=
tionary attacks. VRFs solve that problem, and sensitive names don&#39;t hav=
e to be disclosed at all. More details are in=C2=A0<a href=3D"https://eprin=
t.iacr.org/2017/099.pdf" target=3D"_blank">https://eprint.iacr.org/201<wbr>=
7/099.pdf</a></div><div style=3D"font-size:12.8px"><br></div><div style=3D"=
font-size:12.8px">In CONIKS (also Google Key Transparency, Signal secure me=
ssaging, Yahoo! Coname) you also have some sensitive data (user names) that=
 are put into a Merkle-like authenticated data structure. If you just use s=
tandard hashing, whenever hash values are disclosed, sensitive data is subj=
ect to dictionary attacks. If you use VRFs, sensitive data again can be dis=
closed only on an as-needed basis. More details are in =C2=A0<a href=3D"htt=
ps://eprint.iacr.org/2014/1004.pdf" target=3D"_blank">https://eprint.iacr.o=
rg/2014/<wbr>1004.pdf</a>.</div><div style=3D"font-size:12.8px"><br></div><=
div style=3D"font-size:12.8px">In a cryptocurrency use case, you wish perfo=
rm a coin flip that is deterministic and provably correct, but cannot be do=
ne by just anyone.=C2=A0 More details are in=C2=A0<a href=3D"https://people=
.csail.mit.edu/nickolai/papers/gilad-algorand-eprint.pdf" target=3D"_blank"=
>https://people.csail.mit.ed<wbr>u/nickolai/papers/gilad-algora<wbr>nd-epri=
nt.pdf</a>=C2=A0and possibly other cryptocurrency papers.</div><div style=
=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8px">Bryan Ford =
mentioned an additional usecase at the mic on Tuesday: distributed password=
 protection protocols</div><div style=3D"font-size:12.8px"><br></div><div s=
tyle=3D"font-size:12.8px">Many of these use case are already putting VRFs i=
nto production use (esp. the CONIKS one).=C2=A0 You can see a list of the v=
arious implementations we have found in the &quot;implementation status&quo=
t; section of our draft.=C2=A0 One of the reasons we think this spec is so =
important is that we found flaws in several of the implementations that can=
 be used to trivially break uniqueness. =C2=A0(See eg:=C2=A0<a href=3D"http=
s://github.com/google/keytransparency/issues/567" target=3D"_blank">https:/=
/github.com/google/<wbr>keytransparency/issues/567</a>)</div><div style=3D"=
font-size:12.8px"><br></div><div style=3D"font-size:12.8px"><span style=3D"=
font-size:12.8px">Thanks,</span><br></div><div style=3D"font-size:12.8px">S=
haron=C2=A0</div><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">=
On Fri, Jul 21, 2017 at 7:32 PM, Dan Brown <span dir=3D"ltr">&lt;<a href=3D=
"mailto:danibrown@blackberry.com" target=3D"_blank">danibrown@blackberry.co=
m</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margi=
n:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex=
">




<div lang=3D"EN-US">
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
Answering myself below: VRFs have been around since 1999, so are not so new=
. =C2=A0=E2=80=8EStill don&#39;t like the name, and still have trouble seei=
ng the value.</div>
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
<span style=3D"font-family:Calibri,&quot;Slate Pro&quot;,sans-serif,sans-se=
rif;font-size:initial;line-height:initial;text-align:initial"><br>
</span></div>
<table width=3D"100%" style=3D"background-color:white">
<tbody>
<tr>
<td colspan=3D"2" style=3D"font-size:initial;text-align:initial;background-=
color:rgb(255,255,255)">
<div style=3D"border-style:solid none none;border-top-color:rgb(181,196,223=
);border-top-width:1pt;padding:3pt 0in 0in;font-family:Tahoma,&quot;BB Alph=
a Sans&quot;,&quot;Slate Pro&quot;;font-size:10pt">
<div><b>From: </b>Dan Brown</div>
<div><b>Sent: </b>Tuesday, July 18, 2017 2:29 PM</div>
<div><b>To: </b>Sharon Goldberg; <a href=3D"mailto:cfrg@irtf.org" target=3D=
"_blank">cfrg@irtf.org</a></div>
<div><b>Cc: </b><a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.co=
m</a>; Leonid Reyzin; Dimitrios Papadopoulos</div>
<div><b>Subject: </b>Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functio=
ns</div>
</div>
</td>
</tr>
</tbody>
</table><div><div class=3D"m_4165835283928257204gmail-h5">
<div style=3D"border-style:solid none none;border-top-color:rgb(186,188,209=
);border-top-width:1pt;font-size:initial;text-align:initial;background-colo=
r:rgb(255,255,255)">
</div>
<br>
<div>
<div class=3D"m_4165835283928257204gmail-m_6358749242748202832WordSection1"=
>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Hi Sharon and CFRG,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">On VRFs, my uncertain comments to consider at your leisure:</span=
></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Is it fair to say VRFs are relatively new?=C2=A0 If so, then mayb=
e a little more caution is needed about their use.=C2=A0 It seems a tad has=
ty that it is being used already.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">To me, it seems that VRFs are basically signatures, with an extra=
 feature.=C2=A0 My concern is that this extra feature might get overused, b=
efore it is thoroughly reviewed.=C2=A0
</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">It is unsurprising to me that random oracle model proof can prove=
 the output of a hash to be random.=C2=A0 My intuitive concern is that at l=
east informally, this is kind of circular.=C2=A0
 Hashes often have some non-random-ish properties that might affect the ext=
ra security (over signatures) that VRFs are aiming for.=C2=A0 I guess I wou=
ld much prefer a proof saying if the hash has (well-studied) properties XYZ=
, then your construction are VRFs.=C2=A0 (Maybe
 you have this already?=C2=A0 If so, then tell me so.)</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the w=
ire, I find it hard to see how it could be used to prevent dictionary attac=
ks.=C2=A0 I assume that you are saying the proofs must
 be encrypted when one needs to avoid dictionary models?=C2=A0 I suppose al=
l the details are there in I-D and papers, but for now, I am confused about=
 the threat model (which parties have keys, etc., if they require a secure =
channel and mutual trust, why just use
 plain old hash,=E2=80=A6). To resist dictionary attacks, were already have=
 PAKEs and PBHashing.=C2=A0 Now this?</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Finally, on a bikeshed-coloring note, I object to the name =E2=80=
=9Cverifiable random function=E2=80=9D, on several grounds.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<ol start=3D"1" type=3D"1" style=3D"margin-top:0in">
<li class=3D"m_4165835283928257204gmail-m_6358749242748202832MsoListParagra=
ph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;font-family:Cal=
ibri,sans-serif">It is not a function.=C2=A0 It is at least four functions,=
 keygen, sign, verify, and hashify.</span></li><li class=3D"m_4165835283928=
257204gmail-m_6358749242748202832MsoListParagraph" style=3D"margin-left:0in=
"><span style=3D"font-size:11pt;font-family:Calibri,sans-serif">If you make=
 it into a keyed function F_sk(m), as in prooftohash(sign_sk(m)), it is not=
 verifiable.=C2=A0
</span></li><li class=3D"m_4165835283928257204gmail-m_6358749242748202832Ms=
oListParagraph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;fon=
t-family:Calibri,sans-serif">Verification requires the intermediate proof, =
which is certainly not even pseudorandom (it is easy to distinguish valid s=
ignatures from random).</span></li><li class=3D"m_4165835283928257204gmail-=
m_6358749242748202832MsoListParagraph" style=3D"margin-left:0in"><span styl=
e=3D"font-size:11pt;font-family:Calibri,sans-serif">It is pseudorandom, not=
 random.=C2=A0 (The keys are random, but many crypto has keys, without havi=
ng =E2=80=9Crandom=E2=80=9D in its name: encryption, MAC, signatures,
 key exchange, =E2=80=A6, they also don=E2=80=99t verifiable or random in t=
heir names either.)</span></li><li class=3D"m_4165835283928257204gmail-m_63=
58749242748202832MsoListParagraph" style=3D"margin-left:0in"><span style=3D=
"font-size:11pt;font-family:Calibri,sans-serif">The similar phrase =E2=80=
=9Cverifiably random=E2=80=9D, albeit as a misnomer, has past precedents, s=
ee NIST P-256 and Brainpool, etc.=C2=A0 When I see VRF, I think
 a function, that aims to VR in that sense, and great, now we can improve o=
n Brainpool, etc.</span></li><li class=3D"m_4165835283928257204gmail-m_6358=
749242748202832MsoListParagraph" style=3D"margin-left:0in"><span style=3D"f=
ont-size:11pt;font-family:Calibri,sans-serif">=E2=80=9CRandom function=E2=
=80=9D should be reserved for the ideal random mapping concept, for example=
, as studied by Flajolet-Odlyzko (ok they only studied
 the case of equal size domain and range).=C2=A0 The random oracle model, i=
s the idea of approximating this ideal, etc.=C2=A0 An actual approximation =
should not be name as the ideal (sorry, I=E2=80=99m kind of repeating my po=
int 4).</span></li></ol>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Please forgive the fact that my comments above are not very const=
ructive (or if the tone is wrong).=C2=A0 This is a new topic for me, so I a=
m reluctant too many suggestions.=C2=A0 Nonetheless,
 I suggest (0) waiting a little, (1) a non-random-oracle security proof (if=
 you don=E2=80=99t have it yet), (2) re-naming the scheme to something like=
 re-hashable (or digestible) signatures (and re-name the various parts, i.e=
. proof -&gt; signature, etc.).</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Best regards,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Dan</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><b><span style=3D"font-size:11pt;font-family:Calibri=
,sans-serif">From:</span></b><span style=3D"font-size:11pt;font-family:Cali=
bri,sans-serif"> Cfrg [mailto:<a href=3D"mailto:cfrg-bounces@irtf.org" targ=
et=3D"_blank">cfrg-bounces@irtf.org</a>]
<b>On Behalf Of </b>Sharon Goldberg<br>
<b>Sent:</b> Wednesday, July 12, 2017 5:42 AM<br>
<b>To:</b> <a href=3D"mailto:cfrg@irtf.org" target=3D"_blank">cfrg@irtf.org=
</a><br>
<b>Cc:</b> <a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.com</a>=
; Dimitrios Papadopoulos &lt;<a href=3D"mailto:dipapado@umd.edu" target=3D"=
_blank">dipapado@umd.edu</a>&gt;; Leonid Reyzin &lt;<a href=3D"mailto:reyzi=
n@cs.bu.edu" target=3D"_blank">reyzin@cs.bu.edu</a>&gt;<br>
<b>Subject:</b> [Cfrg] draft-goldbe-vrf: Verifiable Random Functions</span>=
</p>
<p class=3D"MsoNormal">=C2=A0</p>
<div>
<p class=3D"MsoNormal">Dear CFRG,<br>
<br>
I&#39;m presenting at next week&#39;s meeting on Verifiable Random Function=
s. A VRF is the public-key version of keyed cryptographic hash. Only the ho=
lder of the VRF secret key can compute the hash, but anyone with the public=
 key can verify it.=C2=A0 VRFs can be used to
 prevent dictionary attacks on hash-based data structures, and have applica=
tions to key transparency (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (A=
lgorand).<br>
<br>
In advance of the meeting, please see:<br>
<br>
1) Our substantially updated -01 draft:<br>
<a href=3D"https://datatracker.ietf.org/doc/draft-goldbe-vrf/" target=3D"_b=
lank">https://datatracker.ietf.org/d<wbr>oc/draft-goldbe-vrf/</a><br>
<br>
2) Our project page, with links to various VRF implementations:<br>
<a href=3D"https://www.cs.bu.edu/~goldbe/projects/vrf" target=3D"_blank">ht=
tps://www.cs.bu.edu/~goldbe/<wbr>projects/vrf</a><br>
<br>
Comments welcome.=C2=A0 Thanks,<br>
<br>
Sharon<br>
<br>
--<br>
Sharon Goldberg<br>
Computer Science, Boston University<br>
<a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu=
.edu/~goldbe</a></p>
</div>
</div>
</div>
</div></div></div>

</blockquote></div><br><br clear=3D"all"><div><br></div>-- <br><div class=
=3D"m_4165835283928257204gmail_signature">---<br>Sharon Goldberg<br>Compute=
r Science, Boston University<br><a href=3D"http://www.cs.bu.edu/~goldbe" ta=
rget=3D"_blank">http://www.cs.bu.edu/~goldbe</a></div>
</div></div>

--001a114ac81cfb80fa0554f520d4--


From nobody Mon Jul 24 07:40:02 2017
Return-Path: <allison.mankin@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id B9F93131D33; Mon, 24 Jul 2017 07:40:00 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.699
X-Spam-Level: 
X-Spam-Status: No, score=-2.699 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=unavailable autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id FIQmhEUEg2sK; Mon, 24 Jul 2017 07:39:58 -0700 (PDT)
Received: from mail-wm0-x22f.google.com (mail-wm0-x22f.google.com [IPv6:2a00:1450:400c:c09::22f]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 89870131D2F; Mon, 24 Jul 2017 07:39:57 -0700 (PDT)
Received: by mail-wm0-x22f.google.com with SMTP id l81so19862035wmg.1; Mon, 24 Jul 2017 07:39:57 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=u+ytpkHk9XsNWoM4OjOkreWEj35F9nOKZqM9ZbfQdCM=; b=WNSPtmUl9Hl+InM5jVw57dG4O+oy7dVTKJ3yanNQJPKhd4taPxFu+jq1WtZmeEvOyv YLdLlKDcFkpF9phylGtyXJBLvcsSPrJOQadHc9cY6P+zjiwr1yk0rS2GAajnMSxM/+Tn PGJgB0ygv1wGOhQGeh1pKrcefHZBGCWO5S2PdnBOWknfpz3j1vZOsivw1Q3or8pQoLvX 5Yy+KS5Y44WcWGU+5aE5HRkokTFtt+lzdEPP3/4snZgVB7bbS9PTpNjEKfEHbjNG6RlK yyvBwk0i9MaVdo2/xL7RFfvnMFnEez6ttON/gAQ8wI/V19/mIsdxLsp4if4lFdlz0rTA uGrw==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=u+ytpkHk9XsNWoM4OjOkreWEj35F9nOKZqM9ZbfQdCM=; b=UNDkJ8OWc7ZXfkU9IzkTqiJ+zV4vWfOGj1Zwy4hjQFQoVUY3+n0KTufEj70xLuy8BX sMHLN/437Y9x/EuPs2hoiOF4SXFMVSs88iKrirM2kYBjLpOgAjePozzw3hCEUIcDJjeu X6i762E5qDt6cFBDiUjQ/oiFjECp9uJU0lyhD6HniBLNaKE8bXJdlu+dOkidiCWboP3X vdwFXBPt9Ew/jAStFyCG+IShAhQzNpvxJRtapukL6DeAlK761YLp9XB9I/DL2pbelJe8 qA4skDi99JVvYt3BwexAodk9DZrtDAlhnxhz3yxA0MUylGNtF6LwWN/KfjEvdtay+d/r j06g==
X-Gm-Message-State: AIVw110F/RUN1FSLXO8gGHvk4Z6jWfFDyQplXaoYatbPkOE3y+bYXK3N PDWah6bYsDnuIccTAFdD5QK+P151lA==
X-Received: by 10.80.215.7 with SMTP id t7mr15622561edi.19.1500907195956; Mon, 24 Jul 2017 07:39:55 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.80.138.69 with HTTP; Mon, 24 Jul 2017 07:39:55 -0700 (PDT)
In-Reply-To: <4699f3d2-40ce-9c40-d29a-d24ecb3b6cab@huelsing.net>
References: <D4FDAF9D.8D586%kenny.paterson@rhul.ac.uk> <9a878527-5ab9-5429-7c5d-4f7e4ca4e8db@isode.com> <08944dc3-9086-ed47-cc1b-54248b3dac70@cs.tcd.ie> <D566ADE0.963E4%kenny.paterson@rhul.ac.uk> <9e6b6146-e376-86cb-70be-0127a3e72d16@cs.tcd.ie> <D56DBB2C.96A67%kenny.paterson@rhul.ac.uk> <6f90e485-01f4-5ad8-49ef-e51c52e01a46@cs.tcd.ie> <5e328e85-a8a1-67f1-3853-418309b04a17@huelsing.net> <27cc7000-7fd5-27dd-b8b5-9b9518a9f3ad@huelsing.net> <1785b9ed-fb53-889a-9d34-311c7ea5c762@cs.tcd.ie> <4699f3d2-40ce-9c40-d29a-d24ecb3b6cab@huelsing.net>
From: Allison Mankin <allison.mankin@gmail.com>
Date: Mon, 24 Jul 2017 16:39:55 +0200
Message-ID: <CAP8yD=sTXB7trXyjz+VGHOAvh9egiSHmBcukNVN1yiq0mwkfFw@mail.gmail.com>
To: "A. Huelsing" <ietf@huelsing.net>
Cc: Stephen Farrell <stephen.farrell@cs.tcd.ie>,  "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>, Alexey Melnikov <alexey.melnikov@isode.com>,  "irsg@irtf.org" <irsg@irtf.org>, "cfrg@irtf.org" <Cfrg@irtf.org>,  "draft-irtf-cfrg-xmss-hash-based-signatures@ietf.org" <draft-irtf-cfrg-xmss-hash-based-signatures@ietf.org>
Content-Type: multipart/alternative; boundary="f403045dbe944186ed0555113061"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/1YsqTM3_ce6913khnqWZ2Mg0c4Q>
Subject: Re: [Cfrg] [irsg] IRSG review of draft-irtf-cfrg-xmss-hash-based-signatures-08
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 24 Jul 2017 14:40:01 -0000

--f403045dbe944186ed0555113061
Content-Type: text/plain; charset="UTF-8"

Thanks for making the changes.  Stephen, let me know if you are ready to
give this a thumbs-up, and I'll start an IRSG poll.

Allison

On 24 July 2017 at 16:30, A. Huelsing <ietf@huelsing.net> wrote:

> Dear Stephen,
>
> we tried to make the required changes. Please have a look if you are fine
> with the changes (especially regarding section 5 and the reference
> implementation).
>
> You find our answers to your review below and the new draft version
> attached.
>
> Thanks again for your time,
>
> Andreas, Aziz, Denis, Joost & Stefan
>
>
> ################# Answers ####################
> possible errors:
> ----------------
>
> - 3.1.2: Algorithm 2: "if ( (i + s) > w - 1 )..." seems to be
> missing parenthesis around the "(w-1)" to me.  Without those
> brackets I could interpret that test to always result in false.
>
> #Done
>
> - 4.1.9: should the call to setIdx in alg 12 be after treeSig?
>   as-is you seem to have incremented the index too soon so
> that when alg 11 does getIdx it'd presumably get the
> incremented index and cause verification failure. I think
> the same is true of alg 16 as well, in section 4.2.4.
>
> #Done
>
> significant comments, but likely fixable:
> -----------------------------------------
>
> - section 5: there are waaaay too many options defined here.
>   As-is, this will damage potential deployment of xmss. I
> would strongly suggest deleting all of the options except the
> minimum, that being one (and only one) set of parameters for
> XMSS and one for XMSS^MT. If others are needed later, those
> can be defined later. (Note that the damage done here includes
> the hours of developer time that would be wasted debating
> which of these choices to implement/use. Consider the case of
> pre-hash variants of eddsa for an ongoing example.)
>
> ####
> #   We significantly changed section 5, please check if this
> #   satisfies your remarks
> ####
>
> - section 5 (or an appendix) should contain some test vectors
>   (including intermediate values). Without those, implementers
> have a much harder time of getting their code right.
>
> # Added section on reference implementation
>
>
> nits, near-nits and other ignorable things:
> -------------------------------------------
>
> - abstract: I'd suggest s/can withstand attacks/ can withstand
>   so-far known attacks/
>
> # Done
>
> - 1.1: You say if used >1 time "no cryptographic security
>   guarantees remain." It might be clearer to give some
> examples of consequences, e.g. that the attacker can forge new
> signatures or whatever.
>
> # Done
>
> - 1.1: I think you might mention that XMSS and other OTS ideas
>   require some new crypto APIs. I'm not aware if anyone has
> developed proposals for such, but would be interested if
> someone has.
>
> # Done
>
> - 2.3, 2nd last para: you might want to say what happens with
>   e.g.  B<<2 where B=0xf0. I assume the result is 0xc0 but
> someone might think it's 0x3c0 or even 0xc3.
>
> # Done: Removed the left shift as it is never used for single bytes
>
> - 2.5: having the "type word" as octet 15 of a 32 byte address
>   seems odd. Is there a reason why? (Just wondering.)
>
> # Yes: We got the space and think that it simlifies implementation if
> one always has to manipulate whole words (and can treat the address as
> uint32_t[8])
>
> - 2.6: It seems odd to given an example where the input and
>   output of base_w() are the same. A different example may be
> more useful. (More examples generally would be great.)
>
> # Done
>
> - 3.1.3: maybe note that "/" means nothing? Which I assume it
>   does? Better might be to just say that.
>
> # Done
>
> - 3.1.5: "a maximum value of len_1 * (w - 1) * 2^8" is missing
>   units
>
> # Done: value -> Integer value
>
> - 3.1.5: "the variable" - which one?
>
> # Done: Added explanation
>
> - 3.1.5: "For the parameter sets given in Section 5 a 32-bit
>   unsigned integer is sufficient." Sufficient for what?
>
> # Done: Added " to hold the checksum"
>
> - 3.1.5: The ascii art at the end of p16 doesn't help much.
>
> # while the art does not contain new information, we think it's
> a handy reminder. Would prefer to keep it like this.
>
> - 3.1.7: The "MUST match" statement doesn't seem enforceable
>   nor testable so I'm not sure it's a good idea to include.
> OTOH, I do get the idea of using 2119 terms for emphasis.
>
> # Ok, so what should we do? I agree that key handling cannot be
> verified. Still, it seems necessary to emphasize this.
> If it is just about the use of the 2119 term,
> how about:
> "but it is crucial for security that the cryptographic strength
> matches that of the used WOTS+ parameters."?
>
> - 3.1.7: I think it might be useful to point out any specific
>   problems associated with using a low entropy human memorable
> secret (password) for the value S. No matter what you say,
> people will do that, so better if you can say you told them
> specifically about downsides of doing that.
>
> # We adressed this in a new sentence at the end of the
> # paragraph.
>
> - 4.1.12: I'm not sure if the MAY there is correct or not.  If
>   it means "you MAY use a different algorithm to get the same
> output as alg 12" then that'd be fine. If something else is
> meant I'm not sure what you're saying, and it'd probably be
> better to not even mention it.
> # That is exactly what it means. There are far more efficient
> # algorithms to compute that output (but also far more complex)
>
> - section 5 should also spell out the signature and
> public key sizes in bytes and ideally, if you keep multiple
> options, (but please don't:-) describe relative or measured
> timings.
>
> # Done
>
>

--f403045dbe944186ed0555113061
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_default" style=3D"font-family:arial,he=
lvetica,sans-serif">Thanks for making the changes.=C2=A0 Stephen, let me kn=
ow if you are ready to give this a thumbs-up, and I&#39;ll start an IRSG po=
ll.<br><br></div><div class=3D"gmail_default" style=3D"font-family:arial,he=
lvetica,sans-serif">Allison<br></div></div><div class=3D"gmail_extra"><br><=
div class=3D"gmail_quote">On 24 July 2017 at 16:30, A. Huelsing <span dir=
=3D"ltr">&lt;<a href=3D"mailto:ietf@huelsing.net" target=3D"_blank">ietf@hu=
elsing.net</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=
=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Dear Ste=
phen,<br>
<br>
we tried to make the required changes. Please have a look if you are fine<b=
r>
with the changes (especially regarding section 5 and the reference<br>
implementation).<br>
<br>
You find our answers to your review below and the new draft version attache=
d.<br>
<br>
Thanks again for your time,<br>
<br>
Andreas, Aziz, Denis, Joost &amp; Stefan<br>
<br>
<br>
################# Answers ####################<br>
<span class=3D"">possible errors:<br>
----------------<br>
<br>
- 3.1.2: Algorithm 2: &quot;if ( (i + s) &gt; w - 1 )...&quot; seems to be<=
br>
missing parenthesis around the &quot;(w-1)&quot; to me.=C2=A0 Without those=
<br>
brackets I could interpret that test to always result in false.<br>
<br>
</span>#Done<br>
<span class=3D""><br>
- 4.1.9: should the call to setIdx in alg 12 be after treeSig?<br>
=C2=A0 as-is you seem to have incremented the index too soon so<br>
that when alg 11 does getIdx it&#39;d presumably get the<br>
incremented index and cause verification failure. I think<br>
the same is true of alg 16 as well, in section 4.2.4.<br>
<br>
</span>#Done<br>
<span class=3D""><br>
significant comments, but likely fixable:<br>
------------------------------<wbr>-----------<br>
<br>
- section 5: there are waaaay too many options defined here.<br>
=C2=A0 As-is, this will damage potential deployment of xmss. I<br>
would strongly suggest deleting all of the options except the<br>
minimum, that being one (and only one) set of parameters for<br>
XMSS and one for XMSS^MT. If others are needed later, those<br>
can be defined later. (Note that the damage done here includes<br>
the hours of developer time that would be wasted debating<br>
which of these choices to implement/use. Consider the case of<br>
pre-hash variants of eddsa for an ongoing example.)<br>
<br>
</span>####<br>
#=C2=A0 =C2=A0We significantly changed section 5, please check if this<br>
#=C2=A0 =C2=A0satisfies your remarks<br>
####<br>
<span class=3D""><br>
- section 5 (or an appendix) should contain some test vectors<br>
=C2=A0 (including intermediate values). Without those, implementers<br>
have a much harder time of getting their code right.<br>
<br>
</span># Added section on reference implementation<br>
<span class=3D""><br>
<br>
nits, near-nits and other ignorable things:<br>
------------------------------<wbr>-------------<br>
<br>
- abstract: I&#39;d suggest s/can withstand attacks/ can withstand<br>
=C2=A0 so-far known attacks/<br>
<br>
</span># Done<br>
<span class=3D""><br>
- 1.1: You say if used &gt;1 time &quot;no cryptographic security<br>
=C2=A0 guarantees remain.&quot; It might be clearer to give some<br>
examples of consequences, e.g. that the attacker can forge new<br>
signatures or whatever.<br>
<br>
</span># Done<br>
<span class=3D""><br>
- 1.1: I think you might mention that XMSS and other OTS ideas<br>
=C2=A0 require some new crypto APIs. I&#39;m not aware if anyone has<br>
developed proposals for such, but would be interested if<br>
someone has.<br>
<br>
</span># Done<br>
<span class=3D""><br>
- 2.3, 2nd last para: you might want to say what happens with<br>
=C2=A0 e.g.=C2=A0 B&lt;&lt;2 where B=3D0xf0. I assume the result is 0xc0 bu=
t<br>
someone might think it&#39;s 0x3c0 or even 0xc3.<br>
<br>
</span># Done: Removed the left shift as it is never used for single bytes<=
br>
<span class=3D""><br>
- 2.5: having the &quot;type word&quot; as octet 15 of a 32 byte address<br=
>
=C2=A0 seems odd. Is there a reason why? (Just wondering.)<br>
<br>
</span># Yes: We got the space and think that it simlifies implementation i=
f<br>
one always has to manipulate whole words (and can treat the address as<br>
uint32_t[8])<br>
<span class=3D""><br>
- 2.6: It seems odd to given an example where the input and<br>
=C2=A0 output of base_w() are the same. A different example may be<br>
more useful. (More examples generally would be great.)<br>
<br>
</span># Done<br>
<span class=3D""><br>
- 3.1.3: maybe note that &quot;/&quot; means nothing? Which I assume it<br>
=C2=A0 does? Better might be to just say that.<br>
<br>
</span># Done<br>
<span class=3D""><br>
- 3.1.5: &quot;a maximum value of len_1 * (w - 1) * 2^8&quot; is missing<br=
>
=C2=A0 units<br>
<br>
</span># Done: value -&gt; Integer value<br>
<span class=3D""><br>
- 3.1.5: &quot;the variable&quot; - which one?<br>
<br>
</span># Done: Added explanation<br>
<span class=3D""><br>
- 3.1.5: &quot;For the parameter sets given in Section 5 a 32-bit<br>
=C2=A0 unsigned integer is sufficient.&quot; Sufficient for what?<br>
<br>
</span># Done: Added &quot; to hold the checksum&quot;<br>
<span class=3D""><br>
- 3.1.5: The ascii art at the end of p16 doesn&#39;t help much.<br>
<br>
</span># while the art does not contain new information, we think it&#39;s<=
br>
a handy reminder. Would prefer to keep it like this.<br>
<span class=3D""><br>
- 3.1.7: The &quot;MUST match&quot; statement doesn&#39;t seem enforceable<=
br>
=C2=A0 nor testable so I&#39;m not sure it&#39;s a good idea to include.<br=
>
OTOH, I do get the idea of using 2119 terms for emphasis.<br>
<br>
</span># Ok, so what should we do? I agree that key handling cannot be<br>
verified. Still, it seems necessary to emphasize this.<br>
If it is just about the use of the 2119 term,<br>
how about:<br>
&quot;but it is crucial for security that the cryptographic strength<br>
matches that of the used WOTS+ parameters.&quot;?<br>
<span class=3D""><br>
- 3.1.7: I think it might be useful to point out any specific<br>
=C2=A0 problems associated with using a low entropy human memorable<br>
secret (password) for the value S. No matter what you say,<br>
people will do that, so better if you can say you told them<br>
specifically about downsides of doing that.<br>
<br>
</span># We adressed this in a new sentence at the end of the<br>
# paragraph.<br>
<span class=3D""><br>
- 4.1.12: I&#39;m not sure if the MAY there is correct or not.=C2=A0 If<br>
=C2=A0 it means &quot;you MAY use a different algorithm to get the same<br>
output as alg 12&quot; then that&#39;d be fine. If something else is<br>
meant I&#39;m not sure what you&#39;re saying, and it&#39;d probably be<br>
better to not even mention it.<br>
</span># That is exactly what it means. There are far more efficient<br>
# algorithms to compute that output (but also far more complex)<br>
<span class=3D""><br>
- section 5 should also spell out the signature and<br>
public key sizes in bytes and ideally, if you keep multiple<br>
options, (but please don&#39;t:-) describe relative or measured<br>
timings.<br>
<br>
</span># Done<br>
<br>
</blockquote></div><br></div>

--f403045dbe944186ed0555113061--


From nobody Mon Jul 24 07:44:00 2017
Return-Path: <stephen.farrell@cs.tcd.ie>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 086B9131D70; Mon, 24 Jul 2017 07:43:58 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -4.302
X-Spam-Level: 
X-Spam-Status: No, score=-4.302 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, RCVD_IN_DNSWL_MED=-2.3, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=cs.tcd.ie
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id EP-2XQSRrrWk; Mon, 24 Jul 2017 07:43:55 -0700 (PDT)
Received: from mercury.scss.tcd.ie (mercury.scss.tcd.ie [134.226.56.6]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 94C32131D6F; Mon, 24 Jul 2017 07:43:55 -0700 (PDT)
Received: from localhost (localhost [127.0.0.1]) by mercury.scss.tcd.ie (Postfix) with ESMTP id CFF06BE50; Mon, 24 Jul 2017 15:43:53 +0100 (IST)
Received: from mercury.scss.tcd.ie ([127.0.0.1]) by localhost (mercury.scss.tcd.ie [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id KerVh1aHaFrG; Mon, 24 Jul 2017 15:43:53 +0100 (IST)
Received: from [134.226.36.93] (bilbo.dsg.cs.tcd.ie [134.226.36.93]) by mercury.scss.tcd.ie (Postfix) with ESMTPSA id 8FCF3BE4D; Mon, 24 Jul 2017 15:43:53 +0100 (IST)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=cs.tcd.ie; s=mail; t=1500907433; bh=2S9ypQrn2gggphyOnbhoL92EDLT7WOFZT3HuSd5RxeI=; h=Subject:To:Cc:References:From:Date:In-Reply-To:From; b=H3BqAYKuBFGwGM4YkQVifu1hiEzQSUiF3w+Zwj8TOhVIBKhaDBD7f3oGmthmF/M2R uUVpR9PCIRI5xFjZ1jonjNoHxV40HmfTmtCVu+NQvHxnfzCK9nL3wHSrTWFGfzppgf F7GomCDKN8qf/BsSgEWrmu9ySlZK+ZdQ7G+RVSYI=
To: "A. Huelsing" <ietf@huelsing.net>, "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>, Alexey Melnikov <alexey.melnikov@isode.com>, "irsg@irtf.org" <irsg@irtf.org>, "cfrg@irtf.org" <Cfrg@irtf.org>
Cc: "draft-irtf-cfrg-xmss-hash-based-signatures@ietf.org" <draft-irtf-cfrg-xmss-hash-based-signatures@ietf.org>
References: <D4FDAF9D.8D586%kenny.paterson@rhul.ac.uk> <9a878527-5ab9-5429-7c5d-4f7e4ca4e8db@isode.com> <08944dc3-9086-ed47-cc1b-54248b3dac70@cs.tcd.ie> <D566ADE0.963E4%kenny.paterson@rhul.ac.uk> <9e6b6146-e376-86cb-70be-0127a3e72d16@cs.tcd.ie> <D56DBB2C.96A67%kenny.paterson@rhul.ac.uk> <6f90e485-01f4-5ad8-49ef-e51c52e01a46@cs.tcd.ie> <5e328e85-a8a1-67f1-3853-418309b04a17@huelsing.net> <27cc7000-7fd5-27dd-b8b5-9b9518a9f3ad@huelsing.net> <1785b9ed-fb53-889a-9d34-311c7ea5c762@cs.tcd.ie> <4699f3d2-40ce-9c40-d29a-d24ecb3b6cab@huelsing.net>
From: Stephen Farrell <stephen.farrell@cs.tcd.ie>
Openpgp: id=D66EA7906F0B897FB2E97D582F3C8736805F8DA2; url=
Message-ID: <92dbf402-be6b-cf6d-40da-983f6faa5e8c@cs.tcd.ie>
Date: Mon, 24 Jul 2017 15:43:52 +0100
User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.2.1
MIME-Version: 1.0
In-Reply-To: <4699f3d2-40ce-9c40-d29a-d24ecb3b6cab@huelsing.net>
Content-Type: multipart/signed; micalg=pgp-sha256; protocol="application/pgp-signature"; boundary="Q2k6mEjaTdQ1bhwHJ55DK04ULXQssufU0"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/VB41J987wmMGIgsqBolZsoqTdqc>
Subject: Re: [Cfrg] [irsg] IRSG review of draft-irtf-cfrg-xmss-hash-based-signatures-08
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 24 Jul 2017 14:43:58 -0000

This is an OpenPGP/MIME signed message (RFC 4880 and 3156)
--Q2k6mEjaTdQ1bhwHJ55DK04ULXQssufU0
Content-Type: multipart/mixed; boundary="NG0dhUdbis0s2UJlkVDOP5f7x1olDQ8Gp";
 protected-headers="v1"
From: Stephen Farrell <stephen.farrell@cs.tcd.ie>
To: "A. Huelsing" <ietf@huelsing.net>,
 "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>,
 Alexey Melnikov <alexey.melnikov@isode.com>, "irsg@irtf.org"
 <irsg@irtf.org>, "cfrg@irtf.org" <Cfrg@irtf.org>
Cc: "draft-irtf-cfrg-xmss-hash-based-signatures@ietf.org"
 <draft-irtf-cfrg-xmss-hash-based-signatures@ietf.org>
Message-ID: <92dbf402-be6b-cf6d-40da-983f6faa5e8c@cs.tcd.ie>
Subject: Re: [irsg] IRSG review of
 draft-irtf-cfrg-xmss-hash-based-signatures-08
References: <D4FDAF9D.8D586%kenny.paterson@rhul.ac.uk>
 <9a878527-5ab9-5429-7c5d-4f7e4ca4e8db@isode.com>
 <08944dc3-9086-ed47-cc1b-54248b3dac70@cs.tcd.ie>
 <D566ADE0.963E4%kenny.paterson@rhul.ac.uk>
 <9e6b6146-e376-86cb-70be-0127a3e72d16@cs.tcd.ie>
 <D56DBB2C.96A67%kenny.paterson@rhul.ac.uk>
 <6f90e485-01f4-5ad8-49ef-e51c52e01a46@cs.tcd.ie>
 <5e328e85-a8a1-67f1-3853-418309b04a17@huelsing.net>
 <27cc7000-7fd5-27dd-b8b5-9b9518a9f3ad@huelsing.net>
 <1785b9ed-fb53-889a-9d34-311c7ea5c762@cs.tcd.ie>
 <4699f3d2-40ce-9c40-d29a-d24ecb3b6cab@huelsing.net>
In-Reply-To: <4699f3d2-40ce-9c40-d29a-d24ecb3b6cab@huelsing.net>

--NG0dhUdbis0s2UJlkVDOP5f7x1olDQ8Gp
Content-Type: text/plain; charset=utf-8
Content-Language: en-GB
Content-Transfer-Encoding: quoted-printable


Hi Andreas,

I took a look at the diff vs. -09 and all the changes
that I reckon were needed are covered nicely. I also
think that the set of changes as a whole are good
improvements, thanks.

So fwiw, I think this is ready for publication.

Cheers,
S.

PS: I'd still prefer fewer options, but we talked
about that already:-) That oughtn't delay publication
I reckon.

On 24/07/17 15:30, A. Huelsing wrote:
> Dear Stephen,
>=20
> we tried to make the required changes. Please have a look if you are fi=
ne
> with the changes (especially regarding section 5 and the reference
> implementation).
>=20
> You find our answers to your review below and the new draft version att=
ached.
>=20
> Thanks again for your time,
>=20
> Andreas, Aziz, Denis, Joost & Stefan
>=20
>=20
> ################# Answers ####################
> possible errors:
> ----------------
>=20
> - 3.1.2: Algorithm 2: "if ( (i + s) > w - 1 )..." seems to be
> missing parenthesis around the "(w-1)" to me.  Without those
> brackets I could interpret that test to always result in false.
>=20
> #Done
>=20
> - 4.1.9: should the call to setIdx in alg 12 be after treeSig?
>   as-is you seem to have incremented the index too soon so
> that when alg 11 does getIdx it'd presumably get the
> incremented index and cause verification failure. I think
> the same is true of alg 16 as well, in section 4.2.4.
>=20
> #Done
>=20
> significant comments, but likely fixable:
> -----------------------------------------
>=20
> - section 5: there are waaaay too many options defined here.
>   As-is, this will damage potential deployment of xmss. I
> would strongly suggest deleting all of the options except the
> minimum, that being one (and only one) set of parameters for
> XMSS and one for XMSS^MT. If others are needed later, those
> can be defined later. (Note that the damage done here includes
> the hours of developer time that would be wasted debating
> which of these choices to implement/use. Consider the case of
> pre-hash variants of eddsa for an ongoing example.)
>=20
> ####
> #   We significantly changed section 5, please check if this
> #   satisfies your remarks
> ####
>=20
> - section 5 (or an appendix) should contain some test vectors
>   (including intermediate values). Without those, implementers
> have a much harder time of getting their code right.
>=20
> # Added section on reference implementation
>=20
>=20
> nits, near-nits and other ignorable things:
> -------------------------------------------
>=20
> - abstract: I'd suggest s/can withstand attacks/ can withstand
>   so-far known attacks/
> =20
> # Done
>=20
> - 1.1: You say if used >1 time "no cryptographic security
>   guarantees remain." It might be clearer to give some
> examples of consequences, e.g. that the attacker can forge new
> signatures or whatever.
>=20
> # Done
>=20
> - 1.1: I think you might mention that XMSS and other OTS ideas
>   require some new crypto APIs. I'm not aware if anyone has
> developed proposals for such, but would be interested if
> someone has.
>=20
> # Done
>=20
> - 2.3, 2nd last para: you might want to say what happens with
>   e.g.  B<<2 where B=3D0xf0. I assume the result is 0xc0 but
> someone might think it's 0x3c0 or even 0xc3.
>=20
> # Done: Removed the left shift as it is never used for single bytes
>=20
> - 2.5: having the "type word" as octet 15 of a 32 byte address
>   seems odd. Is there a reason why? (Just wondering.)
>=20
> # Yes: We got the space and think that it simlifies implementation if
> one always has to manipulate whole words (and can treat the address as
> uint32_t[8])
> =20
> - 2.6: It seems odd to given an example where the input and
>   output of base_w() are the same. A different example may be
> more useful. (More examples generally would be great.)
>=20
> # Done
>=20
> - 3.1.3: maybe note that "/" means nothing? Which I assume it
>   does? Better might be to just say that.
> =20
> # Done
>=20
> - 3.1.5: "a maximum value of len_1 * (w - 1) * 2^8" is missing
>   units
> =20
> # Done: value -> Integer value
>=20
> - 3.1.5: "the variable" - which one?
>=20
> # Done: Added explanation
>=20
> - 3.1.5: "For the parameter sets given in Section 5 a 32-bit
>   unsigned integer is sufficient." Sufficient for what?
>=20
> # Done: Added " to hold the checksum"
> =20
> - 3.1.5: The ascii art at the end of p16 doesn't help much.
>=20
> # while the art does not contain new information, we think it's
> a handy reminder. Would prefer to keep it like this.
>=20
> - 3.1.7: The "MUST match" statement doesn't seem enforceable
>   nor testable so I'm not sure it's a good idea to include.
> OTOH, I do get the idea of using 2119 terms for emphasis.
>=20
> # Ok, so what should we do? I agree that key handling cannot be
> verified. Still, it seems necessary to emphasize this.
> If it is just about the use of the 2119 term,
> how about:
> "but it is crucial for security that the cryptographic strength
> matches that of the used WOTS+ parameters."?
>=20
> - 3.1.7: I think it might be useful to point out any specific
>   problems associated with using a low entropy human memorable
> secret (password) for the value S. No matter what you say,
> people will do that, so better if you can say you told them
> specifically about downsides of doing that.
>=20
> # We adressed this in a new sentence at the end of the
> # paragraph.
>=20
> - 4.1.12: I'm not sure if the MAY there is correct or not.  If
>   it means "you MAY use a different algorithm to get the same
> output as alg 12" then that'd be fine. If something else is
> meant I'm not sure what you're saying, and it'd probably be
> better to not even mention it.
> # That is exactly what it means. There are far more efficient
> # algorithms to compute that output (but also far more complex)
>=20
> - section 5 should also spell out the signature and
> public key sizes in bytes and ideally, if you keep multiple
> options, (but please don't:-) describe relative or measured
> timings.
>=20
> # Done
>=20


--NG0dhUdbis0s2UJlkVDOP5f7x1olDQ8Gp--

--Q2k6mEjaTdQ1bhwHJ55DK04ULXQssufU0
Content-Type: application/pgp-signature; name="signature.asc"
Content-Description: OpenPGP digital signature
Content-Disposition: attachment; filename="signature.asc"

-----BEGIN PGP SIGNATURE-----

iQEcBAEBCAAGBQJZdgeoAAoJEC88hzaAX42ixBsIALt/4Sz1Ar32uows9Bb7Jtgv
5f8cUblsccRYAjnJiV9qZ7bDzjeQ6J41qiz+Lrmx5Qywj/1jhyg7afPonD3N1AUl
UG6EVG9py5Wv34bD5ASPh/MkZdqWafds9cZu67vQSHjsMyLUu+hsM5EtjECcqjON
CwVymfxqfrw7++mdeSrW9ENd260owqkQuubXToZEnwcSiWt1B/nOHHTYS7gQy+kR
h/3S8+cGg7PM7txZEly1Rl9n3hT7ly7zYSVj1Oiv0i2ZCJdueWJO58LtHy0u0ztD
mtiCbZJ6EJ3NIvQ1Lg0+SDrKfB74voh3/ewFgKEOVFCOm3gb4TNRCdmZvnyXLxU=
=qYNS
-----END PGP SIGNATURE-----

--Q2k6mEjaTdQ1bhwHJ55DK04ULXQssufU0--


From nobody Mon Jul 24 07:45:56 2017
Return-Path: <paul.hoffman@vpnc.org>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id EEAFD131DA6; Mon, 24 Jul 2017 07:45:53 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.9
X-Spam-Level: 
X-Spam-Status: No, score=-1.9 tagged_above=-999 required=5 tests=[BAYES_00=-1.9] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id kK_TWAwrJ1-0; Mon, 24 Jul 2017 07:45:53 -0700 (PDT)
Received: from mail.proper.com (Opus1.Proper.COM [207.182.41.91]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 2D4C0131D2C; Mon, 24 Jul 2017 07:45:53 -0700 (PDT)
Received: from [10.32.60.46] (142-254-101-176.dsl.dynamic.fusionbroadband.com [142.254.101.176]) (authenticated bits=0) by mail.proper.com (8.15.2/8.14.9) with ESMTPSA id v6OEj0fE063532 (version=TLSv1.2 cipher=ECDHE-RSA-AES256-GCM-SHA384 bits=256 verify=NO); Mon, 24 Jul 2017 07:45:01 -0700 (MST) (envelope-from paul.hoffman@vpnc.org)
X-Authentication-Warning: mail.proper.com: Host 142-254-101-176.dsl.dynamic.fusionbroadband.com [142.254.101.176] claimed to be [10.32.60.46]
From: "Paul Hoffman" <paul.hoffman@vpnc.org>
To: "Allison Mankin" <allison.mankin@gmail.com>
Cc: "cfrg@irtf.org" <Cfrg@irtf.org>, "irsg@irtf.org" <irsg@irtf.org>
Date: Mon, 24 Jul 2017 07:45:48 -0700
Message-ID: <69AF34C2-C594-44D2-93E8-EAA9175F1291@vpnc.org>
In-Reply-To: <CAP8yD=sTXB7trXyjz+VGHOAvh9egiSHmBcukNVN1yiq0mwkfFw@mail.gmail.com>
References: <D4FDAF9D.8D586%kenny.paterson@rhul.ac.uk> <9a878527-5ab9-5429-7c5d-4f7e4ca4e8db@isode.com> <08944dc3-9086-ed47-cc1b-54248b3dac70@cs.tcd.ie> <D566ADE0.963E4%kenny.paterson@rhul.ac.uk> <9e6b6146-e376-86cb-70be-0127a3e72d16@cs.tcd.ie> <D56DBB2C.96A67%kenny.paterson@rhul.ac.uk> <6f90e485-01f4-5ad8-49ef-e51c52e01a46@cs.tcd.ie> <5e328e85-a8a1-67f1-3853-418309b04a17@huelsing.net> <27cc7000-7fd5-27dd-b8b5-9b9518a9f3ad@huelsing.net> <1785b9ed-fb53-889a-9d34-311c7ea5c762@cs.tcd.ie> <4699f3d2-40ce-9c40-d29a-d24ecb3b6cab@huelsing.net> <CAP8yD=sTXB7trXyjz+VGHOAvh9egiSHmBcukNVN1yiq0mwkfFw@mail.gmail.com>
MIME-Version: 1.0
Content-Type: text/plain; format=flowed
X-Mailer: MailMate (1.9.6r5347)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/yF4G_FRVnPiW8YDkcsCqtXUeBMs>
Subject: Re: [Cfrg] [irsg] IRSG review of draft-irtf-cfrg-xmss-hash-based-signatures-08
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 24 Jul 2017 14:45:54 -0000

On 24 Jul 2017, at 7:39, Allison Mankin wrote:

> Thanks for making the changes.  Stephen, let me know if you are ready 
> to
> give this a thumbs-up, and I'll start an IRSG poll.

Do the IRSG polls normally happen at the same time as the WG Last calls? 
The RGLC on this document just started a few days ago.

--Paul Hoffman


From nobody Mon Jul 24 07:52:11 2017
Return-Path: <paul.hoffman@vpnc.org>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 13176131DAA; Mon, 24 Jul 2017 07:52:09 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.9
X-Spam-Level: 
X-Spam-Status: No, score=-1.9 tagged_above=-999 required=5 tests=[BAYES_00=-1.9] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id z6NOhXGj-Veb; Mon, 24 Jul 2017 07:52:08 -0700 (PDT)
Received: from mail.proper.com (Opus1.Proper.COM [207.182.41.91]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 574D1131DA2; Mon, 24 Jul 2017 07:52:08 -0700 (PDT)
Received: from [10.32.60.46] (142-254-101-176.dsl.dynamic.fusionbroadband.com [142.254.101.176]) (authenticated bits=0) by mail.proper.com (8.15.2/8.14.9) with ESMTPSA id v6OEpEQP064282 (version=TLSv1.2 cipher=ECDHE-RSA-AES256-GCM-SHA384 bits=256 verify=NO); Mon, 24 Jul 2017 07:51:16 -0700 (MST) (envelope-from paul.hoffman@vpnc.org)
X-Authentication-Warning: mail.proper.com: Host 142-254-101-176.dsl.dynamic.fusionbroadband.com [142.254.101.176] claimed to be [10.32.60.46]
From: "Paul Hoffman" <paul.hoffman@vpnc.org>
To: "Allison Mankin" <allison.mankin@gmail.com>
Cc: "cfrg@irtf.org" <Cfrg@irtf.org>, "irsg@irtf.org" <irsg@irtf.org>
Date: Mon, 24 Jul 2017 07:52:03 -0700
Message-ID: <4ABB7C1F-C43A-485B-85E6-06603D3C1064@vpnc.org>
In-Reply-To: <69AF34C2-C594-44D2-93E8-EAA9175F1291@vpnc.org>
References: <D4FDAF9D.8D586%kenny.paterson@rhul.ac.uk> <9a878527-5ab9-5429-7c5d-4f7e4ca4e8db@isode.com> <08944dc3-9086-ed47-cc1b-54248b3dac70@cs.tcd.ie> <D566ADE0.963E4%kenny.paterson@rhul.ac.uk> <9e6b6146-e376-86cb-70be-0127a3e72d16@cs.tcd.ie> <D56DBB2C.96A67%kenny.paterson@rhul.ac.uk> <6f90e485-01f4-5ad8-49ef-e51c52e01a46@cs.tcd.ie> <5e328e85-a8a1-67f1-3853-418309b04a17@huelsing.net> <27cc7000-7fd5-27dd-b8b5-9b9518a9f3ad@huelsing.net> <1785b9ed-fb53-889a-9d34-311c7ea5c762@cs.tcd.ie> <4699f3d2-40ce-9c40-d29a-d24ecb3b6cab@huelsing.net> <CAP8yD=sTXB7trXyjz+VGHOAvh9egiSHmBcukNVN1yiq0mwkfFw@mail.gmail.com> <69AF34C2-C594-44D2-93E8-EAA9175F1291@vpnc.org>
MIME-Version: 1.0
X-Mailer: MailMate (1.9.6r5347)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/oZVC7M7rv53yMRp1nNDlIzgGQiA>
Subject: Re: [Cfrg] [irsg] IRSG review of draft-irtf-cfrg-xmss-hash-based-signatures-08
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 24 Jul 2017 14:52:09 -0000

Er, n'r mind. I got two similarly-named drafts mixed up.

--Paul Hoffman


From nobody Mon Jul 24 08:02:42 2017
Return-Path: <allison.mankin@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id CC9BE131DAA; Mon, 24 Jul 2017 08:02:40 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.699
X-Spam-Level: 
X-Spam-Status: No, score=-2.699 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 19dhzTMTUbWs; Mon, 24 Jul 2017 08:02:39 -0700 (PDT)
Received: from mail-wm0-x22f.google.com (mail-wm0-x22f.google.com [IPv6:2a00:1450:400c:c09::22f]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 0A998127058; Mon, 24 Jul 2017 08:02:39 -0700 (PDT)
Received: by mail-wm0-x22f.google.com with SMTP id c184so34171454wmd.0; Mon, 24 Jul 2017 08:02:38 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=fD6O6KRdEgVbWdtvYmAOeVNdlBqiN4sx4kArez1weYE=; b=hOm2+w3ZI9in2xma/+j9NbdUg1yywopVDfp6VHBgmxpzjgV+XNSEhC6Ri31xLX9uVn Xe/YizyZIbEQLRnjnLejSxIkHW8iVcIPUoQTYXJ+Z5+UjQYxdaDkad82Eu10M0YjUK6L 3bMz5yU7BtmdaRj/Qb+3ymHLrKmxzbymkodFlMiufSTKwr38B9t+TRoiqlAvnUTx35sQ Mw0aW4KScoM1ZnyLM2YNHAxhySZ1MYyM5ExyJSaHJXclgcobc/OWhtwYYxsRVDeJSalF lrtmqExHGVjT+eR0p/LRkRumGHs2f8RMAl6nbmjm2YZ1BOl/3lLcsgNWWkHb15mgytRm +P5A==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=fD6O6KRdEgVbWdtvYmAOeVNdlBqiN4sx4kArez1weYE=; b=VxoqRY9olWdo7UoMj1EUplayiIf5CkufAxtgpq12BQeUALMwGtbL5nYzsqYeQQVjGn 0Kw2jLLalma52hxBUpVYu7o+kNApXnyd6ekSCGPKKjlH3ggRQQjzzAE6hXBzDU55y138 pWkPJ9QkD6HihEBODubzlgJ3pZkVpfTYK1UUM8wTuBjtuK0Fj7NeRTDzO9WBjX7nvDkI ApbmE/37UTnHoekymwy2aEuG7l/iQ5KEWqMBW793beUBP0qh2zF7NLf8eBPAYikV858i 2yghjYx2HLhzAiqET8/0NhapRy8Q1+llarOfHO1uEW2f9PfnyzA0k4mfGOFmqutZcz4w cZaA==
X-Gm-Message-State: AIVw112PIGTR7+K/cOLfzAypstoDBEaSHBs8RF58fGYJz8Ep6uX/zPVs 1dZNE9cAWSkLiocuiqmSsd8K+YPfYQ==
X-Received: by 10.80.142.165 with SMTP id w34mr14798549edw.34.1500908557426; Mon, 24 Jul 2017 08:02:37 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.80.138.69 with HTTP; Mon, 24 Jul 2017 08:02:36 -0700 (PDT)
In-Reply-To: <4ABB7C1F-C43A-485B-85E6-06603D3C1064@vpnc.org>
References: <D4FDAF9D.8D586%kenny.paterson@rhul.ac.uk> <9a878527-5ab9-5429-7c5d-4f7e4ca4e8db@isode.com> <08944dc3-9086-ed47-cc1b-54248b3dac70@cs.tcd.ie> <D566ADE0.963E4%kenny.paterson@rhul.ac.uk> <9e6b6146-e376-86cb-70be-0127a3e72d16@cs.tcd.ie> <D56DBB2C.96A67%kenny.paterson@rhul.ac.uk> <6f90e485-01f4-5ad8-49ef-e51c52e01a46@cs.tcd.ie> <5e328e85-a8a1-67f1-3853-418309b04a17@huelsing.net> <27cc7000-7fd5-27dd-b8b5-9b9518a9f3ad@huelsing.net> <1785b9ed-fb53-889a-9d34-311c7ea5c762@cs.tcd.ie> <4699f3d2-40ce-9c40-d29a-d24ecb3b6cab@huelsing.net> <CAP8yD=sTXB7trXyjz+VGHOAvh9egiSHmBcukNVN1yiq0mwkfFw@mail.gmail.com> <69AF34C2-C594-44D2-93E8-EAA9175F1291@vpnc.org> <4ABB7C1F-C43A-485B-85E6-06603D3C1064@vpnc.org>
From: Allison Mankin <allison.mankin@gmail.com>
Date: Mon, 24 Jul 2017 17:02:36 +0200
Message-ID: <CAP8yD=tFNONV=shjL+dtbTyCsNwfjX8Y4xoO336bB09aEBXJLA@mail.gmail.com>
To: Paul Hoffman <paul.hoffman@vpnc.org>
Cc: "cfrg@irtf.org" <Cfrg@irtf.org>, "irsg@irtf.org" <irsg@irtf.org>
Content-Type: multipart/alternative; boundary="f403045c529467e7e405551181a0"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/ljeyejoQMoT2LIqfLJEWm2Vir1g>
Subject: Re: [Cfrg] [irsg] IRSG review of draft-irtf-cfrg-xmss-hash-based-signatures-08
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 24 Jul 2017 15:02:41 -0000

--f403045c529467e7e405551181a0
Content-Type: text/plain; charset="UTF-8"

Happens to the best of us :-)

On 24 July 2017 at 16:52, Paul Hoffman <paul.hoffman@vpnc.org> wrote:

> Er, n'r mind. I got two similarly-named drafts mixed up.
>
> --Paul Hoffman
>

--f403045c529467e7e405551181a0
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_default" style=3D"font-family:arial,he=
lvetica,sans-serif">Happens to the best of us :-)<br></div></div><div class=
=3D"gmail_extra"><br><div class=3D"gmail_quote">On 24 July 2017 at 16:52, P=
aul Hoffman <span dir=3D"ltr">&lt;<a href=3D"mailto:paul.hoffman@vpnc.org" =
target=3D"_blank">paul.hoffman@vpnc.org</a>&gt;</span> wrote:<br><blockquot=
e class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc sol=
id;padding-left:1ex">Er, n&#39;r mind. I got two similarly-named drafts mix=
ed up.<br>
<span class=3D"HOEnZb"><font color=3D"#888888"><br>
--Paul Hoffman<br>
</font></span></blockquote></div><br></div>

--f403045c529467e7e405551181a0--


From nobody Mon Jul 24 08:14:41 2017
Return-Path: <internet-drafts@ietf.org>
X-Original-To: cfrg@ietf.org
Delivered-To: cfrg@ietfa.amsl.com
Received: from ietfa.amsl.com (localhost [IPv6:::1]) by ietfa.amsl.com (Postfix) with ESMTP id B4705131E0F; Mon, 24 Jul 2017 08:14:33 -0700 (PDT)
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: 7bit
From: internet-drafts@ietf.org
To: <i-d-announce@ietf.org>
Cc: cfrg@ietf.org
X-Test-IDTracker: no
X-IETF-IDTracker: 6.57.0
Auto-Submitted: auto-generated
Precedence: bulk
Message-ID: <150090927369.32037.9841595916887034298@ietfa.amsl.com>
Date: Mon, 24 Jul 2017 08:14:33 -0700
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/l31mAsxXxRohCSqspr-7v0uSmSE>
Subject: [Cfrg] I-D Action: draft-irtf-cfrg-xmss-hash-based-signatures-10.txt
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 24 Jul 2017 15:14:34 -0000

A New Internet-Draft is available from the on-line Internet-Drafts directories.
This draft is a work item of the Crypto Forum RG of the IRTF.

        Title           : XMSS: Extended Hash-Based Signatures
        Authors         : Andreas Huelsing
                          Denis Butin
                          Stefan-Lukas Gazdag
                          Joost Rijneveld
                          Aziz Mohaisen
	Filename        : draft-irtf-cfrg-xmss-hash-based-signatures-10.txt
	Pages           : 72
	Date            : 2017-07-24

Abstract:
   This note describes the eXtended Merkle Signature Scheme (XMSS), a
   hash-based digital signature system.  It follows existing
   descriptions in scientific literature.  The note specifies the WOTS+
   one-time signature scheme, a single-tree (XMSS) and a multi-tree
   variant (XMSS^MT) of XMSS.  Both variants use WOTS+ as a main
   building block.  XMSS provides cryptographic digital signatures
   without relying on the conjectured hardness of mathematical problems.
   Instead, it is proven that it only relies on the properties of
   cryptographic hash functions.  XMSS provides strong security
   guarantees and is even secure when the collision resistance of the
   underlying hash function is broken.  It is suitable for compact
   implementations, relatively simple to implement, and naturally
   resists side-channel attacks.  Unlike most other signature systems,
   hash-based signatures can withstand so far known attacks using
   quantum computers.


The IETF datatracker status page for this draft is:
https://datatracker.ietf.org/doc/draft-irtf-cfrg-xmss-hash-based-signatures/

There are also htmlized versions available at:
https://tools.ietf.org/html/draft-irtf-cfrg-xmss-hash-based-signatures-10
https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xmss-hash-based-signatures-10

A diff from the previous version is available at:
https://www.ietf.org/rfcdiff?url2=draft-irtf-cfrg-xmss-hash-based-signatures-10


Please note that it may take a couple of minutes from the time of submission
until the htmlized version and diff are available at tools.ietf.org.

Internet-Drafts are also available by anonymous FTP at:
ftp://ftp.ietf.org/internet-drafts/


From nobody Mon Jul 24 09:40:53 2017
Return-Path: <ietf-secretariat-reply@ietf.org>
X-Original-To: cfrg@ietf.org
Delivered-To: cfrg@ietfa.amsl.com
Received: from ietfa.amsl.com (localhost [IPv6:::1]) by ietfa.amsl.com (Postfix) with ESMTP id 0FC3A131EA0 for <cfrg@ietf.org>; Mon, 24 Jul 2017 09:40:52 -0700 (PDT)
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: 7bit
To: <cfrg@ietf.org>
X-Test-IDTracker: no
X-IETF-IDTracker: 6.57.0
Auto-Submitted: auto-generated
Precedence: bulk
Message-ID: <150091445206.31897.1194666585163923378.idtracker@ietfa.amsl.com>
Date: Mon, 24 Jul 2017 09:40:52 -0700
From: IETF Secretariat <ietf-secretariat-reply@ietf.org>
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/6RvlJ9tDHcXfKeypjyN2HQVOlrU>
Subject: [Cfrg] Milestones changed for cfrg RG
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 24 Jul 2017 16:40:52 -0000

Changed milestone "Send "ChaCha20 and Poly1305 for IETF Protocols" to IRSG",
set state to active from review, accepting new milestone.

Changed milestone "Submit "AES-GCM-SIV: Nonce Misuse-Resistant Authenticated
Encryption" to IRSG", set state to active from review, accepting new
milestone.

URL: https://datatracker.ietf.org/rg/cfrg/about/


From nobody Mon Jul 24 15:55:27 2017
Return-Path: <Kenny.Paterson@rhul.ac.uk>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 408DE127867 for <cfrg@ietfa.amsl.com>; Mon, 24 Jul 2017 15:55:25 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -4.701
X-Spam-Level: 
X-Spam-Status: No, score=-4.701 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, RCVD_IN_DNSWL_NONE=-0.0001, RCVD_IN_MSPIKE_H2=-2.8, SPF_HELO_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=rhul.onmicrosoft.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 4ksqc0f4IuTw for <cfrg@ietfa.amsl.com>; Mon, 24 Jul 2017 15:55:23 -0700 (PDT)
Received: from EUR02-HE1-obe.outbound.protection.outlook.com (mail-eopbgr10046.outbound.protection.outlook.com [40.107.1.46]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id BE098124C27 for <cfrg@irtf.org>; Mon, 24 Jul 2017 15:55:22 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=rhul.onmicrosoft.com;  s=selector1-rhul-ac-uk; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version; bh=SCFd1AiQbwWvwQnyUK40e9XSnFMZtgrAE96KYdTFo2c=; b=03v4ayGdUpz2+r9qym3NGcmfUB2DP62PFjm47WXMoWTptA47g+ZGrAEhunuhCk6Z3qNhhtP3fd+v+/Opzv2XrFJ4p7XNkI+adcjHS8/qFlqxLJU9zqo6wTOnqaNtssdIxrMce13AhpK1AneMPz5Kuc89bCaFlhMTYvtRUbGcmK8=
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com (10.168.2.156) by AM4PR0301MB1908.eurprd03.prod.outlook.com (10.168.3.8) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256) id 15.1.1282.10; Mon, 24 Jul 2017 22:55:20 +0000
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::e475:7abc:5c25:5e28]) by AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::e475:7abc:5c25:5e28%14]) with mapi id 15.01.1282.017; Mon, 24 Jul 2017 22:55:19 +0000
From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: Minutes from CFRG meeting at IETF99
Thread-Index: AQHTBM/sGSW+9pGM2Eu8xlKe/bsDVA==
Date: Mon, 24 Jul 2017 22:55:19 +0000
Message-ID: <D59C38E3.99822%kenny.paterson@rhul.ac.uk>
Accept-Language: en-GB, en-US
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
user-agent: Microsoft-MacOutlook/14.7.1.161129
authentication-results: spf=none (sender IP is ) smtp.mailfrom=Kenny.Paterson@rhul.ac.uk; 
x-originating-ip: [78.146.77.209]
x-ms-publictraffictype: Email
x-microsoft-exchange-diagnostics: 1; AM4PR0301MB1908; 7: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
x-forefront-antispam-report: SFV:SKI; SCL:-1; SFV:NSPM; SFS:(10009020)(6009001)(39840400002)(39450400003)(39850400002)(39410400002)(39400400002)(199003)(189002)(14454004)(4326008)(101416001)(72206003)(966005)(7736002)(86362001)(68736007)(413944005)(4001350100001)(6116002)(6506006)(102836003)(6512007)(105586002)(305945005)(3846002)(229853002)(6486002)(6306002)(99286003)(5640700003)(106356001)(6436002)(3280700002)(6916009)(42882006)(2351001)(2900100001)(3660700001)(6246003)(53936002)(2906002)(8936002)(66066001)(8676002)(81166006)(1730700003)(81156014)(74482002)(97736004)(2501003)(5250100002)(189998001)(36756003)(68196006)(478600001)(54356999)(5660300001)(110136004)(50986999)(83506001)(38730400002)(25786009); DIR:OUT; SFP:1101; SCL:1; SRVR:AM4PR0301MB1908; H:AM4PR0301MB1906.eurprd03.prod.outlook.com; FPR:; SPF:None; PTR:InfoNoRecords; A:1; MX:1; LANG:en; 
x-ms-office365-filtering-correlation-id: 47827518-297a-448b-3194-08d4d2e70f12
x-microsoft-antispam: UriScan:; BCL:0; PCL:0; RULEID:(300000500095)(300135000095)(300000501095)(300135300095)(22001)(300000502095)(300135100095)(2017030254075)(300000503095)(300135400095)(2017052603031)(201703131423075)(201703031133081)(300000504095)(300135200095)(300000505095)(300135600095)(300000506095)(300135500095); SRVR:AM4PR0301MB1908; 
x-ms-traffictypediagnostic: AM4PR0301MB1908:
x-exchange-antispam-report-test: UriScan:(120809045254105)(209352067349851)(254730959083279)(91638250987450); 
x-microsoft-antispam-prvs: <AM4PR0301MB1908D4AEA71283FB01A2369EBCBB0@AM4PR0301MB1908.eurprd03.prod.outlook.com>
x-exchange-antispam-report-cfa-test: BCL:0; PCL:0; RULEID:(100000700101)(100105000095)(100000701101)(100105300095)(100000702101)(100105100095)(6040450)(601004)(2401047)(8121501046)(5005006)(93006095)(93001095)(100000703101)(100105400095)(3002001)(10201501046)(6041248)(20161123564025)(20161123555025)(201703131423075)(201702281529075)(201702281528075)(201703061421075)(201703061406153)(20161123560025)(20161123562025)(20161123558100)(6072148)(100000704101)(100105200095)(100000705101)(100105500095); SRVR:AM4PR0301MB1908; BCL:0; PCL:0; RULEID:(100000800101)(100110000095)(100000801101)(100110300095)(100000802101)(100110100095)(100000803101)(100110400095)(100000804101)(100110200095)(100000805101)(100110500095); SRVR:AM4PR0301MB1908; 
x-forefront-prvs: 0378F1E47A
received-spf: None (protection.outlook.com: rhul.ac.uk does not designate permitted sender hosts)
spamdiagnosticoutput: 1:99
spamdiagnosticmetadata: NSPM
Content-Type: text/plain; charset="utf-8"
Content-ID: <A66C3198D1755844BD3EBDB2F44A2C3D@eurprd03.prod.outlook.com>
Content-Transfer-Encoding: base64
MIME-Version: 1.0
X-OriginatorOrg: rhul.ac.uk
X-MS-Exchange-CrossTenant-originalarrivaltime: 24 Jul 2017 22:55:19.6319 (UTC)
X-MS-Exchange-CrossTenant-fromentityheader: Hosted
X-MS-Exchange-CrossTenant-id: 2efd699a-1922-4e69-b601-108008d28a2e
X-MS-Exchange-Transport-CrossTenantHeadersStamped: AM4PR0301MB1908
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/jfB__eoMqLvnET5Mt4OpGoI1Xdg>
Subject: Re: [Cfrg] Minutes from CFRG meeting at IETF99
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 24 Jul 2017 22:55:25 -0000
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From nobody Wed Jul 26 04:32:17 2017
Return-Path: <tgarcia.3141@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 2A907131FFC for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 04:32:15 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.449
X-Spam-Level: 
X-Spam-Status: No, score=-2.449 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_ENVFROM_END_DIGIT=0.25, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id MfXrXFY7S9Vz for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 04:32:11 -0700 (PDT)
Received: from mail-lf0-x232.google.com (mail-lf0-x232.google.com [IPv6:2a00:1450:4010:c07::232]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 5D842131FF7 for <cfrg@irtf.org>; Wed, 26 Jul 2017 04:32:11 -0700 (PDT)
Received: by mail-lf0-x232.google.com with SMTP id t128so37112107lff.2 for <cfrg@irtf.org>; Wed, 26 Jul 2017 04:32:11 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=21q23PDTgBieJNQb+1QskSPHF4nLdTNaN716qy9iYws=; b=iBqLsbTTM+O1XFpSdIALheMumakxS7k8Lk9pIdZIFl9j/l+ngvykDPnG6Oy05iP5of gmt3hg/nNd4Omjs8UEFozHmlJOBDOpBPzHTGDNml2o/nhXXndLN3HN180LHqxx/lpIyY xiKxKabw4m147RFtiw7LSAH/oCauy3RwN9hZOwwaVuuubvuly/mPpBhcu8QFV35Wc/Qx AazUVZ746bC0jURl9GjT/WmSyxX1K/57a5aovVeZkokNb60Kw6XAkgubrKl7nheBZXH1 DSorjLAHaV6Zy0WYpIEVPaDqAO0TpHFnLUo4Z5DszKM1TVAdBxPObi+75l/5kNe/G1ff Sdig==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=21q23PDTgBieJNQb+1QskSPHF4nLdTNaN716qy9iYws=; b=W2TA7XcyVDXv3KbBUHoTkQ62UcHAeAh2JycofS2i31dY307513svhHFuqqpMFljiRK 9CNY8l6vWmSU3BN36X13hMWxA5u71LlrBepj7WoekYNa4n7ZKhkv88/gMOTzte8OO/bV NJ39yw0OG+M0uHLVaS8FeQl5YTUQ2qqeTCt1ke02PpDRS0IqE1MAh1dGUW3lJ6ZFY8Oj osoSselat+bh9LU15kyyMtH3yiy/QbWddBzUBcTNCz5CaiBM0izvNqDMQkv6+HIAD7nT s8XD0oX3/CMwx8kRFq2LHn+96zjYHV1R50woLrEbatgqnD4+0x6+XVa10h18fXJF95LJ JTgQ==
X-Gm-Message-State: AIVw113DXGsLROKq6bFceCbq7JIqgavoV46gLUScqHPsWNvm+2Dgi1AI jgSFyc/wG4Yxsgt9dw4eKitCjTuiCA==
X-Received: by 10.46.69.87 with SMTP id s84mr311183lja.129.1501068729470; Wed, 26 Jul 2017 04:32:09 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.25.37.83 with HTTP; Wed, 26 Jul 2017 04:32:08 -0700 (PDT)
In-Reply-To: <CAJHGrrTbjL3rd_XU9tx28g3QcBe9tJBOxs2t1OebfvZR_c7epA@mail.gmail.com>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com> <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net> <20170721163204.8573013.1016.15939@blackberry.com> <CAJHGrrTbjL3rd_XU9tx28g3QcBe9tJBOxs2t1OebfvZR_c7epA@mail.gmail.com>
From: Thomas Garcia <tgarcia.3141@gmail.com>
Date: Wed, 26 Jul 2017 12:32:08 +0100
Message-ID: <CAFTSWvfwf34uH1AjzQq7zCMEARGH8rH310pSRe7kkYCZ3TMNeQ@mail.gmail.com>
To: Sharon Goldberg <sharon.goldbe@gmail.com>
Cc: Dan Brown <danibrown@blackberry.com>, "jan@ns1.com" <jan@ns1.com>,  "cfrg@irtf.org" <cfrg@irtf.org>, Dimitrios Papadopoulos <dipapado@umd.edu>, Leonid Reyzin <reyzin@cs.bu.edu>
Content-Type: multipart/alternative; boundary="001a114b0cda675212055536cc3a"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/UX1fHbz6wYg557dAF1PNQ-3pyqI>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 26 Jul 2017 11:32:15 -0000

--001a114b0cda675212055536cc3a
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Hello,
A couple of questions:
1. It seems that one of the properties that you are interested that the VRF
will have is determinism. On the other hand, the EC-VRF value is dependent
on the choice of some random number k. How are these two facts compatible?
Am I missing something?
2. The value c calculated in EC-VRF is only 128 bits long for Ed25519. In
normal usage of Ed25519 the signature uses the full length of the hash
output. Doesn't this expose the signature to collision attacks?

Thomas G.

On Sun, Jul 23, 2017 at 6:10 AM, Sharon Goldberg <sharon.goldbe@gmail.com>
wrote:

> Hi Dan,
>
> Thank you for your comments. Indeed, VRFs have been around since 1999.
> They are really "verifiable PRFs" but the name is by now standard in the
> crypto literature, and changing it will cause more confusion than keeping
> it.
>
> In terms of the VRF's security properties, there are three:  uniqueness,
> collision resistance, and pseudorandomness. These are defined in our draf=
t (
> https://tools.ietf.org/html/draft-goldbe-vrf-01#section-3).
>
> How VRFs prevent dictionary attacks: a public hash is subject to a
> dictionary attack because, given the output, an adversary can evaluate th=
e
> hash on different inputs and see what hits the outputs. In a VRF, the
> adversary can't evaluate the hash on different inputs.
>
> You say it's not surprising that "random oracle model proof can prove the
> output of a hash to be random". But actually, the output of a hash is NOT
> random if the input and the hash function are known. This is because the
> output of a hash is deterministic (every input maps to a unique output).
> That's exactly what enables dictionary attacks. This is in contrast to a
> VRF, where the output is (pseudo)random even given knowledge of the input=
.
> Only once the VRF proof is given, does the VRF output stop looking random=
.
> Note that random oracles are not essential for VRFs, and non-random-oracl=
es
> constructions exist (but are less efficient than what we propose to
> standardize).
>
> As far as use cases, here are a few:
>
> In the NSEC5 use case for DNSSEC, you have sensitive data (domain names)
> and you sign consecutive pairs of hashes of domain names in order to be
> able to prove absence of a name. If you just use standard hashing, whenev=
er
> signed hash values are disclosed, your sensitive data is subject to
> dictionary attacks. VRFs solve that problem, and sensitive names don't ha=
ve
> to be disclosed at all. More details are in https://eprint.iacr.org/201
> 7/099.pdf
>
> In CONIKS (also Google Key Transparency, Signal secure messaging, Yahoo!
> Coname) you also have some sensitive data (user names) that are put into =
a
> Merkle-like authenticated data structure. If you just use standard hashin=
g,
> whenever hash values are disclosed, sensitive data is subject to dictiona=
ry
> attacks. If you use VRFs, sensitive data again can be disclosed only on a=
n
> as-needed basis. More details are in  https://eprint.iacr.org/2014/
> 1004.pdf.
>
> In a cryptocurrency use case, you wish perform a coin flip that is
> deterministic and provably correct, but cannot be done by just anyone.
> More details are in https://people.csail.mit.ed
> u/nickolai/papers/gilad-algorand-eprint.pdf and possibly other
> cryptocurrency papers.
>
> Bryan Ford mentioned an additional usecase at the mic on Tuesday:
> distributed password protection protocols
>
> Many of these use case are already putting VRFs into production use (esp.
> the CONIKS one).  You can see a list of the various implementations we ha=
ve
> found in the "implementation status" section of our draft.  One of the
> reasons we think this spec is so important is that we found flaws in
> several of the implementations that can be used to trivially break
> uniqueness.  (See eg: https://github.com/google/keytransparency/issues/56=
7
> )
>
> Thanks,
> Sharon
>
> On Fri, Jul 21, 2017 at 7:32 PM, Dan Brown <danibrown@blackberry.com>
> wrote:
>
>> Answering myself below: VRFs have been around since 1999, so are not so
>> new.  =E2=80=8EStill don't like the name, and still have trouble seeing =
the value.
>>
>> *From: *Dan Brown
>> *Sent: *Tuesday, July 18, 2017 2:29 PM
>> *To: *Sharon Goldberg; cfrg@irtf.org
>> *Cc: *jan@ns1.com; Leonid Reyzin; Dimitrios Papadopoulos
>> *Subject: *Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>
>> Hi Sharon and CFRG,
>>
>>
>>
>> On VRFs, my uncertain comments to consider at your leisure:
>>
>>
>>
>> Is it fair to say VRFs are relatively new?  If so, then maybe a little
>> more caution is needed about their use.  It seems a tad hasty that it is
>> being used already.
>>
>>
>>
>> To me, it seems that VRFs are basically signatures, with an extra
>> feature.  My concern is that this extra feature might get overused, befo=
re
>> it is thoroughly reviewed.
>>
>>
>>
>> It is unsurprising to me that random oracle model proof can prove the
>> output of a hash to be random.  My intuitive concern is that at least
>> informally, this is kind of circular.  Hashes often have some
>> non-random-ish properties that might affect the extra security (over
>> signatures) that VRFs are aiming for.  I guess I would much prefer a pro=
of
>> saying if the hash has (well-studied) properties XYZ, then your
>> construction are VRFs.  (Maybe you have this already?  If so, then tell =
me
>> so.)
>>
>>
>>
>> Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the wire, I =
find it hard to
>> see how it could be used to prevent dictionary attacks.  I assume that y=
ou
>> are saying the proofs must be encrypted when one needs to avoid dictiona=
ry
>> models?  I suppose all the details are there in I-D and papers, but for
>> now, I am confused about the threat model (which parties have keys, etc.=
,
>> if they require a secure channel and mutual trust, why just use plain ol=
d
>> hash,=E2=80=A6). To resist dictionary attacks, were already have PAKEs a=
nd
>> PBHashing.  Now this?
>>
>>
>>
>> Finally, on a bikeshed-coloring note, I object to the name =E2=80=9Cveri=
fiable
>> random function=E2=80=9D, on several grounds.
>>
>>
>>
>>    1. It is not a function.  It is at least four functions, keygen,
>>    sign, verify, and hashify.
>>    2. If you make it into a keyed function F_sk(m), as in
>>    prooftohash(sign_sk(m)), it is not verifiable.
>>    3. Verification requires the intermediate proof, which is certainly
>>    not even pseudorandom (it is easy to distinguish valid signatures fro=
m
>>    random).
>>    4. It is pseudorandom, not random.  (The keys are random, but many
>>    crypto has keys, without having =E2=80=9Crandom=E2=80=9D in its name:=
 encryption, MAC,
>>    signatures, key exchange, =E2=80=A6, they also don=E2=80=99t verifiab=
le or random in their
>>    names either.)
>>    5. The similar phrase =E2=80=9Cverifiably random=E2=80=9D, albeit as =
a misnomer, has
>>    past precedents, see NIST P-256 and Brainpool, etc.  When I see VRF, =
I
>>    think a function, that aims to VR in that sense, and great, now we ca=
n
>>    improve on Brainpool, etc.
>>    6. =E2=80=9CRandom function=E2=80=9D should be reserved for the ideal=
 random mapping
>>    concept, for example, as studied by Flajolet-Odlyzko (ok they only st=
udied
>>    the case of equal size domain and range).  The random oracle model, i=
s the
>>    idea of approximating this ideal, etc.  An actual approximation shoul=
d not
>>    be name as the ideal (sorry, I=E2=80=99m kind of repeating my point 4=
).
>>
>>
>>
>> Please forgive the fact that my comments above are not very constructive
>> (or if the tone is wrong).  This is a new topic for me, so I am reluctan=
t
>> too many suggestions.  Nonetheless, I suggest (0) waiting a little, (1) =
a
>> non-random-oracle security proof (if you don=E2=80=99t have it yet), (2)=
 re-naming
>> the scheme to something like re-hashable (or digestible) signatures (and
>> re-name the various parts, i.e. proof -> signature, etc.).
>>
>>
>>
>> Best regards,
>>
>>
>>
>> Dan
>>
>>
>>
>>
>>
>> *From:* Cfrg [mailto:cfrg-bounces@irtf.org] *On Behalf Of *Sharon
>> Goldberg
>> *Sent:* Wednesday, July 12, 2017 5:42 AM
>> *To:* cfrg@irtf.org
>> *Cc:* jan@ns1.com; Dimitrios Papadopoulos <dipapado@umd.edu>; Leonid
>> Reyzin <reyzin@cs.bu.edu>
>> *Subject:* [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>
>>
>>
>> Dear CFRG,
>>
>> I'm presenting at next week's meeting on Verifiable Random Functions. A
>> VRF is the public-key version of keyed cryptographic hash. Only the hold=
er
>> of the VRF secret key can compute the hash, but anyone with the public k=
ey
>> can verify it.  VRFs can be used to prevent dictionary attacks on
>> hash-based data structures, and have applications to key transparency
>> (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (Algorand).
>>
>> In advance of the meeting, please see:
>>
>> 1) Our substantially updated -01 draft:
>> https://datatracker.ietf.org/doc/draft-goldbe-vrf/
>>
>> 2) Our project page, with links to various VRF implementations:
>> https://www.cs.bu.edu/~goldbe/projects/vrf
>>
>> Comments welcome.  Thanks,
>>
>> Sharon
>>
>> --
>> Sharon Goldberg
>> Computer Science, Boston University
>> http://www.cs.bu.edu/~goldbe
>>
>
>
>
> --
> ---
> Sharon Goldberg
> Computer Science, Boston University
> http://www.cs.bu.edu/~goldbe
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>
>

--001a114b0cda675212055536cc3a
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Hello,<div>A couple of questions:</div><div>1. It seems th=
at one of the properties that you are interested that the VRF will have is =
determinism. On the other hand, the EC-VRF value is dependent on the choice=
 of some random number k. How are these two facts compatible? Am I missing =
something?</div><div>2. The value c calculated in EC-VRF is only 128 bits l=
ong for Ed25519. In normal usage of Ed25519 the signature uses the full len=
gth of the hash output. Doesn&#39;t this expose the signature to collision =
attacks?</div><div><br></div><div>Thomas G.</div></div><div class=3D"gmail_=
extra"><br><div class=3D"gmail_quote">On Sun, Jul 23, 2017 at 6:10 AM, Shar=
on Goldberg <span dir=3D"ltr">&lt;<a href=3D"mailto:sharon.goldbe@gmail.com=
" target=3D"_blank">sharon.goldbe@gmail.com</a>&gt;</span> wrote:<br><block=
quote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc=
 solid;padding-left:1ex"><div dir=3D"ltr"><div style=3D"font-size:12.8px">H=
i Dan,</div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-si=
ze:12.8px">Thank you for your comments. Indeed, VRFs have been around since=
 1999. They are really &quot;verifiable PRFs&quot; but the name is by now s=
tandard in the crypto literature, and changing it will cause more confusion=
 than keeping it.</div><div style=3D"font-size:12.8px"><br></div><div style=
=3D"font-size:12.8px">In terms of the VRF&#39;s security properties, there =
are three: =C2=A0uniqueness, collision resistance, and pseudorandomness. Th=
ese are defined in our draft (<span style=3D"font-size:12.8px"><a href=3D"h=
ttps://tools.ietf.org/html/draft-goldbe-vrf-01#section-3" target=3D"_blank"=
>https://tools.ietf.org/html/d<wbr>raft-goldbe-vrf-01#section-3</a></span><=
span style=3D"font-size:12.8px">).<wbr>=C2=A0</span></div><div style=3D"fon=
t-size:12.8px"><br></div><div style=3D"font-size:12.8px">How VRFs prevent d=
ictionary attacks: a public hash is subject to a dictionary attack because,=
 given the output, an adversary can evaluate the hash on different inputs a=
nd see what hits the outputs. In a VRF, the adversary can&#39;t evaluate th=
e hash on different inputs.=C2=A0</div><div style=3D"font-size:12.8px"><br>=
</div><div style=3D"font-size:12.8px">You say it&#39;s not surprising that =
&quot;random oracle model proof can prove the output of a hash to be random=
&quot;. But actually, the output of a hash is NOT random if the input and t=
he hash function are known. This is because the output of a hash is determi=
nistic (every input maps to a unique output). That&#39;s exactly what enabl=
es dictionary attacks. This is in contrast to a VRF, where the output is (p=
seudo)random even given knowledge of the input. Only once the VRF proof is =
given, does the VRF output stop looking random. Note that random oracles ar=
e not essential for VRFs, and non-random-oracles constructions exist (but a=
re less efficient than what we propose to standardize).</div><div style=3D"=
font-size:12.8px"><br></div><div style=3D"font-size:12.8px">As far as use c=
ases, here are a few:=C2=A0</div><div style=3D"font-size:12.8px"><br></div>=
<div style=3D"font-size:12.8px">In the NSEC5 use case for DNSSEC, you have =
sensitive data (domain names) and you sign consecutive pairs of hashes of d=
omain names in order to be able to prove absence of a name. If you just use=
 standard hashing, whenever signed hash values are disclosed, your sensitiv=
e data is subject to dictionary attacks. VRFs solve that problem, and sensi=
tive names don&#39;t have to be disclosed at all. More details are in=C2=A0=
<a href=3D"https://eprint.iacr.org/2017/099.pdf" target=3D"_blank">https://=
eprint.iacr.org/201<wbr>7/099.pdf</a></div><div style=3D"font-size:12.8px">=
<br></div><div style=3D"font-size:12.8px">In CONIKS (also Google Key Transp=
arency, Signal secure messaging, Yahoo! Coname) you also have some sensitiv=
e data (user names) that are put into a Merkle-like authenticated data stru=
cture. If you just use standard hashing, whenever hash values are disclosed=
, sensitive data is subject to dictionary attacks. If you use VRFs, sensiti=
ve data again can be disclosed only on an as-needed basis. More details are=
 in =C2=A0<a href=3D"https://eprint.iacr.org/2014/1004.pdf" target=3D"_blan=
k">https://eprint.iacr.org/2014/<wbr>1004.pdf</a>.</div><div style=3D"font-=
size:12.8px"><br></div><div style=3D"font-size:12.8px">In a cryptocurrency =
use case, you wish perform a coin flip that is deterministic and provably c=
orrect, but cannot be done by just anyone.=C2=A0 More details are in=C2=A0<=
a href=3D"https://people.csail.mit.edu/nickolai/papers/gilad-algorand-eprin=
t.pdf" target=3D"_blank">https://people.csail.mit.ed<wbr>u/nickolai/papers/=
gilad-algora<wbr>nd-eprint.pdf</a>=C2=A0and possibly other cryptocurrency p=
apers.</div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-si=
ze:12.8px">Bryan Ford mentioned an additional usecase at the mic on Tuesday=
: distributed password protection protocols</div><div style=3D"font-size:12=
.8px"><br></div><div style=3D"font-size:12.8px">Many of these use case are =
already putting VRFs into production use (esp. the CONIKS one).=C2=A0 You c=
an see a list of the various implementations we have found in the &quot;imp=
lementation status&quot; section of our draft.=C2=A0 One of the reasons we =
think this spec is so important is that we found flaws in several of the im=
plementations that can be used to trivially break uniqueness. =C2=A0(See eg=
:=C2=A0<a href=3D"https://github.com/google/keytransparency/issues/567" tar=
get=3D"_blank">https://github.com/google/<wbr>keytransparency/issues/567</a=
>)</div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-size:1=
2.8px"><span style=3D"font-size:12.8px">Thanks,</span><br></div><div style=
=3D"font-size:12.8px">Sharon=C2=A0</div><div class=3D"gmail_extra"><div><di=
v class=3D"h5"><br><div class=3D"gmail_quote">On Fri, Jul 21, 2017 at 7:32 =
PM, Dan Brown <span dir=3D"ltr">&lt;<a href=3D"mailto:danibrown@blackberry.=
com" target=3D"_blank">danibrown@blackberry.com</a>&gt;</span> wrote:<br><b=
lockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-le=
ft:1px solid rgb(204,204,204);padding-left:1ex">




<div lang=3D"EN-US">
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
Answering myself below: VRFs have been around since 1999, so are not so new=
. =C2=A0=E2=80=8EStill don&#39;t like the name, and still have trouble seei=
ng the value.</div>
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
<span style=3D"font-family:Calibri,&quot;Slate Pro&quot;,sans-serif,sans-se=
rif;font-size:initial;line-height:initial;text-align:initial"><br>
</span></div>
<table width=3D"100%" style=3D"background-color:white">
<tbody>
<tr>
<td colspan=3D"2" style=3D"font-size:initial;text-align:initial;background-=
color:rgb(255,255,255)">
<div style=3D"border-style:solid none none;border-top-color:rgb(181,196,223=
);border-top-width:1pt;padding:3pt 0in 0in;font-family:Tahoma,&quot;BB Alph=
a Sans&quot;,&quot;Slate Pro&quot;;font-size:10pt">
<div><b>From: </b>Dan Brown</div>
<div><b>Sent: </b>Tuesday, July 18, 2017 2:29 PM</div>
<div><b>To: </b>Sharon Goldberg; <a href=3D"mailto:cfrg@irtf.org" target=3D=
"_blank">cfrg@irtf.org</a></div>
<div><b>Cc: </b><a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.co=
m</a>; Leonid Reyzin; Dimitrios Papadopoulos</div>
<div><b>Subject: </b>Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functio=
ns</div>
</div>
</td>
</tr>
</tbody>
</table><div><div class=3D"m_-6153101734044142155m_4165835283928257204gmail=
-h5">
<div style=3D"border-style:solid none none;border-top-color:rgb(186,188,209=
);border-top-width:1pt;font-size:initial;text-align:initial;background-colo=
r:rgb(255,255,255)">
</div>
<br>
<div>
<div class=3D"m_-6153101734044142155m_4165835283928257204gmail-m_6358749242=
748202832WordSection1">
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Hi Sharon and CFRG,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">On VRFs, my uncertain comments to consider at your leisure:</span=
></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Is it fair to say VRFs are relatively new?=C2=A0 If so, then mayb=
e a little more caution is needed about their use.=C2=A0 It seems a tad has=
ty that it is being used already.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">To me, it seems that VRFs are basically signatures, with an extra=
 feature.=C2=A0 My concern is that this extra feature might get overused, b=
efore it is thoroughly reviewed.=C2=A0
</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">It is unsurprising to me that random oracle model proof can prove=
 the output of a hash to be random.=C2=A0 My intuitive concern is that at l=
east informally, this is kind of circular.=C2=A0
 Hashes often have some non-random-ish properties that might affect the ext=
ra security (over signatures) that VRFs are aiming for.=C2=A0 I guess I wou=
ld much prefer a proof saying if the hash has (well-studied) properties XYZ=
, then your construction are VRFs.=C2=A0 (Maybe
 you have this already?=C2=A0 If so, then tell me so.)</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the w=
ire, I find it hard to see how it could be used to prevent dictionary attac=
ks.=C2=A0 I assume that you are saying the proofs must
 be encrypted when one needs to avoid dictionary models?=C2=A0 I suppose al=
l the details are there in I-D and papers, but for now, I am confused about=
 the threat model (which parties have keys, etc., if they require a secure =
channel and mutual trust, why just use
 plain old hash,=E2=80=A6). To resist dictionary attacks, were already have=
 PAKEs and PBHashing.=C2=A0 Now this?</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Finally, on a bikeshed-coloring note, I object to the name =E2=80=
=9Cverifiable random function=E2=80=9D, on several grounds.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<ol start=3D"1" type=3D"1" style=3D"margin-top:0in">
<li class=3D"m_-6153101734044142155m_4165835283928257204gmail-m_63587492427=
48202832MsoListParagraph" style=3D"margin-left:0in"><span style=3D"font-siz=
e:11pt;font-family:Calibri,sans-serif">It is not a function.=C2=A0 It is at=
 least four functions, keygen, sign, verify, and hashify.</span></li><li cl=
ass=3D"m_-6153101734044142155m_4165835283928257204gmail-m_63587492427482028=
32MsoListParagraph" style=3D"margin-left:0in"><span style=3D"font-size:11pt=
;font-family:Calibri,sans-serif">If you make it into a keyed function F_sk(=
m), as in prooftohash(sign_sk(m)), it is not verifiable.=C2=A0
</span></li><li class=3D"m_-6153101734044142155m_4165835283928257204gmail-m=
_6358749242748202832MsoListParagraph" style=3D"margin-left:0in"><span style=
=3D"font-size:11pt;font-family:Calibri,sans-serif">Verification requires th=
e intermediate proof, which is certainly not even pseudorandom (it is easy =
to distinguish valid signatures from random).</span></li><li class=3D"m_-61=
53101734044142155m_4165835283928257204gmail-m_6358749242748202832MsoListPar=
agraph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;font-family=
:Calibri,sans-serif">It is pseudorandom, not random.=C2=A0 (The keys are ra=
ndom, but many crypto has keys, without having =E2=80=9Crandom=E2=80=9D in =
its name: encryption, MAC, signatures,
 key exchange, =E2=80=A6, they also don=E2=80=99t verifiable or random in t=
heir names either.)</span></li><li class=3D"m_-6153101734044142155m_4165835=
283928257204gmail-m_6358749242748202832MsoListParagraph" style=3D"margin-le=
ft:0in"><span style=3D"font-size:11pt;font-family:Calibri,sans-serif">The s=
imilar phrase =E2=80=9Cverifiably random=E2=80=9D, albeit as a misnomer, ha=
s past precedents, see NIST P-256 and Brainpool, etc.=C2=A0 When I see VRF,=
 I think
 a function, that aims to VR in that sense, and great, now we can improve o=
n Brainpool, etc.</span></li><li class=3D"m_-6153101734044142155m_416583528=
3928257204gmail-m_6358749242748202832MsoListParagraph" style=3D"margin-left=
:0in"><span style=3D"font-size:11pt;font-family:Calibri,sans-serif">=E2=80=
=9CRandom function=E2=80=9D should be reserved for the ideal random mapping=
 concept, for example, as studied by Flajolet-Odlyzko (ok they only studied
 the case of equal size domain and range).=C2=A0 The random oracle model, i=
s the idea of approximating this ideal, etc.=C2=A0 An actual approximation =
should not be name as the ideal (sorry, I=E2=80=99m kind of repeating my po=
int 4).</span></li></ol>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Please forgive the fact that my comments above are not very const=
ructive (or if the tone is wrong).=C2=A0 This is a new topic for me, so I a=
m reluctant too many suggestions.=C2=A0 Nonetheless,
 I suggest (0) waiting a little, (1) a non-random-oracle security proof (if=
 you don=E2=80=99t have it yet), (2) re-naming the scheme to something like=
 re-hashable (or digestible) signatures (and re-name the various parts, i.e=
. proof -&gt; signature, etc.).</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Best regards,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Dan</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><b><span style=3D"font-size:11pt;font-family:Calibri=
,sans-serif">From:</span></b><span style=3D"font-size:11pt;font-family:Cali=
bri,sans-serif"> Cfrg [mailto:<a href=3D"mailto:cfrg-bounces@irtf.org" targ=
et=3D"_blank">cfrg-bounces@irtf.org</a>]
<b>On Behalf Of </b>Sharon Goldberg<br>
<b>Sent:</b> Wednesday, July 12, 2017 5:42 AM<br>
<b>To:</b> <a href=3D"mailto:cfrg@irtf.org" target=3D"_blank">cfrg@irtf.org=
</a><br>
<b>Cc:</b> <a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.com</a>=
; Dimitrios Papadopoulos &lt;<a href=3D"mailto:dipapado@umd.edu" target=3D"=
_blank">dipapado@umd.edu</a>&gt;; Leonid Reyzin &lt;<a href=3D"mailto:reyzi=
n@cs.bu.edu" target=3D"_blank">reyzin@cs.bu.edu</a>&gt;<br>
<b>Subject:</b> [Cfrg] draft-goldbe-vrf: Verifiable Random Functions</span>=
</p>
<p class=3D"MsoNormal">=C2=A0</p>
<div>
<p class=3D"MsoNormal">Dear CFRG,<br>
<br>
I&#39;m presenting at next week&#39;s meeting on Verifiable Random Function=
s. A VRF is the public-key version of keyed cryptographic hash. Only the ho=
lder of the VRF secret key can compute the hash, but anyone with the public=
 key can verify it.=C2=A0 VRFs can be used to
 prevent dictionary attacks on hash-based data structures, and have applica=
tions to key transparency (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (A=
lgorand).<br>
<br>
In advance of the meeting, please see:<br>
<br>
1) Our substantially updated -01 draft:<br>
<a href=3D"https://datatracker.ietf.org/doc/draft-goldbe-vrf/" target=3D"_b=
lank">https://datatracker.ietf.org/d<wbr>oc/draft-goldbe-vrf/</a><br>
<br>
2) Our project page, with links to various VRF implementations:<br>
<a href=3D"https://www.cs.bu.edu/~goldbe/projects/vrf" target=3D"_blank">ht=
tps://www.cs.bu.edu/~goldbe/<wbr>projects/vrf</a><br>
<br>
Comments welcome.=C2=A0 Thanks,<br>
<br>
Sharon<br>
<br>
--<br>
Sharon Goldberg<br>
Computer Science, Boston University<br>
<a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu=
.edu/~goldbe</a></p>
</div>
</div>
</div>
</div></div></div>

</blockquote></div><br><br clear=3D"all"><div><br></div></div></div>-- <br>=
<div class=3D"m_-6153101734044142155m_4165835283928257204gmail_signature">-=
--<span class=3D""><br>Sharon Goldberg<br>Computer Science, Boston Universi=
ty<br><a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www=
.cs.bu.edu/~goldbe</a></span></div>
</div></div>
<br>______________________________<wbr>_________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/<wbr>listinfo/cfrg</a><br>
<br></blockquote></div><br></div>

--001a114b0cda675212055536cc3a--


From nobody Wed Jul 26 04:42:58 2017
Return-Path: <sharon.goldbe@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id F10CE131FFB for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 04:42:56 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.699
X-Spam-Level: 
X-Spam-Status: No, score=-2.699 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id VYshFKKrnkPa for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 04:42:53 -0700 (PDT)
Received: from mail-io0-x235.google.com (mail-io0-x235.google.com [IPv6:2607:f8b0:4001:c06::235]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 454BC132006 for <cfrg@irtf.org>; Wed, 26 Jul 2017 04:42:53 -0700 (PDT)
Received: by mail-io0-x235.google.com with SMTP id m88so57929194iod.2 for <cfrg@irtf.org>; Wed, 26 Jul 2017 04:42:53 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=wKuos3xs8sP15YWadbD1gSVAX6cwcMDB6a99GeWlMfA=; b=J5hXqGNTSjDzkUY7ZwCUByAHZKHhqvkXeBSWN2fN3jEUe/NnuPzH6AWrQFhWNQCBRn XfRcx+vBG6lsRtEWXHxTJtbMFoor3giiOZc2ScTuGDbwlGUumg/uSk1KRjI2Ljhkw4bt TdLW4MsI90E2QAF1E/hJ85dcXQpUhLxYnCdTMafI9fX1yaCAHZBoaPbIaDROhRiRbk1I WdS+q2U1kZEhEz2b+tO/QhQTTXIxlnVBPkFcOibY1wZgHK4RPdeNxbOeQQPOac8BQ6U2 bd+9Dt1/JDiBh7OnM9ME7finzH8liWdNfk6i3Mp12gq/16YK/t0HZOIiC+H/CltPOrph HqeA==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=wKuos3xs8sP15YWadbD1gSVAX6cwcMDB6a99GeWlMfA=; b=tJ3g6+ubPznAtWI0gPZ6FTwPMWAKbGYL+twXIFSXVTdQvvCnXvKg4qfWEv2WXrdo8V /ML3xpegsW8bvmW3uwfwbKdS2Tz+mD68RgdzmWndVy7lm9oBQ2nCgOjNLZEp/RTAPwQO 8ILiqKny9Sa+JenMNYfultq/P4HnL8GS7drhJFHhFvFdvENGeA3BHHS6hSAWDZHgzmv2 SBqZ+DzLDiMAjDFGduzo+Z7A0BQQXNBNMRaQkoHNUnW1BjO1gyAh0aJJKXQrqk4mfB9M 0Zhcv7gtGSmQl/5KrPXtYvhloQA7qzAtdhqK7k5wBdu9QZ9yAe8kEaHrXDCwTfp6RBAz 3/bQ==
X-Gm-Message-State: AIVw110krVIq23jBGmGCORlCHXv83plkmEaLIhR3c+Yi067anJ7DFFv+ 4ARNN0T5gp2T/LPB3yrMQBIVbCOhZA==
X-Received: by 10.107.131.81 with SMTP id f78mr622260iod.141.1501069372517; Wed, 26 Jul 2017 04:42:52 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.107.39.83 with HTTP; Wed, 26 Jul 2017 04:42:11 -0700 (PDT)
In-Reply-To: <CAFTSWvfwf34uH1AjzQq7zCMEARGH8rH310pSRe7kkYCZ3TMNeQ@mail.gmail.com>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com> <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net> <20170721163204.8573013.1016.15939@blackberry.com> <CAJHGrrTbjL3rd_XU9tx28g3QcBe9tJBOxs2t1OebfvZR_c7epA@mail.gmail.com> <CAFTSWvfwf34uH1AjzQq7zCMEARGH8rH310pSRe7kkYCZ3TMNeQ@mail.gmail.com>
From: Sharon Goldberg <sharon.goldbe@gmail.com>
Date: Wed, 26 Jul 2017 14:42:11 +0300
Message-ID: <CAJHGrrSh27DFzuGDmTD_GuBF7tCtNQsCJ42XTjZWO1LqqAm3wQ@mail.gmail.com>
To: Thomas Garcia <tgarcia.3141@gmail.com>
Cc: Dan Brown <danibrown@blackberry.com>, "jan@ns1.com" <jan@ns1.com>,  "cfrg@irtf.org" <cfrg@irtf.org>, Dimitrios Papadopoulos <dipapado@umd.edu>, Leonid Reyzin <reyzin@cs.bu.edu>
Content-Type: multipart/alternative; boundary="001a113ecb70bb7422055536f20c"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/Ozk2gADlngHWHL1GUnIY_F50PMM>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 26 Jul 2017 11:42:57 -0000

--001a113ecb70bb7422055536f20c
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Hi Thomas,

1. It seems that one of the properties that you are interested that the VRF
> will have is determinism. On the other hand, the EC-VRF value is dependen=
t
> on the choice of some random number k. How are these two facts compatible=
?
> Am I missing something?
>

We require determinism from the VRF hash output, which is obtained from the
VRF proof via the "proof2hash" function.

The EC-VRF proof has 3 values: gamma, c, s
Values c and s depends on the choice of random number k
But value gamma does not depend on k.

We get determinism because the VRF hash output (derived using "proof2hash")
depends only on gamma, but not on c and s.

Slide 28 from my CFRG presentations gives a pictorial explanation of this:
http://www.cs.bu.edu/~goldbe/papers/VRF_ietf99_print.pdf

2. The value c calculated in EC-VRF is only 128 bits long for Ed25519. In
> normal usage of Ed25519 the signature uses the full length of the hash
> output. Doesn't this expose the signature to collision attacks?
>
> No. We worked this out in our proofs of security.  Section B.2.1 of this
paper explains why this works.

https://eprint.iacr.org/2017/099.pdf

Thanks,
Sharon



> Thank you for your comments. Indeed, VRFs have been around since 1999.
>> They are really "verifiable PRFs" but the name is by now standard in the
>> crypto literature, and changing it will cause more confusion than keepin=
g
>> it.
>>
>> In terms of the VRF's security properties, there are three:  uniqueness,
>> collision resistance, and pseudorandomness. These are defined in our dra=
ft (
>> https://tools.ietf.org/html/draft-goldbe-vrf-01#section-3).
>>
>> How VRFs prevent dictionary attacks: a public hash is subject to a
>> dictionary attack because, given the output, an adversary can evaluate t=
he
>> hash on different inputs and see what hits the outputs. In a VRF, the
>> adversary can't evaluate the hash on different inputs.
>>
>> You say it's not surprising that "random oracle model proof can prove th=
e
>> output of a hash to be random". But actually, the output of a hash is NO=
T
>> random if the input and the hash function are known. This is because the
>> output of a hash is deterministic (every input maps to a unique output).
>> That's exactly what enables dictionary attacks. This is in contrast to a
>> VRF, where the output is (pseudo)random even given knowledge of the inpu=
t.
>> Only once the VRF proof is given, does the VRF output stop looking rando=
m.
>> Note that random oracles are not essential for VRFs, and non-random-orac=
les
>> constructions exist (but are less efficient than what we propose to
>> standardize).
>>
>> As far as use cases, here are a few:
>>
>> In the NSEC5 use case for DNSSEC, you have sensitive data (domain names)
>> and you sign consecutive pairs of hashes of domain names in order to be
>> able to prove absence of a name. If you just use standard hashing, whene=
ver
>> signed hash values are disclosed, your sensitive data is subject to
>> dictionary attacks. VRFs solve that problem, and sensitive names don't h=
ave
>> to be disclosed at all. More details are in https://eprint.iacr.org/201
>> 7/099.pdf
>>
>> In CONIKS (also Google Key Transparency, Signal secure messaging, Yahoo!
>> Coname) you also have some sensitive data (user names) that are put into=
 a
>> Merkle-like authenticated data structure. If you just use standard hashi=
ng,
>> whenever hash values are disclosed, sensitive data is subject to diction=
ary
>> attacks. If you use VRFs, sensitive data again can be disclosed only on =
an
>> as-needed basis. More details are in  https://eprint.iacr.org/2014/
>> 1004.pdf.
>>
>> In a cryptocurrency use case, you wish perform a coin flip that is
>> deterministic and provably correct, but cannot be done by just anyone.
>> More details are in https://people.csail.mit.ed
>> u/nickolai/papers/gilad-algorand-eprint.pdf and possibly other
>> cryptocurrency papers.
>>
>> Bryan Ford mentioned an additional usecase at the mic on Tuesday:
>> distributed password protection protocols
>>
>> Many of these use case are already putting VRFs into production use (esp=
.
>> the CONIKS one).  You can see a list of the various implementations we h=
ave
>> found in the "implementation status" section of our draft.  One of the
>> reasons we think this spec is so important is that we found flaws in
>> several of the implementations that can be used to trivially break
>> uniqueness.  (See eg: https://github.com/google/
>> keytransparency/issues/567)
>>
>> Thanks,
>> Sharon
>>
>> On Fri, Jul 21, 2017 at 7:32 PM, Dan Brown <danibrown@blackberry.com>
>> wrote:
>>
>>> Answering myself below: VRFs have been around since 1999, so are not so
>>> new.  =E2=80=8EStill don't like the name, and still have trouble seeing=
 the value.
>>>
>>> *From: *Dan Brown
>>> *Sent: *Tuesday, July 18, 2017 2:29 PM
>>> *To: *Sharon Goldberg; cfrg@irtf.org
>>> *Cc: *jan@ns1.com; Leonid Reyzin; Dimitrios Papadopoulos
>>> *Subject: *Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>>
>>> Hi Sharon and CFRG,
>>>
>>>
>>>
>>> On VRFs, my uncertain comments to consider at your leisure:
>>>
>>>
>>>
>>> Is it fair to say VRFs are relatively new?  If so, then maybe a little
>>> more caution is needed about their use.  It seems a tad hasty that it i=
s
>>> being used already.
>>>
>>>
>>>
>>> To me, it seems that VRFs are basically signatures, with an extra
>>> feature.  My concern is that this extra feature might get overused, bef=
ore
>>> it is thoroughly reviewed.
>>>
>>>
>>>
>>> It is unsurprising to me that random oracle model proof can prove the
>>> output of a hash to be random.  My intuitive concern is that at least
>>> informally, this is kind of circular.  Hashes often have some
>>> non-random-ish properties that might affect the extra security (over
>>> signatures) that VRFs are aiming for.  I guess I would much prefer a pr=
oof
>>> saying if the hash has (well-studied) properties XYZ, then your
>>> construction are VRFs.  (Maybe you have this already?  If so, then tell=
 me
>>> so.)
>>>
>>>
>>>
>>> Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the wire, I=
 find it hard to
>>> see how it could be used to prevent dictionary attacks.  I assume that =
you
>>> are saying the proofs must be encrypted when one needs to avoid diction=
ary
>>> models?  I suppose all the details are there in I-D and papers, but for
>>> now, I am confused about the threat model (which parties have keys, etc=
.,
>>> if they require a secure channel and mutual trust, why just use plain o=
ld
>>> hash,=E2=80=A6). To resist dictionary attacks, were already have PAKEs =
and
>>> PBHashing.  Now this?
>>>
>>>
>>>
>>> Finally, on a bikeshed-coloring note, I object to the name =E2=80=9Cver=
ifiable
>>> random function=E2=80=9D, on several grounds.
>>>
>>>
>>>
>>>    1. It is not a function.  It is at least four functions, keygen,
>>>    sign, verify, and hashify.
>>>    2. If you make it into a keyed function F_sk(m), as in
>>>    prooftohash(sign_sk(m)), it is not verifiable.
>>>    3. Verification requires the intermediate proof, which is certainly
>>>    not even pseudorandom (it is easy to distinguish valid signatures fr=
om
>>>    random).
>>>    4. It is pseudorandom, not random.  (The keys are random, but many
>>>    crypto has keys, without having =E2=80=9Crandom=E2=80=9D in its name=
: encryption, MAC,
>>>    signatures, key exchange, =E2=80=A6, they also don=E2=80=99t verifia=
ble or random in their
>>>    names either.)
>>>    5. The similar phrase =E2=80=9Cverifiably random=E2=80=9D, albeit as=
 a misnomer, has
>>>    past precedents, see NIST P-256 and Brainpool, etc.  When I see VRF,=
 I
>>>    think a function, that aims to VR in that sense, and great, now we c=
an
>>>    improve on Brainpool, etc.
>>>    6. =E2=80=9CRandom function=E2=80=9D should be reserved for the idea=
l random mapping
>>>    concept, for example, as studied by Flajolet-Odlyzko (ok they only s=
tudied
>>>    the case of equal size domain and range).  The random oracle model, =
is the
>>>    idea of approximating this ideal, etc.  An actual approximation shou=
ld not
>>>    be name as the ideal (sorry, I=E2=80=99m kind of repeating my point =
4).
>>>
>>>
>>>
>>> Please forgive the fact that my comments above are not very constructiv=
e
>>> (or if the tone is wrong).  This is a new topic for me, so I am relucta=
nt
>>> too many suggestions.  Nonetheless, I suggest (0) waiting a little, (1)=
 a
>>> non-random-oracle security proof (if you don=E2=80=99t have it yet), (2=
) re-naming
>>> the scheme to something like re-hashable (or digestible) signatures (an=
d
>>> re-name the various parts, i.e. proof -> signature, etc.).
>>>
>>>
>>>
>>> Best regards,
>>>
>>>
>>>
>>> Dan
>>>
>>>
>>>
>>>
>>>
>>> *From:* Cfrg [mailto:cfrg-bounces@irtf.org] *On Behalf Of *Sharon
>>> Goldberg
>>> *Sent:* Wednesday, July 12, 2017 5:42 AM
>>> *To:* cfrg@irtf.org
>>> *Cc:* jan@ns1.com; Dimitrios Papadopoulos <dipapado@umd.edu>; Leonid
>>> Reyzin <reyzin@cs.bu.edu>
>>> *Subject:* [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>>
>>>
>>>
>>> Dear CFRG,
>>>
>>> I'm presenting at next week's meeting on Verifiable Random Functions. A
>>> VRF is the public-key version of keyed cryptographic hash. Only the hol=
der
>>> of the VRF secret key can compute the hash, but anyone with the public =
key
>>> can verify it.  VRFs can be used to prevent dictionary attacks on
>>> hash-based data structures, and have applications to key transparency
>>> (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (Algorand).
>>>
>>> In advance of the meeting, please see:
>>>
>>> 1) Our substantially updated -01 draft:
>>> https://datatracker.ietf.org/doc/draft-goldbe-vrf/
>>>
>>> 2) Our project page, with links to various VRF implementations:
>>> https://www.cs.bu.edu/~goldbe/projects/vrf
>>>
>>> Comments welcome.  Thanks,
>>>
>>> Sharon
>>>
>>> --
>>> Sharon Goldberg
>>> Computer Science, Boston University
>>> http://www.cs.bu.edu/~goldbe
>>>
>>
>>
>>
>> --
>> ---
>> Sharon Goldberg
>> Computer Science, Boston University
>> http://www.cs.bu.edu/~goldbe
>>
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org
>> https://www.irtf.org/mailman/listinfo/cfrg
>>
>>
>


--=20
---
Sharon Goldberg
Computer Science, Boston University
http://www.cs.bu.edu/~goldbe

--001a113ecb70bb7422055536f20c
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Hi Thomas,<div><br></div><div class=3D"gmail_extra"><div c=
lass=3D"gmail_quote"><blockquote class=3D"gmail_quote" style=3D"margin:0px =
0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div=
 dir=3D"ltr"><div>1. It seems that one of the properties that you are inter=
ested that the VRF will have is determinism. On the other hand, the EC-VRF =
value is dependent on the choice of some random number k. How are these two=
 facts compatible? Am I missing something?</div></div></blockquote><div><br=
></div><div>We require determinism from the VRF hash output, which is obtai=
ned from the VRF proof via the &quot;proof2hash&quot; function.</div><div><=
br></div><div>The EC-VRF proof has 3 values: gamma, c, s</div><div>Values c=
 and s depends on the choice of random number k</div><div>But value gamma d=
oes not depend on k.</div><div><br></div><div>We get determinism because th=
e VRF hash output (derived using &quot;proof2hash&quot;) depends only on ga=
mma, but not on c and s.</div><div>=C2=A0</div><div>Slide 28 from my CFRG p=
resentations gives a pictorial explanation of this:</div><div><a href=3D"ht=
tp://www.cs.bu.edu/~goldbe/papers/VRF_ietf99_print.pdf">http://www.cs.bu.ed=
u/~goldbe/papers/VRF_ietf99_print.pdf</a><br></div><div><br></div><blockquo=
te class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px =
solid rgb(204,204,204);padding-left:1ex"><div dir=3D"ltr"><div>2. The value=
 c calculated in EC-VRF is only 128 bits long for Ed25519. In normal usage =
of Ed25519 the signature uses the full length of the hash output. Doesn&#39=
;t this expose the signature to collision attacks?</div><div><br></div></di=
v></blockquote><div>No. We worked this out in our proofs of security.=C2=A0=
 Section B.2.1 of this paper explains why this works.</div><div><br></div><=
div><a href=3D"https://eprint.iacr.org/2017/099.pdf">https://eprint.iacr.or=
g/2017/099.pdf</a><br></div><div><br></div><div>Thanks,</div><div>Sharon</d=
iv><div><br></div><div>=C2=A0</div><blockquote class=3D"gmail_quote" style=
=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding=
-left:1ex"><div class=3D"gmail_extra"><div class=3D"gmail_quote"><blockquot=
e class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px s=
olid rgb(204,204,204);padding-left:1ex"><div><div class=3D"gmail-h5"><div d=
ir=3D"ltr"><div style=3D"font-size:12.8px"></div><div style=3D"font-size:12=
.8px">Thank you for your comments. Indeed, VRFs have been around since 1999=
. They are really &quot;verifiable PRFs&quot; but the name is by now standa=
rd in the crypto literature, and changing it will cause more confusion than=
 keeping it.</div><div style=3D"font-size:12.8px"><br></div><div style=3D"f=
ont-size:12.8px">In terms of the VRF&#39;s security properties, there are t=
hree: =C2=A0uniqueness, collision resistance, and pseudorandomness. These a=
re defined in our draft (<span style=3D"font-size:12.8px"><a href=3D"https:=
//tools.ietf.org/html/draft-goldbe-vrf-01#section-3" target=3D"_blank">http=
s://tools.ietf.org/html/d<wbr>raft-goldbe-vrf-01#section-3</a></span><span =
style=3D"font-size:12.8px">).<wbr>=C2=A0</span></div><div style=3D"font-siz=
e:12.8px"><br></div><div style=3D"font-size:12.8px">How VRFs prevent dictio=
nary attacks: a public hash is subject to a dictionary attack because, give=
n the output, an adversary can evaluate the hash on different inputs and se=
e what hits the outputs. In a VRF, the adversary can&#39;t evaluate the has=
h on different inputs.=C2=A0</div><div style=3D"font-size:12.8px"><br></div=
><div style=3D"font-size:12.8px">You say it&#39;s not surprising that &quot=
;random oracle model proof can prove the output of a hash to be random&quot=
;. But actually, the output of a hash is NOT random if the input and the ha=
sh function are known. This is because the output of a hash is deterministi=
c (every input maps to a unique output). That&#39;s exactly what enables di=
ctionary attacks. This is in contrast to a VRF, where the output is (pseudo=
)random even given knowledge of the input. Only once the VRF proof is given=
, does the VRF output stop looking random. Note that random oracles are not=
 essential for VRFs, and non-random-oracles constructions exist (but are le=
ss efficient than what we propose to standardize).</div><div style=3D"font-=
size:12.8px"><br></div><div style=3D"font-size:12.8px">As far as use cases,=
 here are a few:=C2=A0</div><div style=3D"font-size:12.8px"><br></div><div =
style=3D"font-size:12.8px">In the NSEC5 use case for DNSSEC, you have sensi=
tive data (domain names) and you sign consecutive pairs of hashes of domain=
 names in order to be able to prove absence of a name. If you just use stan=
dard hashing, whenever signed hash values are disclosed, your sensitive dat=
a is subject to dictionary attacks. VRFs solve that problem, and sensitive =
names don&#39;t have to be disclosed at all. More details are in=C2=A0<a hr=
ef=3D"https://eprint.iacr.org/2017/099.pdf" target=3D"_blank">https://eprin=
t.iacr.org/201<wbr>7/099.pdf</a></div><div style=3D"font-size:12.8px"><br><=
/div><div style=3D"font-size:12.8px">In CONIKS (also Google Key Transparenc=
y, Signal secure messaging, Yahoo! Coname) you also have some sensitive dat=
a (user names) that are put into a Merkle-like authenticated data structure=
. If you just use standard hashing, whenever hash values are disclosed, sen=
sitive data is subject to dictionary attacks. If you use VRFs, sensitive da=
ta again can be disclosed only on an as-needed basis. More details are in =
=C2=A0<a href=3D"https://eprint.iacr.org/2014/1004.pdf" target=3D"_blank">h=
ttps://eprint.iacr.org/2014/<wbr>1004.pdf</a>.</div><div style=3D"font-size=
:12.8px"><br></div><div style=3D"font-size:12.8px">In a cryptocurrency use =
case, you wish perform a coin flip that is deterministic and provably corre=
ct, but cannot be done by just anyone.=C2=A0 More details are in=C2=A0<a hr=
ef=3D"https://people.csail.mit.edu/nickolai/papers/gilad-algorand-eprint.pd=
f" target=3D"_blank">https://people.csail.mit.ed<wbr>u/nickolai/papers/gila=
d-algora<wbr>nd-eprint.pdf</a>=C2=A0and possibly other cryptocurrency paper=
s.</div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-size:1=
2.8px">Bryan Ford mentioned an additional usecase at the mic on Tuesday: di=
stributed password protection protocols</div><div style=3D"font-size:12.8px=
"><br></div><div style=3D"font-size:12.8px">Many of these use case are alre=
ady putting VRFs into production use (esp. the CONIKS one).=C2=A0 You can s=
ee a list of the various implementations we have found in the &quot;impleme=
ntation status&quot; section of our draft.=C2=A0 One of the reasons we thin=
k this spec is so important is that we found flaws in several of the implem=
entations that can be used to trivially break uniqueness. =C2=A0(See eg:=C2=
=A0<a href=3D"https://github.com/google/keytransparency/issues/567" target=
=3D"_blank">https://github.com/google/<wbr>keytransparency/issues/567</a>)<=
/div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8=
px"><span style=3D"font-size:12.8px">Thanks,</span><br></div><div style=3D"=
font-size:12.8px">Sharon=C2=A0</div><div class=3D"gmail_extra"><div><div cl=
ass=3D"gmail-m_4922457647511857001h5"><br><div class=3D"gmail_quote">On Fri=
, Jul 21, 2017 at 7:32 PM, Dan Brown <span dir=3D"ltr">&lt;<a href=3D"mailt=
o:danibrown@blackberry.com" target=3D"_blank">danibrown@blackberry.com</a>&=
gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0px =
0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">




<div lang=3D"EN-US">
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
Answering myself below: VRFs have been around since 1999, so are not so new=
. =C2=A0=E2=80=8EStill don&#39;t like the name, and still have trouble seei=
ng the value.</div>
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
<span style=3D"font-family:Calibri,&quot;Slate Pro&quot;,sans-serif,sans-se=
rif;font-size:initial;line-height:initial;text-align:initial"><br>
</span></div>
<table width=3D"100%" style=3D"background-color:white">
<tbody>
<tr>
<td colspan=3D"2" style=3D"font-size:initial;text-align:initial;background-=
color:rgb(255,255,255)">
<div style=3D"border-style:solid none none;border-top-color:rgb(181,196,223=
);border-top-width:1pt;padding:3pt 0in 0in;font-family:Tahoma,&quot;BB Alph=
a Sans&quot;,&quot;Slate Pro&quot;;font-size:10pt">
<div><b>From: </b>Dan Brown</div>
<div><b>Sent: </b>Tuesday, July 18, 2017 2:29 PM</div>
<div><b>To: </b>Sharon Goldberg; <a href=3D"mailto:cfrg@irtf.org" target=3D=
"_blank">cfrg@irtf.org</a></div>
<div><b>Cc: </b><a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.co=
m</a>; Leonid Reyzin; Dimitrios Papadopoulos</div>
<div><b>Subject: </b>Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functio=
ns</div>
</div>
</td>
</tr>
</tbody>
</table><div><div class=3D"gmail-m_4922457647511857001m_-615310173404414215=
5m_4165835283928257204gmail-h5">
<div style=3D"border-style:solid none none;border-top-color:rgb(186,188,209=
);border-top-width:1pt;font-size:initial;text-align:initial;background-colo=
r:rgb(255,255,255)">
</div>
<br>
<div>
<div class=3D"gmail-m_4922457647511857001m_-6153101734044142155m_4165835283=
928257204gmail-m_6358749242748202832WordSection1">
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Hi Sharon and CFRG,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">On VRFs, my uncertain comments to consider at your leisure:</span=
></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Is it fair to say VRFs are relatively new?=C2=A0 If so, then mayb=
e a little more caution is needed about their use.=C2=A0 It seems a tad has=
ty that it is being used already.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">To me, it seems that VRFs are basically signatures, with an extra=
 feature.=C2=A0 My concern is that this extra feature might get overused, b=
efore it is thoroughly reviewed.=C2=A0
</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">It is unsurprising to me that random oracle model proof can prove=
 the output of a hash to be random.=C2=A0 My intuitive concern is that at l=
east informally, this is kind of circular.=C2=A0
 Hashes often have some non-random-ish properties that might affect the ext=
ra security (over signatures) that VRFs are aiming for.=C2=A0 I guess I wou=
ld much prefer a proof saying if the hash has (well-studied) properties XYZ=
, then your construction are VRFs.=C2=A0 (Maybe
 you have this already?=C2=A0 If so, then tell me so.)</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the w=
ire, I find it hard to see how it could be used to prevent dictionary attac=
ks.=C2=A0 I assume that you are saying the proofs must
 be encrypted when one needs to avoid dictionary models?=C2=A0 I suppose al=
l the details are there in I-D and papers, but for now, I am confused about=
 the threat model (which parties have keys, etc., if they require a secure =
channel and mutual trust, why just use
 plain old hash,=E2=80=A6). To resist dictionary attacks, were already have=
 PAKEs and PBHashing.=C2=A0 Now this?</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Finally, on a bikeshed-coloring note, I object to the name =E2=80=
=9Cverifiable random function=E2=80=9D, on several grounds.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<ol start=3D"1" type=3D"1" style=3D"margin-top:0in">
<li class=3D"gmail-m_4922457647511857001m_-6153101734044142155m_41658352839=
28257204gmail-m_6358749242748202832MsoListParagraph" style=3D"margin-left:0=
in"><span style=3D"font-size:11pt;font-family:Calibri,sans-serif">It is not=
 a function.=C2=A0 It is at least four functions, keygen, sign, verify, and=
 hashify.</span></li><li class=3D"gmail-m_4922457647511857001m_-61531017340=
44142155m_4165835283928257204gmail-m_6358749242748202832MsoListParagraph" s=
tyle=3D"margin-left:0in"><span style=3D"font-size:11pt;font-family:Calibri,=
sans-serif">If you make it into a keyed function F_sk(m), as in prooftohash=
(sign_sk(m)), it is not verifiable.=C2=A0
</span></li><li class=3D"gmail-m_4922457647511857001m_-6153101734044142155m=
_4165835283928257204gmail-m_6358749242748202832MsoListParagraph" style=3D"m=
argin-left:0in"><span style=3D"font-size:11pt;font-family:Calibri,sans-seri=
f">Verification requires the intermediate proof, which is certainly not eve=
n pseudorandom (it is easy to distinguish valid signatures from random).</s=
pan></li><li class=3D"gmail-m_4922457647511857001m_-6153101734044142155m_41=
65835283928257204gmail-m_6358749242748202832MsoListParagraph" style=3D"marg=
in-left:0in"><span style=3D"font-size:11pt;font-family:Calibri,sans-serif">=
It is pseudorandom, not random.=C2=A0 (The keys are random, but many crypto=
 has keys, without having =E2=80=9Crandom=E2=80=9D in its name: encryption,=
 MAC, signatures,
 key exchange, =E2=80=A6, they also don=E2=80=99t verifiable or random in t=
heir names either.)</span></li><li class=3D"gmail-m_4922457647511857001m_-6=
153101734044142155m_4165835283928257204gmail-m_6358749242748202832MsoListPa=
ragraph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;font-famil=
y:Calibri,sans-serif">The similar phrase =E2=80=9Cverifiably random=E2=80=
=9D, albeit as a misnomer, has past precedents, see NIST P-256 and Brainpoo=
l, etc.=C2=A0 When I see VRF, I think
 a function, that aims to VR in that sense, and great, now we can improve o=
n Brainpool, etc.</span></li><li class=3D"gmail-m_4922457647511857001m_-615=
3101734044142155m_4165835283928257204gmail-m_6358749242748202832MsoListPara=
graph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;font-family:=
Calibri,sans-serif">=E2=80=9CRandom function=E2=80=9D should be reserved fo=
r the ideal random mapping concept, for example, as studied by Flajolet-Odl=
yzko (ok they only studied
 the case of equal size domain and range).=C2=A0 The random oracle model, i=
s the idea of approximating this ideal, etc.=C2=A0 An actual approximation =
should not be name as the ideal (sorry, I=E2=80=99m kind of repeating my po=
int 4).</span></li></ol>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Please forgive the fact that my comments above are not very const=
ructive (or if the tone is wrong).=C2=A0 This is a new topic for me, so I a=
m reluctant too many suggestions.=C2=A0 Nonetheless,
 I suggest (0) waiting a little, (1) a non-random-oracle security proof (if=
 you don=E2=80=99t have it yet), (2) re-naming the scheme to something like=
 re-hashable (or digestible) signatures (and re-name the various parts, i.e=
. proof -&gt; signature, etc.).</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Best regards,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Dan</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><b><span style=3D"font-size:11pt;font-family:Calibri=
,sans-serif">From:</span></b><span style=3D"font-size:11pt;font-family:Cali=
bri,sans-serif"> Cfrg [mailto:<a href=3D"mailto:cfrg-bounces@irtf.org" targ=
et=3D"_blank">cfrg-bounces@irtf.org</a>]
<b>On Behalf Of </b>Sharon Goldberg<br>
<b>Sent:</b> Wednesday, July 12, 2017 5:42 AM<br>
<b>To:</b> <a href=3D"mailto:cfrg@irtf.org" target=3D"_blank">cfrg@irtf.org=
</a><br>
<b>Cc:</b> <a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.com</a>=
; Dimitrios Papadopoulos &lt;<a href=3D"mailto:dipapado@umd.edu" target=3D"=
_blank">dipapado@umd.edu</a>&gt;; Leonid Reyzin &lt;<a href=3D"mailto:reyzi=
n@cs.bu.edu" target=3D"_blank">reyzin@cs.bu.edu</a>&gt;<br>
<b>Subject:</b> [Cfrg] draft-goldbe-vrf: Verifiable Random Functions</span>=
</p>
<p class=3D"MsoNormal">=C2=A0</p>
<div>
<p class=3D"MsoNormal">Dear CFRG,<br>
<br>
I&#39;m presenting at next week&#39;s meeting on Verifiable Random Function=
s. A VRF is the public-key version of keyed cryptographic hash. Only the ho=
lder of the VRF secret key can compute the hash, but anyone with the public=
 key can verify it.=C2=A0 VRFs can be used to
 prevent dictionary attacks on hash-based data structures, and have applica=
tions to key transparency (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (A=
lgorand).<br>
<br>
In advance of the meeting, please see:<br>
<br>
1) Our substantially updated -01 draft:<br>
<a href=3D"https://datatracker.ietf.org/doc/draft-goldbe-vrf/" target=3D"_b=
lank">https://datatracker.ietf.org/d<wbr>oc/draft-goldbe-vrf/</a><br>
<br>
2) Our project page, with links to various VRF implementations:<br>
<a href=3D"https://www.cs.bu.edu/~goldbe/projects/vrf" target=3D"_blank">ht=
tps://www.cs.bu.edu/~goldbe/<wbr>projects/vrf</a><br>
<br>
Comments welcome.=C2=A0 Thanks,<br>
<br>
Sharon<br>
<br>
--<br>
Sharon Goldberg<br>
Computer Science, Boston University<br>
<a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu=
.edu/~goldbe</a></p>
</div>
</div>
</div>
</div></div></div>

</blockquote></div><br><br clear=3D"all"><div><br></div></div></div>-- <br>=
<div class=3D"gmail-m_4922457647511857001m_-6153101734044142155m_4165835283=
928257204gmail_signature">---<span><br>Sharon Goldberg<br>Computer Science,=
 Boston University<br><a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_b=
lank">http://www.cs.bu.edu/~goldbe</a></span></div>
</div></div>
<br></div></div><span class=3D"gmail-">______________________________<wbr>_=
________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/l<wbr>istinfo/cfrg</a><br>
<br></span></blockquote></div><br></div>
</blockquote></div><br><br clear=3D"all"><div><br></div>-- <br><div class=
=3D"gmail_signature">---<br>Sharon Goldberg<br>Computer Science, Boston Uni=
versity<br><a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http:=
//www.cs.bu.edu/~goldbe</a></div>
</div></div>

--001a113ecb70bb7422055536f20c--


From nobody Wed Jul 26 05:04:59 2017
Return-Path: <yannick.seurin@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 41D9A126E3A for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 05:04:58 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.699
X-Spam-Level: 
X-Spam-Status: No, score=-2.699 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id kg43EQi0JaY0 for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 05:04:55 -0700 (PDT)
Received: from mail-yw0-x22e.google.com (mail-yw0-x22e.google.com [IPv6:2607:f8b0:4002:c05::22e]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 66DEA131C7A for <cfrg@ietf.org>; Wed, 26 Jul 2017 05:04:55 -0700 (PDT)
Received: by mail-yw0-x22e.google.com with SMTP id u207so24569585ywc.3 for <cfrg@ietf.org>; Wed, 26 Jul 2017 05:04:55 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=zf7R6IRnXtKPJXQ2AFrSLpjOZuAIOCcdcoN3Qu8L1qk=; b=SRMqGmBiCfqNefbX4O/nNcIIUJEHqdQRQfEJ3t3DiVvjHdLgykUN6Drm4PMW/NfD3m cHJEzvosZo/tYhbMmkKg8jb7QT/NSmfLIZZIdz5dXNd6xqhyT3KwGeCR9V75/7m4D1bu I2XNhm0WNeG7MXTT9afnwm5J3bLJiYRIHSvjbH5y66Js9ge6Wngh9m3idZnLqkYSOLOF bnoLQ9g7wl3YtwZZuuYpjMRCYPSrQ1/cdeXntOQQ1WhLGcBci/ctoucIee/54IIPqv1e f7GBbqgTKn0MznfUUpOjnE8wVXNdZU8CjsQdXFmPuv4cIZYIMBmaI9mUBFsrkoq+ho16 1HqA==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=zf7R6IRnXtKPJXQ2AFrSLpjOZuAIOCcdcoN3Qu8L1qk=; b=a7lPP0sF4OPT1q8Oe4jhi7w9pcAaubd4HEDzqvIChC9Us4MFfqj3F3Glde4za2QS4C zmLhV9wBsAygOIFL7k9MaGqAAcXsnWCdX0PWSVb8+WsUPd8aVQmc7/CuDlpTRVqoBQBj M5OUpx/4t+6U2DpQrcOdJTTMsPBMt19tkD4sTUV22/FEwWlkLWDYqgaJA35gzMxARQZ1 HuNoJticyqIwed0Ih3AIY3NtjTZVWAlX5ordDdsryxRpLuAVTsc5mFUwaeuTFbeb0ofi ph6RWUJO8YIg68OnD18DompkQb0iDdVSxdGNGTnQqKQGql+7/Vxuh7XtPjRstrx3Qc1T 7yxQ==
X-Gm-Message-State: AIVw111oVadedvDBe8qV7Er7TxE50xp65t3A1xb/NJPVP27AVj4t0zu1 KFTNiNNZXs1BGmy5JxHiFrowo9EmyTGhx+s=
X-Received: by 10.37.206.9 with SMTP id x9mr563933ybe.79.1501070694224; Wed, 26 Jul 2017 05:04:54 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.37.91.7 with HTTP; Wed, 26 Jul 2017 05:04:23 -0700 (PDT)
In-Reply-To: <CAMfhd9UOFNfqoEp31r2moVaEfQZoeppP7h2Anrz0BBP518SeYA@mail.gmail.com>
References: <CAMfhd9UOFNfqoEp31r2moVaEfQZoeppP7h2Anrz0BBP518SeYA@mail.gmail.com>
From: Yannick Seurin <yannick.seurin@gmail.com>
Date: Wed, 26 Jul 2017 14:04:23 +0200
Message-ID: <CAOOV4XvpdCuEc8s5iXr3mzxuCTXj63AP6wATriu=D3Dxs3zz4Q@mail.gmail.com>
To: cfrg@ietf.org
Cc: Tetsu Iwata <iwata@cse.nagoya-u.ac.jp>
Content-Type: multipart/alternative; boundary="94eb2c190112831eac0555374180"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/JHB3l9CpENIIsoFLZlXH9yOypsM>
Subject: Re: [Cfrg] Updated bounds in AES-GCM-SIV paper
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 26 Jul 2017 12:04:58 -0000

--94eb2c190112831eac0555374180
Content-Type: text/plain; charset="UTF-8"

Dear CFRG,

Our paper "Reconsidering the Security Bound of AES-GCM-SIV", which prompted
Adam's email, is now available on ePrint:
https://eprint.iacr.org/2017/708

The main contribution of this paper is an independent security analysis for
AES-GCM-SIV motivated by some problems that we discovered in the security
proofs presented in [1] and [2]. We also propose a different key-derivation
function with similar efficiency but better security than the one currently
specified.

As explained by Adam, we noticed that the security claims made in [2] were
overly optimistic because the PRP-PRF indistinguishability term had been
neglected, whereas it was actually the dominating term of the security
bound. As a consequence, the security guarantees provided by AES-GCM-SIV
must be lowered compared with what was originally announced in [2],
especially for long messages.

We stress that our paper is based on version 20160310:063701 of [1] and
version 20170223:140759 of [2]. Both [1] and [2] were updated after we sent
our paper to AES-GCM-SIV's designers on July 7.

We believe that the CFRG specification (especially Section 9) should be
updated as well to reflect the new security analysis. Recommended usage
limitations for an AEAD scheme (such as the maximal number of messages that
can be encrypted with the same key) should be based on the maximal message
length allowed by its specification (currently, 2^{32} 128-bit blocks).
More fine-grained recommendations (such as "if the maximal message length
in an application is 2^m and the maximal number of nonce repetitions is R,
then the maximal number of messages that can be encrypted with the same key
can be pushed to XXX") are likely to create confusion and incur
implementations errors. For AES-GCM-SIV with randomly generated nonces
(which has been put forward by the designers as the preferred way of
generating nonces when no state can be saved by encrypting devices), this
means that no more than 2^{30} messages should be encrypted with the same
key, which contrasts with the recommended limit of 2^{50} given (without
context) in Section 9 of the CFRG specification and in the abstract of [2].

Cheers,
Tetsu and Yannick.

[1] https://eprint.iacr.org/2015/102
[2] https://eprint.iacr.org/2017/168

2017-07-17 4:09 GMT+02:00 Adam Langley <agl@imperialviolet.org>:

> Dear CFRG,
>
> We would like to thank Yannick Seurin and Tetsu Iwata for alerting us
> to the fact that we had erroneously assumed that one of the terms in
> the security bounds of AES-GCM-SIV was negligible when, for
> indistinguishability, it was not. Thus, while the security proof was
> correct, the example concrete bounds were over optimistic, most
> notably for very large messages. This was most evident in Fig 4.
>
> We have updated the paper[1] to correct this mistake and we draw the
> group's attention to the revised figure four (now called Table 1). For
> typical uses, thankfully, the difference is not material but for we
> wish to highlight that one cannot encrypt many messages of
> many-gigabytes using AES-GCM-SIV, in contrast to what the figures
> previously suggested. However, even in such a case of very long
> messages, the overall number of blocks encrypted safely is still
> significantly higher than previous schemes.
>
> [1] https://eprint.iacr.org/2017/168
>
>
> Cheers
>
> AGL
>
> --
> Adam Langley agl@imperialviolet.org https://www.imperialviolet.org
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>

--94eb2c190112831eac0555374180
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div>Dear CFRG,</div><div><br></div><div>Our paper &quot;R=
econsidering the Security Bound of AES-GCM-SIV&quot;, which prompted Adam&#=
39;s email, is now available on ePrint:</div><div><a href=3D"https://eprint=
.iacr.org/2017/708" target=3D"_blank">https://eprint.iacr.org/2017/<wbr>708=
</a></div><div><br></div><div>The main contribution of this paper is an ind=
ependent security analysis for AES-GCM-SIV motivated by some problems that =
we discovered in the security proofs presented in [1] and [2]. We also prop=
ose a different key-derivation function with similar efficiency but better =
security than the one currently specified.=C2=A0</div><div><br></div><div>A=
s explained by Adam, we noticed that the security claims made in [2] were o=
verly optimistic because the PRP-PRF indistinguishability term had been neg=
lected, whereas it was actually the dominating term of the security bound. =
As a consequence, the security guarantees provided by AES-GCM-SIV must be l=
owered compared with what was originally announced in [2], especially for l=
ong messages.</div><div><br></div><div>We stress that our paper is based on=
 version 20160310:063701 of [1] and version 20170223:140759 of [2]. Both [1=
] and [2] were updated after we sent our paper to AES-GCM-SIV&#39;s designe=
rs on July 7.</div><div><br></div><div>We believe that the CFRG specificati=
on (especially Section 9) should be updated as well to reflect the new secu=
rity analysis. Recommended usage limitations for an AEAD scheme (such as th=
e maximal number of messages that can be encrypted with the same key) shoul=
d be based on the maximal message length allowed by its specification (curr=
ently, 2^{32} 128-bit blocks). More fine-grained recommendations (such as &=
quot;if the maximal message length in an application is 2^m and the maximal=
 number of nonce repetitions is R, then the maximal number of messages that=
 can be encrypted with the same key can be pushed to XXX&quot;) are likely =
to create confusion and incur implementations errors. For AES-GCM-SIV with =
randomly generated nonces (which has been put forward by the designers as t=
he preferred way of generating nonces when no state can be saved by encrypt=
ing devices), this means that no more than 2^{30} messages should be encryp=
ted with the same key, which contrasts with the recommended limit of 2^{50}=
 given (without context) in Section 9 of the CFRG specification and in the =
abstract of [2].</div><div><br></div><div>Cheers,</div><div>Tetsu and Yanni=
ck.</div><div><br></div><div>[1] <a href=3D"https://eprint.iacr.org/2015/10=
2" target=3D"_blank">https://eprint.iacr.org/2015/<wbr>102</a></div><div>[2=
] <a href=3D"https://eprint.iacr.org/2017/168" target=3D"_blank">https://ep=
rint.iacr.org/2017/<wbr>168</a></div><div class=3D"gmail_extra"><br><div cl=
ass=3D"gmail_quote">2017-07-17 4:09 GMT+02:00 Adam Langley <span dir=3D"ltr=
">&lt;<a href=3D"mailto:agl@imperialviolet.org" target=3D"_blank">agl@imper=
ialviolet.org</a>&gt;</span>:<br><blockquote class=3D"gmail_quote" style=3D=
"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-le=
ft:1ex">Dear CFRG,<br>
<br>
We would like to thank Yannick Seurin and Tetsu Iwata for alerting us<br>
to the fact that we had erroneously assumed that one of the terms in<br>
the security bounds of AES-GCM-SIV was negligible when, for<br>
indistinguishability, it was not. Thus, while the security proof was<br>
correct, the example concrete bounds were over optimistic, most<br>
notably for very large messages. This was most evident in Fig 4.<br>
<br>
We have updated the paper[1] to correct this mistake and we draw the<br>
group&#39;s attention to the revised figure four (now called Table 1). For<=
br>
typical uses, thankfully, the difference is not material but for we<br>
wish to highlight that one cannot encrypt many messages of<br>
many-gigabytes using AES-GCM-SIV, in contrast to what the figures<br>
previously suggested. However, even in such a case of very long<br>
messages, the overall number of blocks encrypted safely is still<br>
significantly higher than previous schemes.<br>
<br>
[1] <a href=3D"https://eprint.iacr.org/2017/168" rel=3D"noreferrer" target=
=3D"_blank">https://eprint.iacr.org/2017/1<wbr>68</a><br>
<br>
<br>
Cheers<br>
<br>
AGL<br>
<span class=3D"gmail-m_-9098168409608561249gmail-HOEnZb"><font color=3D"#88=
8888"><br>
--<br>
Adam Langley <a href=3D"mailto:agl@imperialviolet.org" target=3D"_blank">ag=
l@imperialviolet.org</a> <a href=3D"https://www.imperialviolet.org" rel=3D"=
noreferrer" target=3D"_blank">https://www.imperialviolet.org</a><br>
<br>
______________________________<wbr>_________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/l<wbr>istinfo/cfrg</a><br>
</font></span></blockquote></div><br></div></div>

--94eb2c190112831eac0555374180--


From nobody Wed Jul 26 08:07:47 2017
Return-Path: <ietf@huelsing.net>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 80CF5131D69; Mon, 24 Jul 2017 07:30:27 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.901
X-Spam-Level: 
X-Spam-Status: No, score=-1.901 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 6NHrfZZ3aG-X; Mon, 24 Jul 2017 07:30:18 -0700 (PDT)
Received: from www363.your-server.de (www363.your-server.de [78.46.179.9]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 200F3131D3D; Mon, 24 Jul 2017 07:30:17 -0700 (PDT)
Received: from [88.198.220.132] (helo=sslproxy03.your-server.de) by www363.your-server.de with esmtpsa (TLSv1.2:DHE-RSA-AES256-GCM-SHA384:256) (Exim 4.85_2) (envelope-from <ietf@huelsing.net>) id 1dZeNB-0000Bv-Lb; Mon, 24 Jul 2017 16:30:13 +0200
Received: from [131.155.70.110] by sslproxy03.your-server.de with esmtpsa (TLSv1.2:DHE-RSA-AES256-SHA:256) (Exim 4.84_2) (envelope-from <ietf@huelsing.net>) id 1dZeNB-0004sE-4D; Mon, 24 Jul 2017 16:30:13 +0200
To: Stephen Farrell <stephen.farrell@cs.tcd.ie>, "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>, Alexey Melnikov <alexey.melnikov@isode.com>, "irsg@irtf.org" <irsg@irtf.org>, "cfrg@irtf.org" <Cfrg@irtf.org>
Cc: "draft-irtf-cfrg-xmss-hash-based-signatures@ietf.org" <draft-irtf-cfrg-xmss-hash-based-signatures@ietf.org>
References: <D4FDAF9D.8D586%kenny.paterson@rhul.ac.uk> <9a878527-5ab9-5429-7c5d-4f7e4ca4e8db@isode.com> <08944dc3-9086-ed47-cc1b-54248b3dac70@cs.tcd.ie> <D566ADE0.963E4%kenny.paterson@rhul.ac.uk> <9e6b6146-e376-86cb-70be-0127a3e72d16@cs.tcd.ie> <D56DBB2C.96A67%kenny.paterson@rhul.ac.uk> <6f90e485-01f4-5ad8-49ef-e51c52e01a46@cs.tcd.ie> <5e328e85-a8a1-67f1-3853-418309b04a17@huelsing.net> <27cc7000-7fd5-27dd-b8b5-9b9518a9f3ad@huelsing.net> <1785b9ed-fb53-889a-9d34-311c7ea5c762@cs.tcd.ie>
From: "A. Huelsing" <ietf@huelsing.net>
Message-ID: <4699f3d2-40ce-9c40-d29a-d24ecb3b6cab@huelsing.net>
Date: Mon, 24 Jul 2017 16:30:10 +0200
User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.2.1
MIME-Version: 1.0
In-Reply-To: <1785b9ed-fb53-889a-9d34-311c7ea5c762@cs.tcd.ie>
Content-Type: multipart/mixed; boundary="------------EDA0ADC751965DA00E77AF10"
Content-Language: en-GB
X-Authenticated-Sender: ietf@huelsing.net
X-Virus-Scanned: Clear (ClamAV 0.99.2/23592/Mon Jul 24 10:18:33 2017)
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/28D93ZZnznUixrj6c0aMGCyvhrk>
X-Mailman-Approved-At: Wed, 26 Jul 2017 08:07:38 -0700
Subject: Re: [Cfrg] [irsg] IRSG review of draft-irtf-cfrg-xmss-hash-based-signatures-08
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 24 Jul 2017 14:30:28 -0000

This is a multi-part message in MIME format.
--------------EDA0ADC751965DA00E77AF10
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 7bit

Dear Stephen,

we tried to make the required changes. Please have a look if you are fine
with the changes (especially regarding section 5 and the reference
implementation).

You find our answers to your review below and the new draft version attached.

Thanks again for your time,

Andreas, Aziz, Denis, Joost & Stefan


################# Answers ####################
possible errors:
----------------

- 3.1.2: Algorithm 2: "if ( (i + s) > w - 1 )..." seems to be
missing parenthesis around the "(w-1)" to me.  Without those
brackets I could interpret that test to always result in false.

#Done

- 4.1.9: should the call to setIdx in alg 12 be after treeSig?
  as-is you seem to have incremented the index too soon so
that when alg 11 does getIdx it'd presumably get the
incremented index and cause verification failure. I think
the same is true of alg 16 as well, in section 4.2.4.

#Done

significant comments, but likely fixable:
-----------------------------------------

- section 5: there are waaaay too many options defined here.
  As-is, this will damage potential deployment of xmss. I
would strongly suggest deleting all of the options except the
minimum, that being one (and only one) set of parameters for
XMSS and one for XMSS^MT. If others are needed later, those
can be defined later. (Note that the damage done here includes
the hours of developer time that would be wasted debating
which of these choices to implement/use. Consider the case of
pre-hash variants of eddsa for an ongoing example.)

####
#   We significantly changed section 5, please check if this
#   satisfies your remarks
####

- section 5 (or an appendix) should contain some test vectors
  (including intermediate values). Without those, implementers
have a much harder time of getting their code right.

# Added section on reference implementation


nits, near-nits and other ignorable things:
-------------------------------------------

- abstract: I'd suggest s/can withstand attacks/ can withstand
  so-far known attacks/
 
# Done

- 1.1: You say if used >1 time "no cryptographic security
  guarantees remain." It might be clearer to give some
examples of consequences, e.g. that the attacker can forge new
signatures or whatever.

# Done

- 1.1: I think you might mention that XMSS and other OTS ideas
  require some new crypto APIs. I'm not aware if anyone has
developed proposals for such, but would be interested if
someone has.

# Done

- 2.3, 2nd last para: you might want to say what happens with
  e.g.  B<<2 where B=0xf0. I assume the result is 0xc0 but
someone might think it's 0x3c0 or even 0xc3.

# Done: Removed the left shift as it is never used for single bytes

- 2.5: having the "type word" as octet 15 of a 32 byte address
  seems odd. Is there a reason why? (Just wondering.)

# Yes: We got the space and think that it simlifies implementation if
one always has to manipulate whole words (and can treat the address as
uint32_t[8])
 
- 2.6: It seems odd to given an example where the input and
  output of base_w() are the same. A different example may be
more useful. (More examples generally would be great.)

# Done

- 3.1.3: maybe note that "/" means nothing? Which I assume it
  does? Better might be to just say that.
 
# Done

- 3.1.5: "a maximum value of len_1 * (w - 1) * 2^8" is missing
  units
 
# Done: value -> Integer value

- 3.1.5: "the variable" - which one?

# Done: Added explanation

- 3.1.5: "For the parameter sets given in Section 5 a 32-bit
  unsigned integer is sufficient." Sufficient for what?

# Done: Added " to hold the checksum"
 
- 3.1.5: The ascii art at the end of p16 doesn't help much.

# while the art does not contain new information, we think it's
a handy reminder. Would prefer to keep it like this.

- 3.1.7: The "MUST match" statement doesn't seem enforceable
  nor testable so I'm not sure it's a good idea to include.
OTOH, I do get the idea of using 2119 terms for emphasis.

# Ok, so what should we do? I agree that key handling cannot be
verified. Still, it seems necessary to emphasize this.
If it is just about the use of the 2119 term,
how about:
"but it is crucial for security that the cryptographic strength
matches that of the used WOTS+ parameters."?

- 3.1.7: I think it might be useful to point out any specific
  problems associated with using a low entropy human memorable
secret (password) for the value S. No matter what you say,
people will do that, so better if you can say you told them
specifically about downsides of doing that.

# We adressed this in a new sentence at the end of the
# paragraph.

- 4.1.12: I'm not sure if the MAY there is correct or not.  If
  it means "you MAY use a different algorithm to get the same
output as alg 12" then that'd be fine. If something else is
meant I'm not sure what you're saying, and it'd probably be
better to not even mention it.
# That is exactly what it means. There are far more efficient
# algorithms to compute that output (but also far more complex)

- section 5 should also spell out the signature and
public key sizes in bytes and ideally, if you keep multiple
options, (but please don't:-) describe relative or measured
timings.

# Done


--------------EDA0ADC751965DA00E77AF10
Content-Type: text/plain; charset=UTF-8;
 name="draft-irtf-cfrg-xmss-hash-based-signatures-10.txt"
Content-Transfer-Encoding: base64
Content-Disposition: attachment;
 filename="draft-irtf-cfrg-xmss-hash-based-signatures-10.txt"
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--------------EDA0ADC751965DA00E77AF10--


From nobody Wed Jul 26 13:57:01 2017
Return-Path: <Kenny.Paterson@rhul.ac.uk>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 45F6E13146C for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 13:57:00 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.921
X-Spam-Level: 
X-Spam-Status: No, score=-1.921 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, RCVD_IN_DNSWL_NONE=-0.0001, RCVD_IN_MSPIKE_H3=-0.01, RCVD_IN_MSPIKE_WL=-0.01, SPF_HELO_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (1024-bit key) header.d=rhul.onmicrosoft.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id N1iR4iXlA6jo for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 13:56:57 -0700 (PDT)
Received: from EUR02-HE1-obe.outbound.protection.outlook.com (mail-eopbgr10078.outbound.protection.outlook.com [40.107.1.78]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-SHA384 (256/256 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 88521129A9F for <cfrg@ietf.org>; Wed, 26 Jul 2017 13:56:56 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=rhul.onmicrosoft.com;  s=selector1-rhul-ac-uk; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version; bh=hd/iMxrQRUEhkcAW+2MvR2ph9uL7lBVnI3wksr5Jg8U=; b=0mwSdmYdpdG1C3JCWPzKmtDiVEFqg2uKPA1HYKdDST9pWAUanNUXLXvKRIwG12VJFGiz1bkK24/dm1UK2s/LAsn/AoGpCv9W8Im6ZDpW1Li4UXAn7HdRbhrbP9EER/2Kad+B7i5uIzpr1G6NpbwOIITK/taRO7DKFJzKJ3MBn/0=
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com (10.168.2.156) by AM4PR0301MB1907.eurprd03.prod.outlook.com (10.168.3.7) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256) id 15.1.1282.10; Wed, 26 Jul 2017 20:56:53 +0000
Received: from AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::e475:7abc:5c25:5e28]) by AM4PR0301MB1906.eurprd03.prod.outlook.com ([fe80::e475:7abc:5c25:5e28%14]) with mapi id 15.01.1282.021; Wed, 26 Jul 2017 20:56:52 +0000
From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: Yannick Seurin <yannick.seurin@gmail.com>, Tetsu Iwata <iwata@cse.nagoya-u.ac.jp>
CC: "cfrg@ietf.org" <cfrg@ietf.org>, Adam Langley <agl@imperialviolet.org>, Yehuda Lindell <Yehuda.Lindell@biu.ac.il>, Shay Gueron <shay.gueron@gmail.com>, Alexey Melnikov <alexey.melnikov@isode.com>
Thread-Topic: [Cfrg] Updated bounds in AES-GCM-SIV paper
Thread-Index: AQHS/qHBtQ7+7q8LEkGkBdeni4MsaKJmEV+AgAClr4A=
Date: Wed, 26 Jul 2017 20:56:52 +0000
Message-ID: <D59EBEFD.99A8F%kenny.paterson@rhul.ac.uk>
References: <CAMfhd9UOFNfqoEp31r2moVaEfQZoeppP7h2Anrz0BBP518SeYA@mail.gmail.com> <CAOOV4XvpdCuEc8s5iXr3mzxuCTXj63AP6wATriu=D3Dxs3zz4Q@mail.gmail.com>
In-Reply-To: <CAOOV4XvpdCuEc8s5iXr3mzxuCTXj63AP6wATriu=D3Dxs3zz4Q@mail.gmail.com>
Accept-Language: en-GB, en-US
Content-Language: en-US
X-MS-Has-Attach: 
X-MS-TNEF-Correlator: 
user-agent: Microsoft-MacOutlook/14.7.1.161129
authentication-results: spf=none (sender IP is ) smtp.mailfrom=Kenny.Paterson@rhul.ac.uk; 
x-originating-ip: [78.25.226.140]
x-ms-publictraffictype: Email
x-microsoft-exchange-diagnostics: 1; AM4PR0301MB1907; 7: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
x-forefront-antispam-report: SFV:SKI; SCL:-1; SFV:NSPM; SFS:(10009020)(6009001)(39400400002)(39410400002)(39840400002)(39450400003)(39850400002)(189002)(377424004)(66654002)(199003)(24454002)(2950100002)(106356001)(36756003)(39060400002)(42882006)(54906002)(6512007)(6306002)(966005)(4001350100001)(72206003)(97736004)(2906002)(74482002)(38730400002)(68736007)(53936002)(99286003)(4326008)(105586002)(66066001)(6246003)(25786009)(83506001)(2900100001)(101416001)(3280700002)(7736002)(14454004)(189998001)(15650500001)(102836003)(6116002)(305945005)(3660700001)(5660300001)(561944003)(3846002)(50986999)(6436002)(8676002)(81166006)(81156014)(8936002)(230783001)(478600001)(5250100002)(6506006)(6486002)(76176999)(53546010)(54356999)(229853002)(86362001)(21314002); DIR:OUT; SFP:1101; SCL:1; SRVR:AM4PR0301MB1907; H:AM4PR0301MB1906.eurprd03.prod.outlook.com; FPR:; SPF:None; PTR:InfoNoRecords; MX:1; A:1; LANG:en; 
x-ms-office365-filtering-correlation-id: 4bc9ed72-c2db-4a68-1126-08d4d468d7de
x-microsoft-antispam: UriScan:; BCL:0; PCL:0; RULEID:(300000500095)(300135000095)(300000501095)(300135300095)(22001)(300000502095)(300135100095)(2017030254075)(300000503095)(300135400095)(2017052603031)(201703131423075)(201703031133081)(300000504095)(300135200095)(300000505095)(300135600095)(300000506095)(300135500095); SRVR:AM4PR0301MB1907; 
x-ms-traffictypediagnostic: AM4PR0301MB1907:
x-exchange-antispam-report-test: UriScan:(192374486261705);
x-microsoft-antispam-prvs: <AM4PR0301MB1907A09C3415390F852B0579BCB90@AM4PR0301MB1907.eurprd03.prod.outlook.com>
x-exchange-antispam-report-cfa-test: BCL:0; PCL:0; RULEID:(100000700101)(100105000095)(100000701101)(100105300095)(100000702101)(100105100095)(6040450)(601004)(2401047)(8121501046)(5005006)(100000703101)(100105400095)(93006095)(93001095)(10201501046)(3002001)(6041248)(201703131423075)(201702281529075)(201702281528075)(201703061421075)(201703061406153)(20161123564025)(20161123555025)(20161123562025)(20161123560025)(20161123558100)(6072148)(100000704101)(100105200095)(100000705101)(100105500095); SRVR:AM4PR0301MB1907; BCL:0; PCL:0; RULEID:(100000800101)(100110000095)(100000801101)(100110300095)(100000802101)(100110100095)(100000803101)(100110400095)(100000804101)(100110200095)(100000805101)(100110500095); SRVR:AM4PR0301MB1907; 
x-forefront-prvs: 038002787A
received-spf: None (protection.outlook.com: rhul.ac.uk does not designate permitted sender hosts)
spamdiagnosticoutput: 1:99
spamdiagnosticmetadata: NSPM
Content-Type: text/plain; charset="utf-8"
Content-ID: <6178C87165B28043A59220DE50B1DED3@eurprd03.prod.outlook.com>
Content-Transfer-Encoding: base64
MIME-Version: 1.0
X-OriginatorOrg: rhul.ac.uk
X-MS-Exchange-CrossTenant-originalarrivaltime: 26 Jul 2017 20:56:52.8113 (UTC)
X-MS-Exchange-CrossTenant-fromentityheader: Hosted
X-MS-Exchange-CrossTenant-id: 2efd699a-1922-4e69-b601-108008d28a2e
X-MS-Exchange-Transport-CrossTenantHeadersStamped: AM4PR0301MB1907
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/7UmXqC2y9x4iTkb-0Ggd0SJ2FJk>
Subject: Re: [Cfrg] Updated bounds in AES-GCM-SIV paper
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 26 Jul 2017 20:57:00 -0000
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From nobody Wed Jul 26 15:21:10 2017
Return-Path: <internet-drafts@ietf.org>
X-Original-To: cfrg@ietf.org
Delivered-To: cfrg@ietfa.amsl.com
Received: from ietfa.amsl.com (localhost [IPv6:::1]) by ietfa.amsl.com (Postfix) with ESMTP id F1E9212EC05; Wed, 26 Jul 2017 15:21:08 -0700 (PDT)
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: 7bit
From: internet-drafts@ietf.org
To: <i-d-announce@ietf.org>
Cc: cfrg@ietf.org
X-Test-IDTracker: no
X-IETF-IDTracker: 6.57.0
Auto-Submitted: auto-generated
Precedence: bulk
Message-ID: <150110766894.11509.12368469438683367329@ietfa.amsl.com>
Date: Wed, 26 Jul 2017 15:21:08 -0700
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/culQiRayohbwueIE7JKQGy7w7Ik>
Subject: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-06.txt
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 26 Jul 2017 22:21:09 -0000

A New Internet-Draft is available from the on-line Internet-Drafts directories.
This draft is a work item of the Crypto Forum RG of the IRTF.

        Title           : AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption
        Authors         : Shay Gueron
                          Adam Langley
                          Yehuda Lindell
	Filename        : draft-irtf-cfrg-gcmsiv-06.txt
	Pages           : 38
	Date            : 2017-07-26

Abstract:
   This memo specifies two authenticated encryption algorithms that are
   nonce misuse-resistant - that is that they do not fail
   catastrophically if a nonce is repeated.


The IETF datatracker status page for this draft is:
https://datatracker.ietf.org/doc/draft-irtf-cfrg-gcmsiv/

There are also htmlized versions available at:
https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-06
https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-gcmsiv-06

A diff from the previous version is available at:
https://www.ietf.org/rfcdiff?url2=draft-irtf-cfrg-gcmsiv-06


Please note that it may take a couple of minutes from the time of submission
until the htmlized version and diff are available at tools.ietf.org.

Internet-Drafts are also available by anonymous FTP at:
ftp://ftp.ietf.org/internet-drafts/


From nobody Wed Jul 26 15:22:12 2017
Return-Path: <alangley@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 02057131E82 for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 15:22:11 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.4
X-Spam-Level: 
X-Spam-Status: No, score=-2.4 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, FREEMAIL_FORGED_FROMDOMAIN=0.199, FREEMAIL_FROM=0.001, HEADER_FROM_DIFFERENT_DOMAINS=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id W7CGHOfMGb4g for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 15:22:08 -0700 (PDT)
Received: from mail-io0-x22f.google.com (mail-io0-x22f.google.com [IPv6:2607:f8b0:4001:c06::22f]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id A7EB712EC05 for <cfrg@irtf.org>; Wed, 26 Jul 2017 15:22:08 -0700 (PDT)
Received: by mail-io0-x22f.google.com with SMTP id g35so40424900ioi.3 for <cfrg@irtf.org>; Wed, 26 Jul 2017 15:22:08 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:sender:in-reply-to:references:from:date:message-id :subject:to:cc:content-transfer-encoding; bh=4BfszeuYLcJl1hco6lUcftjec0LsDK2yykXR8t3AbVU=; b=Zgg+aQyss0jHA7ZIuTQXGFUAUe3uaCGNpn0Ov0m01s0HlPqN7AyZBlKtTYbqIjJHOY nwv8TDhONekif7R0qd15uyC1pv3yiiDqKYfSC+/SSSXFhdq0rekdICJX7QWOdl3fKfMc BxsXpWUi/jWZ+tonDvJR5EFVbkDBtN8lmN+5C2TaKT4Jp3a/2WLIgzpyyIR+7f1ddQSi UbIs2JrARfmhLzwdMbTDosM/FFucxULKULSscNn8qrUoxm8tMbmp0BKk9WxRd3bMO/bE s168aH/kXPb87TD9s7E0ogIRw/5GPsT+HFUSfAmSFLUQnpmpGb4QXtHstTw7VyPzmFlQ ZQJw==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:sender:in-reply-to:references:from :date:message-id:subject:to:cc:content-transfer-encoding; bh=4BfszeuYLcJl1hco6lUcftjec0LsDK2yykXR8t3AbVU=; b=Ki6JkHE2LaMC85SMUP/Nag9dFBAk9jiI67F/FQHVRWKTZf0zdaxvoRbNQUKChdN8TG cP8F0hjF9ZlEW5UALs1M9ZlxIjq8HuLo/TE8ecl6iUoNb6LB+JiyJ7JEb8SWqOmEqrOY Zwx+jfi6znmVuCMl/cBu9ytg6FfFdHGy3ia3/RYeVU5FUSWUJl45CB8oyp1S8KTQ3F1A iHgHqoCA5DbvCvaAuqIuKsTezDBqfUu4asiyf6YXcAbbX1kywYyTf3WeE36/74Cndc+b +juVEh5ANGCFPr5gCEidDwkYjPBQkyPTIt3vtNRdlQX7YDExtImUohri6gYizdIoJvWm BBjg==
X-Gm-Message-State: AIVw111rugeDKSzvN4qoueCdHqcBAca6Jy2eLjT6eWjcZcrD8Cuh2Nem yBCqXuLZg3IXdK9DI8zT1wy+kgR7Jw==
X-Received: by 10.107.182.132 with SMTP id g126mr2728642iof.216.1501107727824;  Wed, 26 Jul 2017 15:22:07 -0700 (PDT)
MIME-Version: 1.0
Sender: alangley@gmail.com
Received: by 10.79.38.216 with HTTP; Wed, 26 Jul 2017 15:22:07 -0700 (PDT)
In-Reply-To: <D5825737.9801A%kenny.paterson@rhul.ac.uk>
References: <D5825737.9801A%kenny.paterson@rhul.ac.uk>
From: Adam Langley <agl@imperialviolet.org>
Date: Wed, 26 Jul 2017 15:22:07 -0700
X-Google-Sender-Auth: gNPVqrNj0iTxQwxv_u0eREQlv5Q
Message-ID: <CAMfhd9WgRC8YWWZCgHopH9piX6s6yaUPKBgMOH-8Frw0POCD_Q@mail.gmail.com>
To: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
Cc: Shay Gueron <shay.gueron@gmail.com>, Yehuda Lindell <Yehuda.Lindell@biu.ac.il>, "cfrg@irtf.org" <cfrg@irtf.org>
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/iSi3hljAviSb6wdGrgDozZYjbTc>
Subject: Re: [Cfrg] Reviews of AES-GCM-SIV (draft-irtf-cfrg-gcmsiv-04.txt)
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 26 Jul 2017 22:22:11 -0000

On Wed, Jul 5, 2017 at 12:43 AM, Paterson, Kenny
<Kenny.Paterson@rhul.ac.uk> wrote:
> Please read these reviews carefully and take them into account in the nex=
t
> version of your draft. It would be helpful if you could respond on list a=
s
> to how you have handled the various comments.

Now that the IETF meeting is complete and the submission window has
reopened, we've just published -06. Please see below for details on
the changes. We would like to thank the reviewers for their time and
attention.


All three reviewers requested that pseudo-code be included in addition
to the English descriptions. This has been done.

Several requested clarity about whether inputs that are not a whole
number of bytes are valid. We have clarified that they are not.
However, the lengths in the length block are still multiplied by eight
in keeping with AES-GCM. As noted in the appendix, POLYVAL and GHASH
have a simple relationship and it may be useful for implementations
that which to support both in minimal space to be able to exploit
this.

> One thing that may be problematic to an implementor was the nonces listed
> in the test vectors.  AES-GCM-SIV takes 12 byte nonces, the nonces listed
> are 16 bytes long.  While this is unlikely to be a major source of
> confusion for an implementator, I suggest that the nonces be trimmed down
> before publishing.

This was a mistake on our part and has been corrected.

> While the test vectors are quite good in general, they use only one nonce=
,
> and two keys (one for each key length).

Eight additional test vectors have been added (for each of the 128-
and 256-bit versions) that have random keys, nonces and inputs.

> The bytes in the test vector are listed LSB to MSB.  This rather assumes
> that the implementor is using little-endian byte ordering; I would sugges=
t
> that this be changed to a more endian-neutral notation (possibly by just
> omitted the LSB and MSB labels).

The labels have been removed.

> Reviewer: Tibor Jager

> Section 1 "Introduction", 1st paragraph: I suggest to replace
>   "...that is easier for practitioners to use correctly."
> with
>   "that is easier to use correctly."

Agreed. Done.

> In Section 4, first paragraph, the text suggests that plaintexts and
> additional data of arbitrary length can be encrypted. However, the
> description of the decryption procedure in Section 5 rejects ciphertexts
> of size larger than 2^36+16 bytes, and Section 6 gives upper bounds on
> the plaintext and AD sizes P_MAX and A_MAX.

"arbitrary" has been replaced with "variable".

> In Section 4, last paragraph, the result of encryption is the "resulting
> ciphertext ... followed by the tag". Thus, in this notation, the tag is
> not part of the "ciphertext", but it is separate and sent along with the
> ciphertext.
> However, at the beginning of Section 5, decryption algorithm receives as
> input key, nonce, AD, and a ciphertext, and the ciphertext is split into
> the encrypted plaintext and the tag, thus the "ciphertext" contains the
> tag here. One could unify this, by always considering the tag as part of
> the ciphertext.

We agree that this is confusing and have changed the wording so that
the "ciphertext" that results from AES-GCM-SIV always refers to the
final result.

> Section 8, very very nitpicking: One could mention here that the
> plaintext are the bit strings corresponding to the *ASCII encoding* of
> "Hello world" and "example".

Done.

> Section 8, 5th paragraph, again very nitpicking: Some developers may
> have difficulties in understanding immediately which numbers are given
> in hexadecimal notation, and which in decimal notation. For clarity, one
> could write here something like:
> "example": 7 characters =3D 56 bits =3D 0x38 bits
> "Hello world": 11 characters =3D 88 bits =3D 0x58 bits

Done.

> Section 9, 7th paragraph: "Suzuki et al. [multibirthday]", the reference
> lists Kazuhiro as first author, so it seems this should be Kazuhiro et al=
.

The authors are likely Japanese and thus typically would put their
family name first. However, as best we can tell, the family name is
"Suzuki" and thus it seems that the authors may have written their
names in the western style for this paper. The BibTeX citation
provided by Springer supports this. So we /think/ that "Suzuki et al"
is correct here.

> Reviewer: Bjoern Tackmann

> In that description, I stumbled particularly over the =E2=80=9C_length bl=
ock_=E2=80=9D -
> why the underscores?

The underscores are how xml2rfc was interpreting <spanx> in plain text
format. We agree that that's not the correct notation in that case and
have changed to quotation marks.

> Also, I think it would make sense to explicitly
> clarify that the 32-bit counter value for the CTR part is explicitly
> allowed to overflow.

Done. There are also now test vectors that depend on the overflow behaviour=
.

> One aspect that read a bit arbitrary to me was the domain separation for
> AES by setting the first bit of the last byte to 1/0, and in particular
> that seemed a bit wasteful since it is evaluated only once with the bit
> set to 0. Wouldn't it be simpler (and possibly even with better security,
> but at the cost of limiting the length to 2^32 - 1 blocks) to not fiddle
> with the bits but just use the first counter-block to compute the tag?
> Note that this would certainly require re-doing some part of the security
> analysis, and the gains seem moderate, so I=E2=80=99m fine with this comm=
ent being
> discarded. (Just wanted to make sure it is discarded consciously.)

There may be a small security gain to be had by using a more subtle
method for domain separation. But we believe that the benefit would be
minor and the current design has the advantage the the separation is
completely unambiguous. Our feeling is that the clarity here is
useful, so the gain from changing is unclear and not worth redoing the
proofs for.


Cheers

AGL


From nobody Wed Jul 26 15:26:13 2017
Return-Path: <alangley@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 4DE81131E92 for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 15:26:11 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.7
X-Spam-Level: 
X-Spam-Status: No, score=-1.7 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, FREEMAIL_FORGED_FROMDOMAIN=0.199, FREEMAIL_FROM=0.001, HEADER_FROM_DIFFERENT_DOMAINS=0.001, SPF_PASS=-0.001] autolearn=no autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id ZAjUwUILCbJy for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 15:26:09 -0700 (PDT)
Received: from mail-io0-x231.google.com (mail-io0-x231.google.com [IPv6:2607:f8b0:4001:c06::231]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id AE319131E8F for <cfrg@ietf.org>; Wed, 26 Jul 2017 15:26:09 -0700 (PDT)
Received: by mail-io0-x231.google.com with SMTP id g13so72907292ioj.5 for <cfrg@ietf.org>; Wed, 26 Jul 2017 15:26:09 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:sender:in-reply-to:references:from:date:message-id :subject:to:cc; bh=kLcoOjvEzo7C4Lt5TcaB65/AVcWwIHj7R4wrQOlFxds=; b=lNBy5ASetdQgACJwfS6HB//2is0HkFqiscECcaFEKkjOoWDKPS9GAu7sgfcU4aPG7n XIhBVVODpdUVihEBXm0/hPLqpm0Snd4mgUoR0pVYGRLpelxIcCsjVJQFtpENgRLbwCnY YqqEMHUwdZ6JNIuqtOwdsQGOe+CoyfYYDjGM1OhM6ec2xvvIdJyiqmVFdMuhznGPXL9o 9WKWvuYo/XyEa9xSVDIJNoGMxwhk8ufw0kWace/ieG7/+araGfbACtTxPMQ0dbWVjtKl WyvZW/ruzH9UEwlh+ORMndM/evFdFqNh5SlrMSC70HFykKIICMqixvgbaL5tA2m0KtBf ngVw==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:sender:in-reply-to:references:from :date:message-id:subject:to:cc; bh=kLcoOjvEzo7C4Lt5TcaB65/AVcWwIHj7R4wrQOlFxds=; b=d2SHvUzPYNF6pT5DnDRtqjc9Cmx63JGTTObYZAiwsaAMPApPECUgsTm+2q49CgqqP1 ufcvngiCGaD//eJsJo/0L94N9Mq4sJSmq69PCxy0y2sJMjSUv37OcfcYMW9yLm8DJzvo mt7WkYmulxWzkA70EjgRbvRQOot1qFPI82ES5pKsSi1L8jSW3wcUXK7Zl+hPDGZtLn/x AD/tGENd1wgoYSok83zDqJUGB+z9a0/fj88caLon/28+Zsg5me/ZCoLoliCtIr1opATc mkD+zIGxAglPWp0US0Mf8vMK5ejxu54oBT2weGzqAUlgIJXoqkIh0VVV6zyxyGDhR3oV KQsg==
X-Gm-Message-State: AIVw110zpg+0ltzvZJQZF6Hdwvh5hG0nfnggPGuBEMb7qGZjNJ29FTLB LpCTJUeAYggIe1nVCvCJwYOfDNagsg==
X-Received: by 10.107.157.8 with SMTP id g8mr2999688ioe.200.1501107968919; Wed, 26 Jul 2017 15:26:08 -0700 (PDT)
MIME-Version: 1.0
Sender: alangley@gmail.com
Received: by 10.79.38.216 with HTTP; Wed, 26 Jul 2017 15:26:08 -0700 (PDT)
In-Reply-To: <CAOOV4XvpdCuEc8s5iXr3mzxuCTXj63AP6wATriu=D3Dxs3zz4Q@mail.gmail.com>
References: <CAMfhd9UOFNfqoEp31r2moVaEfQZoeppP7h2Anrz0BBP518SeYA@mail.gmail.com> <CAOOV4XvpdCuEc8s5iXr3mzxuCTXj63AP6wATriu=D3Dxs3zz4Q@mail.gmail.com>
From: Adam Langley <agl@imperialviolet.org>
Date: Wed, 26 Jul 2017 15:26:08 -0700
X-Google-Sender-Auth: j0xIBh_SpRK6xLdTSV6THJzBJBI
Message-ID: <CAMfhd9UuZAfUFQpv0L_WZnhSUrpYdEMFzyZARO-12pchBc0AGA@mail.gmail.com>
To: Yannick Seurin <yannick.seurin@gmail.com>
Cc: cfrg@ietf.org, Tetsu Iwata <iwata@cse.nagoya-u.ac.jp>
Content-Type: text/plain; charset="UTF-8"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/jaC1Y0TIl9pefzTJ8Mf4lNGJ2mU>
Subject: Re: [Cfrg] Updated bounds in AES-GCM-SIV paper
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 26 Jul 2017 22:26:11 -0000

On Wed, Jul 26, 2017 at 5:04 AM, Yannick Seurin
<yannick.seurin@gmail.com> wrote:
> We believe that the CFRG specification (especially Section 9) should be
> updated as well to reflect the new security analysis. Recommended usage
> limitations for an AEAD scheme (such as the maximal number of messages that
> can be encrypted with the same key) should be based on the maximal message
> length allowed by its specification (currently, 2^{32} 128-bit blocks). More
> fine-grained recommendations (such as "if the maximal message length in an
> application is 2^m and the maximal number of nonce repetitions is R, then
> the maximal number of messages that can be encrypted with the same key can
> be pushed to XXX") are likely to create confusion and incur implementations
> errors. For AES-GCM-SIV with randomly generated nonces (which has been put
> forward by the designers as the preferred way of generating nonces when no
> state can be saved by encrypting devices), this means that no more than
> 2^{30} messages should be encrypted with the same key, which contrasts with
> the recommended limit of 2^{50} given (without context) in Section 9 of the
> CFRG specification and in the abstract of [2].

While the maximal message length of AES-GCM-SIV is very large, we do
not think it useful to limit the total number of messages based on
it. Using such large messages is very rare (at best) and unwise with
any AEAD: large messages pressure consumers to process plaintext
before the whole message has been received and authenticated, because
buffering would be so costly.

We have just published -06, which contains updates in response to
several reviewer's feedback and also contains updated guidance
on the maximum number of messages for the case where the
maximum number of nonce repeats is 256 (which covers choosing nonces
randomly):

2^29 messages, where each plaintext is at most 1GiB
2^35 messages, where each plaintext is at most 128MiB
2^49 messages, where each plaintext is at most 1MiB
2^61 messages, where each plaintext is at most 16KiB


Cheers

AGL


From nobody Wed Jul 26 15:28:42 2017
Return-Path: <alangley@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id A0D5C12EC14 for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 15:28:40 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.4
X-Spam-Level: 
X-Spam-Status: No, score=-2.4 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, FREEMAIL_FORGED_FROMDOMAIN=0.199, FREEMAIL_FROM=0.001, HEADER_FROM_DIFFERENT_DOMAINS=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id QrlzOkD9zJ2f for <cfrg@ietfa.amsl.com>; Wed, 26 Jul 2017 15:28:39 -0700 (PDT)
Received: from mail-it0-x22c.google.com (mail-it0-x22c.google.com [IPv6:2607:f8b0:4001:c0b::22c]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id D69A51252BA for <cfrg@ietf.org>; Wed, 26 Jul 2017 15:28:38 -0700 (PDT)
Received: by mail-it0-x22c.google.com with SMTP id v127so74991335itd.0 for <cfrg@ietf.org>; Wed, 26 Jul 2017 15:28:38 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:sender:in-reply-to:references:from:date:message-id :subject:to; bh=GC/SCW8taJ7dnrLUW1b1XGERIjvOf5yUvlaIqzkIaac=; b=shw3io2JaLQlY42MhwlCWESfHJ4BnPfOjRv65+g573XefPV5oqtUE+hC0B2JbnFWWj LUAoxGa5Ba+df3JnoYy7QtD8P44jeQW6AWHY7pPJaG8EQoThZQjliP1c1aPEyczvzY/m nONVwRyxjq7ifcE1SfhIB3oQL4IQZG/T9xSQf6n79moCf036Cb+KHxkZRDk+xMFdOQLn xG4FwE48UHh//Kab1F23XJdORJBfatq/lyQZ+LsfPt1Q+4gK++tf8Nob9LbSU8Npc4gV DDm9aESX5rSdv6wJlo9ckIpn7hmBxNOfBlFXr8gnC01LMk/oHomJXbAVkZIYioOMUs8+ Xh1Q==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:sender:in-reply-to:references:from :date:message-id:subject:to; bh=GC/SCW8taJ7dnrLUW1b1XGERIjvOf5yUvlaIqzkIaac=; b=cRWkAljImtLzf76CIGNyHN28+XaWD/8PKvM7QLiwlY5SngjGNXBWokgHk2kVdZ8u1m uwXeJvflP1zfSOrBHdb7jL7eqLoblxhh6X6XelNMPuDHb2BfNop9l2j9rsaF1WlNSYxh qKB28fqHF13XKMmmfs0Lat3JWkpZf/o24hlM30b8lGQm0KGuefjjHl+8YtTNia37a1L7 d6bCPPg9Y/Gf2d2kGYG/EReEhDUoPy0vQJnC1mktDY5xKxqVximbvci4YHjAvmEwJgxo V9bKOSjNwzLb8mpWoUBAowq7eWpB47MjY2Yqm9puaAiRrbQbVUMUIXudx5uFfJJi2jhm DEBA==
X-Gm-Message-State: AIVw110Nnpd/eEgv2xxbEhO0bMRCx3Un4PZKb0uDe8ZXnklMbe+fYDD4 HPph+zcDmHOkQa+UN3+aROd1Sz0neyoIdpQ=
X-Received: by 10.36.227.130 with SMTP id d124mr2704607ith.173.1501108118068;  Wed, 26 Jul 2017 15:28:38 -0700 (PDT)
MIME-Version: 1.0
Sender: alangley@gmail.com
Received: by 10.79.38.216 with HTTP; Wed, 26 Jul 2017 15:28:37 -0700 (PDT)
In-Reply-To: <150110766894.11509.12368469438683367329@ietfa.amsl.com>
References: <150110766894.11509.12368469438683367329@ietfa.amsl.com>
From: Adam Langley <agl@imperialviolet.org>
Date: Wed, 26 Jul 2017 15:28:37 -0700
X-Google-Sender-Auth: K7F9lsmaSuf-LEJX6QeGJPiiP3Y
Message-ID: <CAMfhd9UDLqgtwdFONDtqPbz2KQeT453atEs_p03YEXkoEFO8DQ@mail.gmail.com>
To: cfrg@ietf.org
Content-Type: text/plain; charset="UTF-8"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/m6ffFmhquVhgQD3QTlBWSNraqUk>
Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-06.txt
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Wed, 26 Jul 2017 22:28:40 -0000

On Wed, Jul 26, 2017 at 3:21 PM,  <internet-drafts@ietf.org> wrote:
> A New Internet-Draft is available from the on-line Internet-Drafts directories.
> This draft is a work item of the Crypto Forum RG of the IRTF.
>
>         Title           : AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption
>         Authors         : Shay Gueron
>                           Adam Langley
>                           Yehuda Lindell
>         Filename        : draft-irtf-cfrg-gcmsiv-06.txt
>         Pages           : 38
>         Date            : 2017-07-26

This version contains updates in response to the CFRG reviewers'
feedback, as detailed in the thread "Reviews of AES-GCM-SIV
(draft-irtf-cfrg-gcmsiv-04.txt)", and also in response to the bounds
issue noted in the thread "Updated bounds in AES-GCM-SIV paper".


Cheers

AGL


From nobody Thu Jul 27 01:51:56 2017
Return-Path: <tgarcia.3141@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id BF2E0131FBF for <cfrg@ietfa.amsl.com>; Thu, 27 Jul 2017 01:51:54 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.448
X-Spam-Level: 
X-Spam-Status: No, score=-2.448 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_ENVFROM_END_DIGIT=0.25, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id pEC9TJPQ4orx for <cfrg@ietfa.amsl.com>; Thu, 27 Jul 2017 01:51:51 -0700 (PDT)
Received: from mail-lf0-x22e.google.com (mail-lf0-x22e.google.com [IPv6:2a00:1450:4010:c07::22e]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id 09A03127136 for <cfrg@irtf.org>; Thu, 27 Jul 2017 01:51:51 -0700 (PDT)
Received: by mail-lf0-x22e.google.com with SMTP id g25so73737045lfh.1 for <cfrg@irtf.org>; Thu, 27 Jul 2017 01:51:50 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=qwOrxtq/CICr1raa85Ces1FmQWjyllGldEGZGtHNTCw=; b=Yd9v6Xv7BFzBSyxUJ48uDBVA/GkK+UA4HeAdoUFY5Hb6mPUtwN7jHQJz3aZ7Pm+0WO j9+3FZKQMmosh+b3xplG5YtPmUWo7IKOzosBq4GwPn/9UAdICe9cVRQ4tY0Y7RqwBiB3 4BhXJCQuLzQK1kEgXCevI8X6Dxa4FiOqRTvCE1x8HFe+F+lneIH8It+Lt/tJA5H4Fq2P tGzvLw7rAsgnX08kbUAVdceSu1Z2VOAvyzUgjbKf2pO8BMiNqGmS9Ebdd3Yu7d1TDzYF k7y0aH9PO8oyFqT+JILqpMWhymPYtBVLiiVVU9QbltnmUd5jwIdc4xngWIOc0Bn6DC0u WcLQ==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=qwOrxtq/CICr1raa85Ces1FmQWjyllGldEGZGtHNTCw=; b=Xu+uYCzwbjEuCnqAUWdCChx2BPfL8W9OxdeVpDk6mafyBB84prX/r/AVoKNr7LJJPI j0uSUbn/mYx00pZd6XnZOFU+Gyg0FoIxLdd+fXb/UYTRFi5MRMT1+JzhD25byT36Hyn9 pmoYx03VXN8U3VUVE9jEP14MNE+hQaGPQqekgKXS51Wf4uMepdu0uw92pmnwb6BTRqyA Hq/pOpOZnDkBv5SX/oeUqfte8SA3+1f0OR1X2lGkbyfQinwsfDtKfqBZpeaVxTUyfo/Z AQtdHEizCEaBceTc6i5XKFz7w5GKt9bW4+PqNcqdOSp74L/a/SbUck7lvzUPn9it+pFJ WqAw==
X-Gm-Message-State: AIVw113MeSkHzRKdrI0OEhsWzHBM2C2yGvJqItiGB9XwiZVI0PqZLwVv rSieLtna1JEcH8QqnY6tHkqKXydhLg==
X-Received: by 10.46.84.83 with SMTP id y19mr1588622ljd.186.1501145509149; Thu, 27 Jul 2017 01:51:49 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.25.22.40 with HTTP; Thu, 27 Jul 2017 01:51:48 -0700 (PDT)
In-Reply-To: <CAJHGrrSh27DFzuGDmTD_GuBF7tCtNQsCJ42XTjZWO1LqqAm3wQ@mail.gmail.com>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com> <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net> <20170721163204.8573013.1016.15939@blackberry.com> <CAJHGrrTbjL3rd_XU9tx28g3QcBe9tJBOxs2t1OebfvZR_c7epA@mail.gmail.com> <CAFTSWvfwf34uH1AjzQq7zCMEARGH8rH310pSRe7kkYCZ3TMNeQ@mail.gmail.com> <CAJHGrrSh27DFzuGDmTD_GuBF7tCtNQsCJ42XTjZWO1LqqAm3wQ@mail.gmail.com>
From: Thomas Garcia <tgarcia.3141@gmail.com>
Date: Thu, 27 Jul 2017 09:51:48 +0100
Message-ID: <CAFTSWvd5GR_WsesCrfs3QNR1hPNtN-GW7-yn9PwC4GUiq0AxKw@mail.gmail.com>
To: Sharon Goldberg <sharon.goldbe@gmail.com>
Cc: Dan Brown <danibrown@blackberry.com>, "jan@ns1.com" <jan@ns1.com>,  "cfrg@irtf.org" <cfrg@irtf.org>, Dimitrios Papadopoulos <dipapado@umd.edu>, Leonid Reyzin <reyzin@cs.bu.edu>
Content-Type: multipart/alternative; boundary="f403045fc2f2d43ee0055548acd5"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/7jNNr8G6S5TctogT4mXwRvWtDSM>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Thu, 27 Jul 2017 08:51:55 -0000

--f403045fc2f2d43ee0055548acd5
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Thanks for helping me clear those things up!

Thomas G.

On Wed, Jul 26, 2017 at 12:42 PM, Sharon Goldberg <sharon.goldbe@gmail.com>
wrote:

> Hi Thomas,
>
> 1. It seems that one of the properties that you are interested that the
>> VRF will have is determinism. On the other hand, the EC-VRF value is
>> dependent on the choice of some random number k. How are these two facts
>> compatible? Am I missing something?
>>
>
> We require determinism from the VRF hash output, which is obtained from
> the VRF proof via the "proof2hash" function.
>
> The EC-VRF proof has 3 values: gamma, c, s
> Values c and s depends on the choice of random number k
> But value gamma does not depend on k.
>
> We get determinism because the VRF hash output (derived using
> "proof2hash") depends only on gamma, but not on c and s.
>
> Slide 28 from my CFRG presentations gives a pictorial explanation of this=
:
> http://www.cs.bu.edu/~goldbe/papers/VRF_ietf99_print.pdf
>
> 2. The value c calculated in EC-VRF is only 128 bits long for Ed25519. In
>> normal usage of Ed25519 the signature uses the full length of the hash
>> output. Doesn't this expose the signature to collision attacks?
>>
>> No. We worked this out in our proofs of security.  Section B.2.1 of this
> paper explains why this works.
>
> https://eprint.iacr.org/2017/099.pdf
>
> Thanks,
> Sharon
>
>
>
>> Thank you for your comments. Indeed, VRFs have been around since 1999.
>>> They are really "verifiable PRFs" but the name is by now standard in th=
e
>>> crypto literature, and changing it will cause more confusion than keepi=
ng
>>> it.
>>>
>>> In terms of the VRF's security properties, there are three:  uniqueness=
,
>>> collision resistance, and pseudorandomness. These are defined in our dr=
aft (
>>> https://tools.ietf.org/html/draft-goldbe-vrf-01#section-3).
>>>
>>> How VRFs prevent dictionary attacks: a public hash is subject to a
>>> dictionary attack because, given the output, an adversary can evaluate =
the
>>> hash on different inputs and see what hits the outputs. In a VRF, the
>>> adversary can't evaluate the hash on different inputs.
>>>
>>> You say it's not surprising that "random oracle model proof can prove
>>> the output of a hash to be random". But actually, the output of a hash =
is
>>> NOT random if the input and the hash function are known. This is becaus=
e
>>> the output of a hash is deterministic (every input maps to a unique
>>> output). That's exactly what enables dictionary attacks. This is in
>>> contrast to a VRF, where the output is (pseudo)random even given knowle=
dge
>>> of the input. Only once the VRF proof is given, does the VRF output sto=
p
>>> looking random. Note that random oracles are not essential for VRFs, an=
d
>>> non-random-oracles constructions exist (but are less efficient than wha=
t we
>>> propose to standardize).
>>>
>>> As far as use cases, here are a few:
>>>
>>> In the NSEC5 use case for DNSSEC, you have sensitive data (domain names=
)
>>> and you sign consecutive pairs of hashes of domain names in order to be
>>> able to prove absence of a name. If you just use standard hashing, when=
ever
>>> signed hash values are disclosed, your sensitive data is subject to
>>> dictionary attacks. VRFs solve that problem, and sensitive names don't =
have
>>> to be disclosed at all. More details are in https://eprint.iacr.org/201
>>> 7/099.pdf
>>>
>>> In CONIKS (also Google Key Transparency, Signal secure messaging, Yahoo=
!
>>> Coname) you also have some sensitive data (user names) that are put int=
o a
>>> Merkle-like authenticated data structure. If you just use standard hash=
ing,
>>> whenever hash values are disclosed, sensitive data is subject to dictio=
nary
>>> attacks. If you use VRFs, sensitive data again can be disclosed only on=
 an
>>> as-needed basis. More details are in  https://eprint.iacr.org/2014/
>>> 1004.pdf.
>>>
>>> In a cryptocurrency use case, you wish perform a coin flip that is
>>> deterministic and provably correct, but cannot be done by just anyone.
>>> More details are in https://people.csail.mit.ed
>>> u/nickolai/papers/gilad-algorand-eprint.pdf and possibly other
>>> cryptocurrency papers.
>>>
>>> Bryan Ford mentioned an additional usecase at the mic on Tuesday:
>>> distributed password protection protocols
>>>
>>> Many of these use case are already putting VRFs into production use
>>> (esp. the CONIKS one).  You can see a list of the various implementatio=
ns
>>> we have found in the "implementation status" section of our draft.  One=
 of
>>> the reasons we think this spec is so important is that we found flaws i=
n
>>> several of the implementations that can be used to trivially break
>>> uniqueness.  (See eg: https://github.com/google/
>>> keytransparency/issues/567)
>>>
>>> Thanks,
>>> Sharon
>>>
>>> On Fri, Jul 21, 2017 at 7:32 PM, Dan Brown <danibrown@blackberry.com>
>>> wrote:
>>>
>>>> Answering myself below: VRFs have been around since 1999, so are not s=
o
>>>> new.  =E2=80=8EStill don't like the name, and still have trouble seein=
g the value.
>>>>
>>>> *From: *Dan Brown
>>>> *Sent: *Tuesday, July 18, 2017 2:29 PM
>>>> *To: *Sharon Goldberg; cfrg@irtf.org
>>>> *Cc: *jan@ns1.com; Leonid Reyzin; Dimitrios Papadopoulos
>>>> *Subject: *Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>>>
>>>> Hi Sharon and CFRG,
>>>>
>>>>
>>>>
>>>> On VRFs, my uncertain comments to consider at your leisure:
>>>>
>>>>
>>>>
>>>> Is it fair to say VRFs are relatively new?  If so, then maybe a little
>>>> more caution is needed about their use.  It seems a tad hasty that it =
is
>>>> being used already.
>>>>
>>>>
>>>>
>>>> To me, it seems that VRFs are basically signatures, with an extra
>>>> feature.  My concern is that this extra feature might get overused, be=
fore
>>>> it is thoroughly reviewed.
>>>>
>>>>
>>>>
>>>> It is unsurprising to me that random oracle model proof can prove the
>>>> output of a hash to be random.  My intuitive concern is that at least
>>>> informally, this is kind of circular.  Hashes often have some
>>>> non-random-ish properties that might affect the extra security (over
>>>> signatures) that VRFs are aiming for.  I guess I would much prefer a p=
roof
>>>> saying if the hash has (well-studied) properties XYZ, then your
>>>> construction are VRFs.  (Maybe you have this already?  If so, then tel=
l me
>>>> so.)
>>>>
>>>>
>>>>
>>>> Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the wire, =
I find it hard to
>>>> see how it could be used to prevent dictionary attacks.  I assume that=
 you
>>>> are saying the proofs must be encrypted when one needs to avoid dictio=
nary
>>>> models?  I suppose all the details are there in I-D and papers, but fo=
r
>>>> now, I am confused about the threat model (which parties have keys, et=
c.,
>>>> if they require a secure channel and mutual trust, why just use plain =
old
>>>> hash,=E2=80=A6). To resist dictionary attacks, were already have PAKEs=
 and
>>>> PBHashing.  Now this?
>>>>
>>>>
>>>>
>>>> Finally, on a bikeshed-coloring note, I object to the name =E2=80=9Cve=
rifiable
>>>> random function=E2=80=9D, on several grounds.
>>>>
>>>>
>>>>
>>>>    1. It is not a function.  It is at least four functions, keygen,
>>>>    sign, verify, and hashify.
>>>>    2. If you make it into a keyed function F_sk(m), as in
>>>>    prooftohash(sign_sk(m)), it is not verifiable.
>>>>    3. Verification requires the intermediate proof, which is certainly
>>>>    not even pseudorandom (it is easy to distinguish valid signatures f=
rom
>>>>    random).
>>>>    4. It is pseudorandom, not random.  (The keys are random, but many
>>>>    crypto has keys, without having =E2=80=9Crandom=E2=80=9D in its nam=
e: encryption, MAC,
>>>>    signatures, key exchange, =E2=80=A6, they also don=E2=80=99t verifi=
able or random in their
>>>>    names either.)
>>>>    5. The similar phrase =E2=80=9Cverifiably random=E2=80=9D, albeit a=
s a misnomer,
>>>>    has past precedents, see NIST P-256 and Brainpool, etc.  When I see=
 VRF, I
>>>>    think a function, that aims to VR in that sense, and great, now we =
can
>>>>    improve on Brainpool, etc.
>>>>    6. =E2=80=9CRandom function=E2=80=9D should be reserved for the ide=
al random
>>>>    mapping concept, for example, as studied by Flajolet-Odlyzko (ok th=
ey only
>>>>    studied the case of equal size domain and range).  The random oracl=
e model,
>>>>    is the idea of approximating this ideal, etc.  An actual approximat=
ion
>>>>    should not be name as the ideal (sorry, I=E2=80=99m kind of repeati=
ng my point 4).
>>>>
>>>>
>>>>
>>>> Please forgive the fact that my comments above are not very
>>>> constructive (or if the tone is wrong).  This is a new topic for me, s=
o I
>>>> am reluctant too many suggestions.  Nonetheless, I suggest (0) waiting=
 a
>>>> little, (1) a non-random-oracle security proof (if you don=E2=80=99t h=
ave it yet),
>>>> (2) re-naming the scheme to something like re-hashable (or digestible)
>>>> signatures (and re-name the various parts, i.e. proof -> signature, et=
c.).
>>>>
>>>>
>>>>
>>>> Best regards,
>>>>
>>>>
>>>>
>>>> Dan
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> *From:* Cfrg [mailto:cfrg-bounces@irtf.org] *On Behalf Of *Sharon
>>>> Goldberg
>>>> *Sent:* Wednesday, July 12, 2017 5:42 AM
>>>> *To:* cfrg@irtf.org
>>>> *Cc:* jan@ns1.com; Dimitrios Papadopoulos <dipapado@umd.edu>; Leonid
>>>> Reyzin <reyzin@cs.bu.edu>
>>>> *Subject:* [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>>>
>>>>
>>>>
>>>> Dear CFRG,
>>>>
>>>> I'm presenting at next week's meeting on Verifiable Random Functions. =
A
>>>> VRF is the public-key version of keyed cryptographic hash. Only the ho=
lder
>>>> of the VRF secret key can compute the hash, but anyone with the public=
 key
>>>> can verify it.  VRFs can be used to prevent dictionary attacks on
>>>> hash-based data structures, and have applications to key transparency
>>>> (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (Algorand).
>>>>
>>>> In advance of the meeting, please see:
>>>>
>>>> 1) Our substantially updated -01 draft:
>>>> https://datatracker.ietf.org/doc/draft-goldbe-vrf/
>>>>
>>>> 2) Our project page, with links to various VRF implementations:
>>>> https://www.cs.bu.edu/~goldbe/projects/vrf
>>>>
>>>> Comments welcome.  Thanks,
>>>>
>>>> Sharon
>>>>
>>>> --
>>>> Sharon Goldberg
>>>> Computer Science, Boston University
>>>> http://www.cs.bu.edu/~goldbe
>>>>
>>>
>>>
>>>
>>> --
>>> ---
>>> Sharon Goldberg
>>> Computer Science, Boston University
>>> http://www.cs.bu.edu/~goldbe
>>>
>>> _______________________________________________
>>> Cfrg mailing list
>>> Cfrg@irtf.org
>>> https://www.irtf.org/mailman/listinfo/cfrg
>>>
>>>
>>
>
>
> --
> ---
> Sharon Goldberg
> Computer Science, Boston University
> http://www.cs.bu.edu/~goldbe
>

--f403045fc2f2d43ee0055548acd5
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div><br></div><div>Thanks for helping me clear those thin=
gs up!</div><div><br></div><div>Thomas G.</div></div><div class=3D"gmail_ex=
tra"><br><div class=3D"gmail_quote">On Wed, Jul 26, 2017 at 12:42 PM, Sharo=
n Goldberg <span dir=3D"ltr">&lt;<a href=3D"mailto:sharon.goldbe@gmail.com"=
 target=3D"_blank">sharon.goldbe@gmail.com</a>&gt;</span> wrote:<br><blockq=
uote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc =
solid;padding-left:1ex"><div dir=3D"ltr">Hi Thomas,<div><br></div><div clas=
s=3D"gmail_extra"><div class=3D"gmail_quote"><span class=3D""><blockquote c=
lass=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px soli=
d rgb(204,204,204);padding-left:1ex"><div dir=3D"ltr"><div>1. It seems that=
 one of the properties that you are interested that the VRF will have is de=
terminism. On the other hand, the EC-VRF value is dependent on the choice o=
f some random number k. How are these two facts compatible? Am I missing so=
mething?</div></div></blockquote><div><br></div></span><div>We require dete=
rminism from the VRF hash output, which is obtained from the VRF proof via =
the &quot;proof2hash&quot; function.</div><div><br></div><div>The EC-VRF pr=
oof has 3 values: gamma, c, s</div><div>Values c and s depends on the choic=
e of random number k</div><div>But value gamma does not depend on k.</div><=
div><br></div><div>We get determinism because the VRF hash output (derived =
using &quot;proof2hash&quot;) depends only on gamma, but not on c and s.</d=
iv><div>=C2=A0</div><div>Slide 28 from my CFRG presentations gives a pictor=
ial explanation of this:</div><div><a href=3D"http://www.cs.bu.edu/~goldbe/=
papers/VRF_ietf99_print.pdf" target=3D"_blank">http://www.cs.bu.edu/~goldbe=
/<wbr>papers/VRF_ietf99_print.pdf</a><br></div><span class=3D""><div><br></=
div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;bor=
der-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir=3D"ltr"><div=
>2. The value c calculated in EC-VRF is only 128 bits long for Ed25519. In =
normal usage of Ed25519 the signature uses the full length of the hash outp=
ut. Doesn&#39;t this expose the signature to collision attacks?</div><div><=
br></div></div></blockquote></span><div>No. We worked this out in our proof=
s of security.=C2=A0 Section B.2.1 of this paper explains why this works.</=
div><div><br></div><div><a href=3D"https://eprint.iacr.org/2017/099.pdf" ta=
rget=3D"_blank">https://eprint.iacr.org/2017/<wbr>099.pdf</a><br></div><div=
><br></div><div>Thanks,</div><div>Sharon</div><div><div class=3D"h5"><div><=
br></div><div>=C2=A0</div><blockquote class=3D"gmail_quote" style=3D"margin=
:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"=
><div class=3D"gmail_extra"><div class=3D"gmail_quote"><blockquote class=3D=
"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(2=
04,204,204);padding-left:1ex"><div><div class=3D"m_2913212881139340244gmail=
-h5"><div dir=3D"ltr"><div style=3D"font-size:12.8px"></div><div style=3D"f=
ont-size:12.8px">Thank you for your comments. Indeed, VRFs have been around=
 since 1999. They are really &quot;verifiable PRFs&quot; but the name is by=
 now standard in the crypto literature, and changing it will cause more con=
fusion than keeping it.</div><div style=3D"font-size:12.8px"><br></div><div=
 style=3D"font-size:12.8px">In terms of the VRF&#39;s security properties, =
there are three: =C2=A0uniqueness, collision resistance, and pseudorandomne=
ss. These are defined in our draft (<span style=3D"font-size:12.8px"><a hre=
f=3D"https://tools.ietf.org/html/draft-goldbe-vrf-01#section-3" target=3D"_=
blank">https://tools.ietf.org/html/d<wbr>raft-goldbe-vrf-01#section-3</a></=
span><span style=3D"font-size:12.8px">).<wbr>=C2=A0</span></div><div style=
=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8px">How VRFs pr=
event dictionary attacks: a public hash is subject to a dictionary attack b=
ecause, given the output, an adversary can evaluate the hash on different i=
nputs and see what hits the outputs. In a VRF, the adversary can&#39;t eval=
uate the hash on different inputs.=C2=A0</div><div style=3D"font-size:12.8p=
x"><br></div><div style=3D"font-size:12.8px">You say it&#39;s not surprisin=
g that &quot;random oracle model proof can prove the output of a hash to be=
 random&quot;. But actually, the output of a hash is NOT random if the inpu=
t and the hash function are known. This is because the output of a hash is =
deterministic (every input maps to a unique output). That&#39;s exactly wha=
t enables dictionary attacks. This is in contrast to a VRF, where the outpu=
t is (pseudo)random even given knowledge of the input. Only once the VRF pr=
oof is given, does the VRF output stop looking random. Note that random ora=
cles are not essential for VRFs, and non-random-oracles constructions exist=
 (but are less efficient than what we propose to standardize).</div><div st=
yle=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8px">As far a=
s use cases, here are a few:=C2=A0</div><div style=3D"font-size:12.8px"><br=
></div><div style=3D"font-size:12.8px">In the NSEC5 use case for DNSSEC, yo=
u have sensitive data (domain names) and you sign consecutive pairs of hash=
es of domain names in order to be able to prove absence of a name. If you j=
ust use standard hashing, whenever signed hash values are disclosed, your s=
ensitive data is subject to dictionary attacks. VRFs solve that problem, an=
d sensitive names don&#39;t have to be disclosed at all. More details are i=
n=C2=A0<a href=3D"https://eprint.iacr.org/2017/099.pdf" target=3D"_blank">h=
ttps://eprint.iacr.org/201<wbr>7/099.pdf</a></div><div style=3D"font-size:1=
2.8px"><br></div><div style=3D"font-size:12.8px">In CONIKS (also Google Key=
 Transparency, Signal secure messaging, Yahoo! Coname) you also have some s=
ensitive data (user names) that are put into a Merkle-like authenticated da=
ta structure. If you just use standard hashing, whenever hash values are di=
sclosed, sensitive data is subject to dictionary attacks. If you use VRFs, =
sensitive data again can be disclosed only on an as-needed basis. More deta=
ils are in =C2=A0<a href=3D"https://eprint.iacr.org/2014/1004.pdf" target=
=3D"_blank">https://eprint.iacr.org/2014/<wbr>1004.pdf</a>.</div><div style=
=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8px">In a crypto=
currency use case, you wish perform a coin flip that is deterministic and p=
rovably correct, but cannot be done by just anyone.=C2=A0 More details are =
in=C2=A0<a href=3D"https://people.csail.mit.edu/nickolai/papers/gilad-algor=
and-eprint.pdf" target=3D"_blank">https://people.csail.mit.ed<wbr>u/nickola=
i/papers/gilad-algora<wbr>nd-eprint.pdf</a>=C2=A0and possibly other cryptoc=
urrency papers.</div><div style=3D"font-size:12.8px"><br></div><div style=
=3D"font-size:12.8px">Bryan Ford mentioned an additional usecase at the mic=
 on Tuesday: distributed password protection protocols</div><div style=3D"f=
ont-size:12.8px"><br></div><div style=3D"font-size:12.8px">Many of these us=
e case are already putting VRFs into production use (esp. the CONIKS one).=
=C2=A0 You can see a list of the various implementations we have found in t=
he &quot;implementation status&quot; section of our draft.=C2=A0 One of the=
 reasons we think this spec is so important is that we found flaws in sever=
al of the implementations that can be used to trivially break uniqueness. =
=C2=A0(See eg:=C2=A0<a href=3D"https://github.com/google/keytransparency/is=
sues/567" target=3D"_blank">https://github.com/google/<wbr>keytransparency/=
issues/567</a>)</div><div style=3D"font-size:12.8px"><br></div><div style=
=3D"font-size:12.8px"><span style=3D"font-size:12.8px">Thanks,</span><br></=
div><div style=3D"font-size:12.8px">Sharon=C2=A0</div><div class=3D"gmail_e=
xtra"><div><div class=3D"m_2913212881139340244gmail-m_4922457647511857001h5=
"><br><div class=3D"gmail_quote">On Fri, Jul 21, 2017 at 7:32 PM, Dan Brown=
 <span dir=3D"ltr">&lt;<a href=3D"mailto:danibrown@blackberry.com" target=
=3D"_blank">danibrown@blackberry.com</a>&gt;</span> wrote:<br><blockquote c=
lass=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px soli=
d rgb(204,204,204);padding-left:1ex">




<div lang=3D"EN-US">
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
Answering myself below: VRFs have been around since 1999, so are not so new=
. =C2=A0=E2=80=8EStill don&#39;t like the name, and still have trouble seei=
ng the value.</div>
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
<span style=3D"font-family:Calibri,&quot;Slate Pro&quot;,sans-serif,sans-se=
rif;font-size:initial;line-height:initial;text-align:initial"><br>
</span></div>
<table width=3D"100%" style=3D"background-color:white">
<tbody>
<tr>
<td colspan=3D"2" style=3D"font-size:initial;text-align:initial;background-=
color:rgb(255,255,255)">
<div style=3D"border-style:solid none none;border-top-color:rgb(181,196,223=
);border-top-width:1pt;padding:3pt 0in 0in;font-family:Tahoma,&quot;BB Alph=
a Sans&quot;,&quot;Slate Pro&quot;;font-size:10pt">
<div><b>From: </b>Dan Brown</div>
<div><b>Sent: </b>Tuesday, July 18, 2017 2:29 PM</div>
<div><b>To: </b>Sharon Goldberg; <a href=3D"mailto:cfrg@irtf.org" target=3D=
"_blank">cfrg@irtf.org</a></div>
<div><b>Cc: </b><a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.co=
m</a>; Leonid Reyzin; Dimitrios Papadopoulos</div>
<div><b>Subject: </b>Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functio=
ns</div>
</div>
</td>
</tr>
</tbody>
</table><div><div class=3D"m_2913212881139340244gmail-m_4922457647511857001=
m_-6153101734044142155m_4165835283928257204gmail-h5">
<div style=3D"border-style:solid none none;border-top-color:rgb(186,188,209=
);border-top-width:1pt;font-size:initial;text-align:initial;background-colo=
r:rgb(255,255,255)">
</div>
<br>
<div>
<div class=3D"m_2913212881139340244gmail-m_4922457647511857001m_-6153101734=
044142155m_4165835283928257204gmail-m_6358749242748202832WordSection1">
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Hi Sharon and CFRG,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">On VRFs, my uncertain comments to consider at your leisure:</span=
></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Is it fair to say VRFs are relatively new?=C2=A0 If so, then mayb=
e a little more caution is needed about their use.=C2=A0 It seems a tad has=
ty that it is being used already.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">To me, it seems that VRFs are basically signatures, with an extra=
 feature.=C2=A0 My concern is that this extra feature might get overused, b=
efore it is thoroughly reviewed.=C2=A0
</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">It is unsurprising to me that random oracle model proof can prove=
 the output of a hash to be random.=C2=A0 My intuitive concern is that at l=
east informally, this is kind of circular.=C2=A0
 Hashes often have some non-random-ish properties that might affect the ext=
ra security (over signatures) that VRFs are aiming for.=C2=A0 I guess I wou=
ld much prefer a proof saying if the hash has (well-studied) properties XYZ=
, then your construction are VRFs.=C2=A0 (Maybe
 you have this already?=C2=A0 If so, then tell me so.)</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the w=
ire, I find it hard to see how it could be used to prevent dictionary attac=
ks.=C2=A0 I assume that you are saying the proofs must
 be encrypted when one needs to avoid dictionary models?=C2=A0 I suppose al=
l the details are there in I-D and papers, but for now, I am confused about=
 the threat model (which parties have keys, etc., if they require a secure =
channel and mutual trust, why just use
 plain old hash,=E2=80=A6). To resist dictionary attacks, were already have=
 PAKEs and PBHashing.=C2=A0 Now this?</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Finally, on a bikeshed-coloring note, I object to the name =E2=80=
=9Cverifiable random function=E2=80=9D, on several grounds.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<ol start=3D"1" type=3D"1" style=3D"margin-top:0in">
<li class=3D"m_2913212881139340244gmail-m_4922457647511857001m_-61531017340=
44142155m_4165835283928257204gmail-m_6358749242748202832MsoListParagraph" s=
tyle=3D"margin-left:0in"><span style=3D"font-size:11pt;font-family:Calibri,=
sans-serif">It is not a function.=C2=A0 It is at least four functions, keyg=
en, sign, verify, and hashify.</span></li><li class=3D"m_291321288113934024=
4gmail-m_4922457647511857001m_-6153101734044142155m_4165835283928257204gmai=
l-m_6358749242748202832MsoListParagraph" style=3D"margin-left:0in"><span st=
yle=3D"font-size:11pt;font-family:Calibri,sans-serif">If you make it into a=
 keyed function F_sk(m), as in prooftohash(sign_sk(m)), it is not verifiabl=
e.=C2=A0
</span></li><li class=3D"m_2913212881139340244gmail-m_4922457647511857001m_=
-6153101734044142155m_4165835283928257204gmail-m_6358749242748202832MsoList=
Paragraph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;font-fam=
ily:Calibri,sans-serif">Verification requires the intermediate proof, which=
 is certainly not even pseudorandom (it is easy to distinguish valid signat=
ures from random).</span></li><li class=3D"m_2913212881139340244gmail-m_492=
2457647511857001m_-6153101734044142155m_4165835283928257204gmail-m_63587492=
42748202832MsoListParagraph" style=3D"margin-left:0in"><span style=3D"font-=
size:11pt;font-family:Calibri,sans-serif">It is pseudorandom, not random.=
=C2=A0 (The keys are random, but many crypto has keys, without having =E2=
=80=9Crandom=E2=80=9D in its name: encryption, MAC, signatures,
 key exchange, =E2=80=A6, they also don=E2=80=99t verifiable or random in t=
heir names either.)</span></li><li class=3D"m_2913212881139340244gmail-m_49=
22457647511857001m_-6153101734044142155m_4165835283928257204gmail-m_6358749=
242748202832MsoListParagraph" style=3D"margin-left:0in"><span style=3D"font=
-size:11pt;font-family:Calibri,sans-serif">The similar phrase =E2=80=9Cveri=
fiably random=E2=80=9D, albeit as a misnomer, has past precedents, see NIST=
 P-256 and Brainpool, etc.=C2=A0 When I see VRF, I think
 a function, that aims to VR in that sense, and great, now we can improve o=
n Brainpool, etc.</span></li><li class=3D"m_2913212881139340244gmail-m_4922=
457647511857001m_-6153101734044142155m_4165835283928257204gmail-m_635874924=
2748202832MsoListParagraph" style=3D"margin-left:0in"><span style=3D"font-s=
ize:11pt;font-family:Calibri,sans-serif">=E2=80=9CRandom function=E2=80=9D =
should be reserved for the ideal random mapping concept, for example, as st=
udied by Flajolet-Odlyzko (ok they only studied
 the case of equal size domain and range).=C2=A0 The random oracle model, i=
s the idea of approximating this ideal, etc.=C2=A0 An actual approximation =
should not be name as the ideal (sorry, I=E2=80=99m kind of repeating my po=
int 4).</span></li></ol>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Please forgive the fact that my comments above are not very const=
ructive (or if the tone is wrong).=C2=A0 This is a new topic for me, so I a=
m reluctant too many suggestions.=C2=A0 Nonetheless,
 I suggest (0) waiting a little, (1) a non-random-oracle security proof (if=
 you don=E2=80=99t have it yet), (2) re-naming the scheme to something like=
 re-hashable (or digestible) signatures (and re-name the various parts, i.e=
. proof -&gt; signature, etc.).</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Best regards,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Dan</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><b><span style=3D"font-size:11pt;font-family:Calibri=
,sans-serif">From:</span></b><span style=3D"font-size:11pt;font-family:Cali=
bri,sans-serif"> Cfrg [mailto:<a href=3D"mailto:cfrg-bounces@irtf.org" targ=
et=3D"_blank">cfrg-bounces@irtf.org</a>]
<b>On Behalf Of </b>Sharon Goldberg<br>
<b>Sent:</b> Wednesday, July 12, 2017 5:42 AM<br>
<b>To:</b> <a href=3D"mailto:cfrg@irtf.org" target=3D"_blank">cfrg@irtf.org=
</a><br>
<b>Cc:</b> <a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.com</a>=
; Dimitrios Papadopoulos &lt;<a href=3D"mailto:dipapado@umd.edu" target=3D"=
_blank">dipapado@umd.edu</a>&gt;; Leonid Reyzin &lt;<a href=3D"mailto:reyzi=
n@cs.bu.edu" target=3D"_blank">reyzin@cs.bu.edu</a>&gt;<br>
<b>Subject:</b> [Cfrg] draft-goldbe-vrf: Verifiable Random Functions</span>=
</p>
<p class=3D"MsoNormal">=C2=A0</p>
<div>
<p class=3D"MsoNormal">Dear CFRG,<br>
<br>
I&#39;m presenting at next week&#39;s meeting on Verifiable Random Function=
s. A VRF is the public-key version of keyed cryptographic hash. Only the ho=
lder of the VRF secret key can compute the hash, but anyone with the public=
 key can verify it.=C2=A0 VRFs can be used to
 prevent dictionary attacks on hash-based data structures, and have applica=
tions to key transparency (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (A=
lgorand).<br>
<br>
In advance of the meeting, please see:<br>
<br>
1) Our substantially updated -01 draft:<br>
<a href=3D"https://datatracker.ietf.org/doc/draft-goldbe-vrf/" target=3D"_b=
lank">https://datatracker.ietf.org/d<wbr>oc/draft-goldbe-vrf/</a><br>
<br>
2) Our project page, with links to various VRF implementations:<br>
<a href=3D"https://www.cs.bu.edu/~goldbe/projects/vrf" target=3D"_blank">ht=
tps://www.cs.bu.edu/~goldbe/<wbr>projects/vrf</a><br>
<br>
Comments welcome.=C2=A0 Thanks,<br>
<br>
Sharon<br>
<br>
--<br>
Sharon Goldberg<br>
Computer Science, Boston University<br>
<a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu=
.edu/~goldbe</a></p>
</div>
</div>
</div>
</div></div></div>

</blockquote></div><br><br clear=3D"all"><div><br></div></div></div>-- <br>=
<div class=3D"m_2913212881139340244gmail-m_4922457647511857001m_-6153101734=
044142155m_4165835283928257204gmail_signature">---<span><br>Sharon Goldberg=
<br>Computer Science, Boston University<br><a href=3D"http://www.cs.bu.edu/=
~goldbe" target=3D"_blank">http://www.cs.bu.edu/~goldbe</a></span></div>
</div></div>
<br></div></div><span class=3D"m_2913212881139340244gmail-">_______________=
_______________<wbr>_________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/l<wbr>istinfo/cfrg</a><br>
<br></span></blockquote></div><br></div>
</blockquote></div></div></div><div><div class=3D"h5"><br><br clear=3D"all"=
><div><br></div>-- <br><div class=3D"m_2913212881139340244gmail_signature">=
---<br>Sharon Goldberg<br>Computer Science, Boston University<br><a href=3D=
"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu.edu/~gold=
be</a></div>
</div></div></div></div>
</blockquote></div><br></div>

--f403045fc2f2d43ee0055548acd5--


From nobody Thu Jul 27 07:43:45 2017
Return-Path: <jon49175@yahoo.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id BC0CF1200C5 for <cfrg@ietfa.amsl.com>; Thu, 27 Jul 2017 07:43:44 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: 0.809
X-Spam-Level: 
X-Spam-Status: No, score=0.809 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FORGED_MUA_MOZILLA=2.309, FREEMAIL_ENVFROM_END_DIGIT=0.25, FREEMAIL_FROM=0.001, FREEMAIL_REPLYTO_END_DIGIT=0.25, RCVD_IN_DNSWL_NONE=-0.0001, RP_MATCHES_RCVD=-0.001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=no autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=yahoo.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id BYeoluUchfar for <cfrg@ietfa.amsl.com>; Thu, 27 Jul 2017 07:43:43 -0700 (PDT)
Received: from sonic309-47.consmr.mail.gq1.yahoo.com (sonic309-47.consmr.mail.gq1.yahoo.com [98.137.65.173]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id E997D1317CC for <cfrg@ietf.org>; Thu, 27 Jul 2017 07:43:42 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=yahoo.com; s=s2048; t=1501166622; bh=xyxh6/CwsHUAW0NlKH8wbyw1htULd9dthy1TVB9A83I=; h=Date:From:Reply-To:To:Cc:Subject:References:From:Subject; b=BmKNnKaU+4VGmj0b1zEVfwTmS8AQumATqbhRqiiHnoa1w8nHy8ZvAhXGsRHTRJBkzF3Y8Xvqt94JqhY6Tjd3ZGMTDzv0AoTBH98PwXklZe+4qEvGJNe53qOplHPqKsolHcFHgf2A+zDvh2AdR4NXYwBa3LkXS350zCuIz1yzHQlmtsMmpwVfaSadzVzd8fc5So1GSnLuImQasIIvTHOyTq7j+rK2zAUQt6S14v4QyeNfOpLbx504RaJKR1bm0rm3zpwRzQayuiLr1BK7lklTj9xCzPQTPOHA6IeoVZPOFknXlFBn3PNSe29fC50qoRQu+SkN9WkPm++Vsc6UQc1tfw==
X-YMail-OSG: 7pFz9g4VM1n8xRMsit.X1268zRG5MlyjrRr9JwXnXwvcJWIrEgmYTvOYFHVUUic uGUyV.rm7RmBpccABI_LA1CfkxRA7QpTMAPVNglaWBG956n4rjhzakksotgS5Ml5RINZVErHNd5Q 6XxiKs2HFX9uTFhO.XKU7OYdEtbL3w6MHfaLgGWja499RcnpXoYST.cd5hD3ZmQx3pk3fMsgUWK2 iDWZLpWzpWXN_4opC1A7Z8UmbwW7bzSqBWJtu_3a6eicCq_IpCeCZ0bT1AIu9NGhRbwVOYp16Aar KE56_wnSRiVpvdhIwVz_Uv8IkF2iHMJ_0HdY8QprDVJAod67prMs6cF0XHitak27gEFr9enuHdCg fhjwBQ_U5spLMgEB9IWEHIQQTopD9Jp1oXNqyuwxvohCICTKrSXUBeyLm1Cb3RyRAg8T22gcMGLL ofSH03Y5LIs.z585.RDVHaI0P.1w1EROcF4.DiRq5bShYxB0w84Cy3S7kwy4OXMLjXkKGf70_MFV T4gO2rNO0iEavXQEt5qpGLCChi9M7GxM5kyUL6teytjIv4GHLmQ--
Received: from sonic.gate.mail.ne1.yahoo.com by sonic309.consmr.mail.gq1.yahoo.com with HTTP; Thu, 27 Jul 2017 14:43:42 +0000
Date: Thu, 27 Jul 2017 14:39:41 +0000 (UTC)
From: Jonathan Trostle <jon49175@yahoo.com>
Reply-To: Jonathan Trostle <jon49175@yahoo.com>
To: <cfrg@ietf.org>, Yannick Seurin <yannick.seurin@gmail.com>
Cc: Tetsu Iwata <iwata@cse.nagoya-u.ac.jp>,  <jon49175@yahoo.com>
Message-ID: <428591570.717584.1501166381333@mail.yahoo.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
References: <428591570.717584.1501166381333.ref@mail.yahoo.com>
X-Mailer: WebService/1.1.10181 YahooMailBasic Mozilla/5.0 (Windows NT 6.1; WOW64; rv:54.0) Gecko/20100101 Firefox/54.0
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/BiWF5GV6sf3Iqu0ILBvhTGZeK0g>
Subject: Re: [Cfrg] Updated bounds in AES-GCM-SIV paper
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Thu, 27 Jul 2017 14:43:45 -0000

[2] incorrectly states that the only fully nonce misuse-resistant AE scheme=
s submitted to Caesar were Julius, AEZ, and HS1-SIV. CMCC is also fully non=
ce misuse-resistant.

Jonathan

--------------------------------------------
On Wed, 7/26/17, Yannick Seurin <yannick.seurin@gmail.com> wrote:

 Subject: Re: [Cfrg] Updated bounds in AES-GCM-SIV paper
 To: cfrg@ietf.org
 Cc: "Tetsu Iwata" <iwata@cse.nagoya-u.ac.jp>
 Date: Wednesday, July 26, 2017, 5:04 AM
=20
 Dear
 CFRG,
 Our paper
 "Reconsidering the Security Bound of AES-GCM-SIV",
 which prompted Adam's email, is now available on
 ePrint:https://eprint.iacr.org/2017/
 708
 The main
 contribution of this paper is an independent security
 analysis for AES-GCM-SIV motivated by some problems that we
 discovered in the security proofs presented in [1] and [2].
 We also propose a different key-derivation function with
 similar efficiency but better security than the one
 currently specified.=C2=A0
 As explained by Adam, we noticed
 that the security claims made in [2] were overly optimistic
 because the PRP-PRF indistinguishability term had been
 neglected, whereas it was actually the dominating term of
 the security bound. As a consequence, the security
 guarantees provided by AES-GCM-SIV must be lowered compared
 with what was originally announced in [2], especially for
 long messages.
 We
 stress that our paper is based on version 20160310:063701 of
 [1] and version 20170223:140759 of [2]. Both [1] and [2]
 were updated after we sent our paper to AES-GCM-SIV's
 designers on July 7.
 We believe that the CFRG
 specification (especially Section 9) should be updated as
 well to reflect the new security analysis. Recommended usage
 limitations for an AEAD scheme (such as the maximal number
 of messages that can be encrypted with the same key) should
 be based on the maximal message length allowed by its
 specification (currently, 2^{32} 128-bit blocks). More
 fine-grained recommendations (such as "if the maximal
 message length in an application is 2^m and the maximal
 number of nonce repetitions is R, then the maximal number of
 messages that can be encrypted with the same key can be
 pushed to XXX") are likely to create confusion and
 incur implementations errors. For AES-GCM-SIV with randomly
 generated nonces (which has been put forward by the
 designers as the preferred way of generating nonces when no
 state can be saved by encrypting devices), this means that
 no more than 2^{30} messages should be encrypted with the
 same key, which contrasts with the recommended limit of
 2^{50} given (without context) in Section 9 of the CFRG
 specification and in the abstract of [2].
 Cheers,Tetsu and
 Yannick.
 [1] https://eprint.iacr.org/2015/
 102[2] https://eprint.iacr.org/2017/
 168
 2017-07-17 4:09 GMT+02:00
 Adam Langley <agl@imperialviolet.org>:
 Dear CFRG,
=20
=20
=20
 We would like to thank Yannick Seurin and Tetsu Iwata for
 alerting us
=20
 to the fact that we had erroneously assumed that one of the
 terms in
=20
 the security bounds of AES-GCM-SIV was negligible when,
 for
=20
 indistinguishability, it was not. Thus, while the security
 proof was
=20
 correct, the example concrete bounds were over optimistic,
 most
=20
 notably for very large messages. This was most evident in
 Fig 4.
=20
=20
=20
 We have updated the paper[1] to correct this mistake and we
 draw the
=20
 group's attention to the revised figure four (now called
 Table 1). For
=20
 typical uses, thankfully, the difference is not material but
 for we
=20
 wish to highlight that one cannot encrypt many messages
 of
=20
 many-gigabytes using AES-GCM-SIV, in contrast to what the
 figures
=20
 previously suggested. However, even in such a case of very
 long
=20
 messages, the overall number of blocks encrypted safely is
 still
=20
 significantly higher than previous schemes.
=20
=20
=20
 [1] https://eprint.iacr.org/2017/1
 68
=20
=20
=20
=20
=20
 Cheers
=20
=20
=20
 AGL
=20
=20
=20
 --
=20
 Adam Langley agl@imperialviolet.org
 https://www.imperialviolet.org
=20
=20
=20
 ______________________________ _________________
=20
 Cfrg mailing list
=20
 Cfrg@irtf.org
=20
 https://www.irtf.org/mailman/l
 istinfo/cfrg
=20
=20
 _______________________________________________
 Cfrg mailing list
 Cfrg@irtf.org
 https://www.irtf.org/mailman/listinfo/cfrg
=20
 -----Inline Attachment Follows-----
=20
=20


From nobody Sun Jul 30 10:02:47 2017
Return-Path: <philippl.lee@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id D1FD5129AB2 for <cfrg@ietfa.amsl.com>; Sun, 30 Jul 2017 10:02:44 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -2.699
X-Spam-Level: 
X-Spam-Status: No, score=-2.699 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_LOW=-0.7, SPF_PASS=-0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 0ouZpt2fv4BO for <cfrg@ietfa.amsl.com>; Sun, 30 Jul 2017 10:02:42 -0700 (PDT)
Received: from mail-yw0-x230.google.com (mail-yw0-x230.google.com [IPv6:2607:f8b0:4002:c05::230]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id CE60B1200C5 for <cfrg@irtf.org>; Sun, 30 Jul 2017 10:02:41 -0700 (PDT)
Received: by mail-yw0-x230.google.com with SMTP id u207so84284525ywc.3 for <cfrg@irtf.org>; Sun, 30 Jul 2017 10:02:41 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=eU6Zbo0rsgWt09yie6qxkdXrZSD7fZ7hNFJgYSAOC24=; b=CBgcPlLp+OO1ffzIyfftYbYUx3GNi5v8NbALyG91TjnMe2WpwV0+kmozjiuII+uILM uuf3VdMRN+phwQrASWkT2Z/POisnD4xCPEKqoKk1WXcus6j0YO1yUbKBFDUs/4u0rDQP OXu30rQUQz5nrBJBKnb9Fy48LZcydQY97I+03aYcEataDrluDFrho+yVxv8EYGIrUjMI HOhbIdCEL9gDxUvahc80lhdZZSn6gYoJKkE2rbFetOQg/ipzP/l/CPaNpuCQXaZbvB1i WiXIFV1kGo0PG8aMrKCaqTcTspxZyahzx2o7OpaQm4wqIHT4xdBaVtyW/IED/TJn5evb HUhw==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=eU6Zbo0rsgWt09yie6qxkdXrZSD7fZ7hNFJgYSAOC24=; b=DdADwBBMYfGt8XwdREUrTm9DYJEy7nu1D9t8yLqHw7hVCQxHDVr7anGjay8iqDac6O /2hGhwx4dxUF7chlUC4VSOWLLV8vj6kgZ8IGQrKmUQlXmsDIvPKaUhurzyMJi4jhzn31 qXBCVX2Tq5G7mKsiby8LL1lxPEviet86qd5kIZn+Jv433QsLStdxZku/ILlbMSEOcwRB WBQ1PkowXapAQ6cKm9tSjoabjfymgOdvULTFhD5BxX0Bxc1KDPTZUK7PbDJ4LCuyJ8U0 DEoqQx2vcdOO1jVF0Kqowmx1yiv1T+/pGFE86KYZhKEUb/wz0a2O/PecOFkNhVvEzUGJ WMKA==
X-Gm-Message-State: AIVw111RdOwWEgq18fob6NYu+Bi8BVqDeb5tfYJ1JkOXqw271GRL50fP D9xZUOQjz02ur1ZCTxaSRIBy/kljiw==
X-Received: by 10.13.219.80 with SMTP id d77mr10280653ywe.2.1501434160931; Sun, 30 Jul 2017 10:02:40 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.129.53.208 with HTTP; Sun, 30 Jul 2017 10:02:20 -0700 (PDT)
In-Reply-To: <CAFTSWvd5GR_WsesCrfs3QNR1hPNtN-GW7-yn9PwC4GUiq0AxKw@mail.gmail.com>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com> <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net> <20170721163204.8573013.1016.15939@blackberry.com> <CAJHGrrTbjL3rd_XU9tx28g3QcBe9tJBOxs2t1OebfvZR_c7epA@mail.gmail.com> <CAFTSWvfwf34uH1AjzQq7zCMEARGH8rH310pSRe7kkYCZ3TMNeQ@mail.gmail.com> <CAJHGrrSh27DFzuGDmTD_GuBF7tCtNQsCJ42XTjZWO1LqqAm3wQ@mail.gmail.com> <CAFTSWvd5GR_WsesCrfs3QNR1hPNtN-GW7-yn9PwC4GUiq0AxKw@mail.gmail.com>
From: Philip L <philippl.lee@gmail.com>
Date: Sun, 30 Jul 2017 13:02:20 -0400
Message-ID: <CANQLCQTn27qjJ5-cpgu_nAPjaE6FOu34LCtG=iV7MPRrrmdTHg@mail.gmail.com>
To: Thomas Garcia <tgarcia.3141@gmail.com>
Cc: Sharon Goldberg <sharon.goldbe@gmail.com>, "cfrg@irtf.org" <cfrg@irtf.org>, "jan@ns1.com" <jan@ns1.com>,  Leonid Reyzin <reyzin@cs.bu.edu>, Dimitrios Papadopoulos <dipapado@umd.edu>
Content-Type: multipart/alternative; boundary="001a114fab7ed0eced05558be18f"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/KF56qceP9NzLb9_81X4M5Qqq_a8>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Sun, 30 Jul 2017 17:02:45 -0000

--001a114fab7ed0eced05558be18f
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

Please excuse the spam. I thought for just a moment somehow that the
function was verifiably random... like one of those hard problems (for
decidability?).

Just a random thought...

On Thu, Jul 27, 2017 at 4:51 AM, Thomas Garcia <tgarcia.3141@gmail.com>
wrote:

>
> Thanks for helping me clear those things up!
>
> Thomas G.
>
> On Wed, Jul 26, 2017 at 12:42 PM, Sharon Goldberg <sharon.goldbe@gmail.co=
m
> > wrote:
>
>> Hi Thomas,
>>
>> 1. It seems that one of the properties that you are interested that the
>>> VRF will have is determinism. On the other hand, the EC-VRF value is
>>> dependent on the choice of some random number k. How are these two fact=
s
>>> compatible? Am I missing something?
>>>
>>
>> We require determinism from the VRF hash output, which is obtained from
>> the VRF proof via the "proof2hash" function.
>>
>> The EC-VRF proof has 3 values: gamma, c, s
>> Values c and s depends on the choice of random number k
>> But value gamma does not depend on k.
>>
>> We get determinism because the VRF hash output (derived using
>> "proof2hash") depends only on gamma, but not on c and s.
>>
>> Slide 28 from my CFRG presentations gives a pictorial explanation of thi=
s:
>> http://www.cs.bu.edu/~goldbe/papers/VRF_ietf99_print.pdf
>>
>> 2. The value c calculated in EC-VRF is only 128 bits long for Ed25519. I=
n
>>> normal usage of Ed25519 the signature uses the full length of the hash
>>> output. Doesn't this expose the signature to collision attacks?
>>>
>>> No. We worked this out in our proofs of security.  Section B.2.1 of thi=
s
>> paper explains why this works.
>>
>> https://eprint.iacr.org/2017/099.pdf
>>
>> Thanks,
>> Sharon
>>
>>
>>
>>> Thank you for your comments. Indeed, VRFs have been around since 1999.
>>>> They are really "verifiable PRFs" but the name is by now standard in t=
he
>>>> crypto literature, and changing it will cause more confusion than keep=
ing
>>>> it.
>>>>
>>>> In terms of the VRF's security properties, there are three:
>>>>  uniqueness, collision resistance, and pseudorandomness. These are def=
ined
>>>> in our draft (https://tools.ietf.org/html/draft-goldbe-vrf-01#section-=
3
>>>> ).
>>>>
>>>> How VRFs prevent dictionary attacks: a public hash is subject to a
>>>> dictionary attack because, given the output, an adversary can evaluate=
 the
>>>> hash on different inputs and see what hits the outputs. In a VRF, the
>>>> adversary can't evaluate the hash on different inputs.
>>>>
>>>> You say it's not surprising that "random oracle model proof can prove
>>>> the output of a hash to be random". But actually, the output of a hash=
 is
>>>> NOT random if the input and the hash function are known. This is becau=
se
>>>> the output of a hash is deterministic (every input maps to a unique
>>>> output). That's exactly what enables dictionary attacks. This is in
>>>> contrast to a VRF, where the output is (pseudo)random even given knowl=
edge
>>>> of the input. Only once the VRF proof is given, does the VRF output st=
op
>>>> looking random. Note that random oracles are not essential for VRFs, a=
nd
>>>> non-random-oracles constructions exist (but are less efficient than wh=
at we
>>>> propose to standardize).
>>>>
>>>> As far as use cases, here are a few:
>>>>
>>>> In the NSEC5 use case for DNSSEC, you have sensitive data (domain
>>>> names) and you sign consecutive pairs of hashes of domain names in ord=
er to
>>>> be able to prove absence of a name. If you just use standard hashing,
>>>> whenever signed hash values are disclosed, your sensitive data is subj=
ect
>>>> to dictionary attacks. VRFs solve that problem, and sensitive names do=
n't
>>>> have to be disclosed at all. More details are in
>>>> https://eprint.iacr.org/2017/099.pdf
>>>>
>>>> In CONIKS (also Google Key Transparency, Signal secure messaging,
>>>> Yahoo! Coname) you also have some sensitive data (user names) that are=
 put
>>>> into a Merkle-like authenticated data structure. If you just use stand=
ard
>>>> hashing, whenever hash values are disclosed, sensitive data is subject=
 to
>>>> dictionary attacks. If you use VRFs, sensitive data again can be discl=
osed
>>>> only on an as-needed basis. More details are in
>>>> https://eprint.iacr.org/2014/1004.pdf.
>>>>
>>>> In a cryptocurrency use case, you wish perform a coin flip that is
>>>> deterministic and provably correct, but cannot be done by just anyone.
>>>> More details are in https://people.csail.mit.ed
>>>> u/nickolai/papers/gilad-algorand-eprint.pdf and possibly other
>>>> cryptocurrency papers.
>>>>
>>>> Bryan Ford mentioned an additional usecase at the mic on Tuesday:
>>>> distributed password protection protocols
>>>>
>>>> Many of these use case are already putting VRFs into production use
>>>> (esp. the CONIKS one).  You can see a list of the various implementati=
ons
>>>> we have found in the "implementation status" section of our draft.  On=
e of
>>>> the reasons we think this spec is so important is that we found flaws =
in
>>>> several of the implementations that can be used to trivially break
>>>> uniqueness.  (See eg: https://github.com/google/
>>>> keytransparency/issues/567)
>>>>
>>>> Thanks,
>>>> Sharon
>>>>
>>>> On Fri, Jul 21, 2017 at 7:32 PM, Dan Brown <danibrown@blackberry.com>
>>>> wrote:
>>>>
>>>>> Answering myself below: VRFs have been around since 1999, so are not
>>>>> so new.  =E2=80=8EStill don't like the name, and still have trouble s=
eeing the
>>>>> value.
>>>>>
>>>>> *From: *Dan Brown
>>>>> *Sent: *Tuesday, July 18, 2017 2:29 PM
>>>>> *To: *Sharon Goldberg; cfrg@irtf.org
>>>>> *Cc: *jan@ns1.com; Leonid Reyzin; Dimitrios Papadopoulos
>>>>> *Subject: *Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>>>>
>>>>> Hi Sharon and CFRG,
>>>>>
>>>>>
>>>>>
>>>>> On VRFs, my uncertain comments to consider at your leisure:
>>>>>
>>>>>
>>>>>
>>>>> Is it fair to say VRFs are relatively new?  If so, then maybe a littl=
e
>>>>> more caution is needed about their use.  It seems a tad hasty that it=
 is
>>>>> being used already.
>>>>>
>>>>>
>>>>>
>>>>> To me, it seems that VRFs are basically signatures, with an extra
>>>>> feature.  My concern is that this extra feature might get overused, b=
efore
>>>>> it is thoroughly reviewed.
>>>>>
>>>>>
>>>>>
>>>>> It is unsurprising to me that random oracle model proof can prove the
>>>>> output of a hash to be random.  My intuitive concern is that at least
>>>>> informally, this is kind of circular.  Hashes often have some
>>>>> non-random-ish properties that might affect the extra security (over
>>>>> signatures) that VRFs are aiming for.  I guess I would much prefer a =
proof
>>>>> saying if the hash has (well-studied) properties XYZ, then your
>>>>> construction are VRFs.  (Maybe you have this already?  If so, then te=
ll me
>>>>> so.)
>>>>>
>>>>>
>>>>>
>>>>> Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the wire,=
 I find it hard
>>>>> to see how it could be used to prevent dictionary attacks.  I assume =
that
>>>>> you are saying the proofs must be encrypted when one needs to avoid
>>>>> dictionary models?  I suppose all the details are there in I-D and pa=
pers,
>>>>> but for now, I am confused about the threat model (which parties have=
 keys,
>>>>> etc., if they require a secure channel and mutual trust, why just use=
 plain
>>>>> old hash,=E2=80=A6). To resist dictionary attacks, were already have =
PAKEs and
>>>>> PBHashing.  Now this?
>>>>>
>>>>>
>>>>>
>>>>> Finally, on a bikeshed-coloring note, I object to the name =E2=80=9Cv=
erifiable
>>>>> random function=E2=80=9D, on several grounds.
>>>>>
>>>>>
>>>>>
>>>>>    1. It is not a function.  It is at least four functions, keygen,
>>>>>    sign, verify, and hashify.
>>>>>    2. If you make it into a keyed function F_sk(m), as in
>>>>>    prooftohash(sign_sk(m)), it is not verifiable.
>>>>>    3. Verification requires the intermediate proof, which is
>>>>>    certainly not even pseudorandom (it is easy to distinguish valid s=
ignatures
>>>>>    from random).
>>>>>    4. It is pseudorandom, not random.  (The keys are random, but many
>>>>>    crypto has keys, without having =E2=80=9Crandom=E2=80=9D in its na=
me: encryption, MAC,
>>>>>    signatures, key exchange, =E2=80=A6, they also don=E2=80=99t verif=
iable or random in their
>>>>>    names either.)
>>>>>    5. The similar phrase =E2=80=9Cverifiably random=E2=80=9D, albeit =
as a misnomer,
>>>>>    has past precedents, see NIST P-256 and Brainpool, etc.  When I se=
e VRF, I
>>>>>    think a function, that aims to VR in that sense, and great, now we=
 can
>>>>>    improve on Brainpool, etc.
>>>>>    6. =E2=80=9CRandom function=E2=80=9D should be reserved for the id=
eal random
>>>>>    mapping concept, for example, as studied by Flajolet-Odlyzko (ok t=
hey only
>>>>>    studied the case of equal size domain and range).  The random orac=
le model,
>>>>>    is the idea of approximating this ideal, etc.  An actual approxima=
tion
>>>>>    should not be name as the ideal (sorry, I=E2=80=99m kind of repeat=
ing my point 4).
>>>>>
>>>>>
>>>>>
>>>>> Please forgive the fact that my comments above are not very
>>>>> constructive (or if the tone is wrong).  This is a new topic for me, =
so I
>>>>> am reluctant too many suggestions.  Nonetheless, I suggest (0) waitin=
g a
>>>>> little, (1) a non-random-oracle security proof (if you don=E2=80=99t =
have it yet),
>>>>> (2) re-naming the scheme to something like re-hashable (or digestible=
)
>>>>> signatures (and re-name the various parts, i.e. proof -> signature, e=
tc.).
>>>>>
>>>>>
>>>>>
>>>>> Best regards,
>>>>>
>>>>>
>>>>>
>>>>> Dan
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> *From:* Cfrg [mailto:cfrg-bounces@irtf.org] *On Behalf Of *Sharon
>>>>> Goldberg
>>>>> *Sent:* Wednesday, July 12, 2017 5:42 AM
>>>>> *To:* cfrg@irtf.org
>>>>> *Cc:* jan@ns1.com; Dimitrios Papadopoulos <dipapado@umd.edu>; Leonid
>>>>> Reyzin <reyzin@cs.bu.edu>
>>>>> *Subject:* [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>>>>
>>>>>
>>>>>
>>>>> Dear CFRG,
>>>>>
>>>>> I'm presenting at next week's meeting on Verifiable Random Functions.
>>>>> A VRF is the public-key version of keyed cryptographic hash. Only the
>>>>> holder of the VRF secret key can compute the hash, but anyone with th=
e
>>>>> public key can verify it.  VRFs can be used to prevent dictionary att=
acks
>>>>> on hash-based data structures, and have applications to key transpare=
ncy
>>>>> (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (Algorand).
>>>>>
>>>>> In advance of the meeting, please see:
>>>>>
>>>>> 1) Our substantially updated -01 draft:
>>>>> https://datatracker.ietf.org/doc/draft-goldbe-vrf/
>>>>>
>>>>> 2) Our project page, with links to various VRF implementations:
>>>>> https://www.cs.bu.edu/~goldbe/projects/vrf
>>>>>
>>>>> Comments welcome.  Thanks,
>>>>>
>>>>> Sharon
>>>>>
>>>>> --
>>>>> Sharon Goldberg
>>>>> Computer Science, Boston University
>>>>> http://www.cs.bu.edu/~goldbe
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> ---
>>>> Sharon Goldberg
>>>> Computer Science, Boston University
>>>> http://www.cs.bu.edu/~goldbe
>>>>
>>>> _______________________________________________
>>>> Cfrg mailing list
>>>> Cfrg@irtf.org
>>>> https://www.irtf.org/mailman/listinfo/cfrg
>>>>
>>>>
>>>
>>
>>
>> --
>> ---
>> Sharon Goldberg
>> Computer Science, Boston University
>> http://www.cs.bu.edu/~goldbe
>>
>
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>
>

--001a114fab7ed0eced05558be18f
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Please excuse the spam. I thought for just a moment someho=
w that the function was verifiably random... like one of those hard problem=
s (for decidability?).<br><br>Just a random thought...<br></div><div class=
=3D"gmail_extra"><br><div class=3D"gmail_quote">On Thu, Jul 27, 2017 at 4:5=
1 AM, Thomas Garcia <span dir=3D"ltr">&lt;<a href=3D"mailto:tgarcia.3141@gm=
ail.com" target=3D"_blank">tgarcia.3141@gmail.com</a>&gt;</span> wrote:<br>=
<blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p=
x #ccc solid;padding-left:1ex"><div dir=3D"ltr"><div><br></div><div>Thanks =
for helping me clear those things up!</div><div><br></div><div>Thomas G.</d=
iv></div><div class=3D"HOEnZb"><div class=3D"h5"><div class=3D"gmail_extra"=
><br><div class=3D"gmail_quote">On Wed, Jul 26, 2017 at 12:42 PM, Sharon Go=
ldberg <span dir=3D"ltr">&lt;<a href=3D"mailto:sharon.goldbe@gmail.com" tar=
get=3D"_blank">sharon.goldbe@gmail.com</a>&gt;</span> wrote:<br><blockquote=
 class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc soli=
d;padding-left:1ex"><div dir=3D"ltr">Hi Thomas,<div><br></div><div class=3D=
"gmail_extra"><div class=3D"gmail_quote"><span><blockquote class=3D"gmail_q=
uote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,2=
04);padding-left:1ex"><div dir=3D"ltr"><div>1. It seems that one of the pro=
perties that you are interested that the VRF will have is determinism. On t=
he other hand, the EC-VRF value is dependent on the choice of some random n=
umber k. How are these two facts compatible? Am I missing something?</div><=
/div></blockquote><div><br></div></span><div>We require determinism from th=
e VRF hash output, which is obtained from the VRF proof via the &quot;proof=
2hash&quot; function.</div><div><br></div><div>The EC-VRF proof has 3 value=
s: gamma, c, s</div><div>Values c and s depends on the choice of random num=
ber k</div><div>But value gamma does not depend on k.</div><div><br></div><=
div>We get determinism because the VRF hash output (derived using &quot;pro=
of2hash&quot;) depends only on gamma, but not on c and s.</div><div>=C2=A0<=
/div><div>Slide 28 from my CFRG presentations gives a pictorial explanation=
 of this:</div><div><a href=3D"http://www.cs.bu.edu/~goldbe/papers/VRF_ietf=
99_print.pdf" target=3D"_blank">http://www.cs.bu.edu/~goldbe/p<wbr>apers/VR=
F_ietf99_print.pdf</a><br></div><span><div><br></div><blockquote class=3D"g=
mail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204=
,204,204);padding-left:1ex"><div dir=3D"ltr"><div>2. The value c calculated=
 in EC-VRF is only 128 bits long for Ed25519. In normal usage of Ed25519 th=
e signature uses the full length of the hash output. Doesn&#39;t this expos=
e the signature to collision attacks?</div><div><br></div></div></blockquot=
e></span><div>No. We worked this out in our proofs of security.=C2=A0 Secti=
on B.2.1 of this paper explains why this works.</div><div><br></div><div><a=
 href=3D"https://eprint.iacr.org/2017/099.pdf" target=3D"_blank">https://ep=
rint.iacr.org/2017/0<wbr>99.pdf</a><br></div><div><br></div><div>Thanks,</d=
iv><div>Sharon</div><div><div class=3D"m_-5638161815282581577h5"><div><br><=
/div><div>=C2=A0</div><blockquote class=3D"gmail_quote" style=3D"margin:0px=
 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><di=
v class=3D"gmail_extra"><div class=3D"gmail_quote"><blockquote class=3D"gma=
il_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,2=
04,204);padding-left:1ex"><div><div class=3D"m_-5638161815282581577m_291321=
2881139340244gmail-h5"><div dir=3D"ltr"><div style=3D"font-size:12.8px"></d=
iv><div style=3D"font-size:12.8px">Thank you for your comments. Indeed, VRF=
s have been around since 1999. They are really &quot;verifiable PRFs&quot; =
but the name is by now standard in the crypto literature, and changing it w=
ill cause more confusion than keeping it.</div><div style=3D"font-size:12.8=
px"><br></div><div style=3D"font-size:12.8px">In terms of the VRF&#39;s sec=
urity properties, there are three: =C2=A0uniqueness, collision resistance, =
and pseudorandomness. These are defined in our draft (<span style=3D"font-s=
ize:12.8px"><a href=3D"https://tools.ietf.org/html/draft-goldbe-vrf-01#sect=
ion-3" target=3D"_blank">https://tools.ietf.org/html/d<wbr>raft-goldbe-vrf-=
01#section-3</a></span><span style=3D"font-size:12.8px">).<wbr>=C2=A0</span=
></div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-size:12=
.8px">How VRFs prevent dictionary attacks: a public hash is subject to a di=
ctionary attack because, given the output, an adversary can evaluate the ha=
sh on different inputs and see what hits the outputs. In a VRF, the adversa=
ry can&#39;t evaluate the hash on different inputs.=C2=A0</div><div style=
=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8px">You say it&=
#39;s not surprising that &quot;random oracle model proof can prove the out=
put of a hash to be random&quot;. But actually, the output of a hash is NOT=
 random if the input and the hash function are known. This is because the o=
utput of a hash is deterministic (every input maps to a unique output). Tha=
t&#39;s exactly what enables dictionary attacks. This is in contrast to a V=
RF, where the output is (pseudo)random even given knowledge of the input. O=
nly once the VRF proof is given, does the VRF output stop looking random. N=
ote that random oracles are not essential for VRFs, and non-random-oracles =
constructions exist (but are less efficient than what we propose to standar=
dize).</div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-si=
ze:12.8px">As far as use cases, here are a few:=C2=A0</div><div style=3D"fo=
nt-size:12.8px"><br></div><div style=3D"font-size:12.8px">In the NSEC5 use =
case for DNSSEC, you have sensitive data (domain names) and you sign consec=
utive pairs of hashes of domain names in order to be able to prove absence =
of a name. If you just use standard hashing, whenever signed hash values ar=
e disclosed, your sensitive data is subject to dictionary attacks. VRFs sol=
ve that problem, and sensitive names don&#39;t have to be disclosed at all.=
 More details are in=C2=A0<a href=3D"https://eprint.iacr.org/2017/099.pdf" =
target=3D"_blank">https://eprint.iacr.org/201<wbr>7/099.pdf</a></div><div s=
tyle=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8px">In CONI=
KS (also Google Key Transparency, Signal secure messaging, Yahoo! Coname) y=
ou also have some sensitive data (user names) that are put into a Merkle-li=
ke authenticated data structure. If you just use standard hashing, whenever=
 hash values are disclosed, sensitive data is subject to dictionary attacks=
. If you use VRFs, sensitive data again can be disclosed only on an as-need=
ed basis. More details are in =C2=A0<a href=3D"https://eprint.iacr.org/2014=
/1004.pdf" target=3D"_blank">https://eprint.iacr.org/2014/<wbr>1004.pdf</a>=
.</div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-size:12=
.8px">In a cryptocurrency use case, you wish perform a coin flip that is de=
terministic and provably correct, but cannot be done by just anyone.=C2=A0 =
More details are in=C2=A0<a href=3D"https://people.csail.mit.edu/nickolai/p=
apers/gilad-algorand-eprint.pdf" target=3D"_blank">https://people.csail.mit=
.ed<wbr>u/nickolai/papers/gilad-algora<wbr>nd-eprint.pdf</a>=C2=A0and possi=
bly other cryptocurrency papers.</div><div style=3D"font-size:12.8px"><br><=
/div><div style=3D"font-size:12.8px">Bryan Ford mentioned an additional use=
case at the mic on Tuesday: distributed password protection protocols</div>=
<div style=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8px">M=
any of these use case are already putting VRFs into production use (esp. th=
e CONIKS one).=C2=A0 You can see a list of the various implementations we h=
ave found in the &quot;implementation status&quot; section of our draft.=C2=
=A0 One of the reasons we think this spec is so important is that we found =
flaws in several of the implementations that can be used to trivially break=
 uniqueness. =C2=A0(See eg:=C2=A0<a href=3D"https://github.com/google/keytr=
ansparency/issues/567" target=3D"_blank">https://github.com/google/<wbr>key=
transparency/issues/567</a>)</div><div style=3D"font-size:12.8px"><br></div=
><div style=3D"font-size:12.8px"><span style=3D"font-size:12.8px">Thanks,</=
span><br></div><div style=3D"font-size:12.8px">Sharon=C2=A0</div><div class=
=3D"gmail_extra"><div><div class=3D"m_-5638161815282581577m_291321288113934=
0244gmail-m_4922457647511857001h5"><br><div class=3D"gmail_quote">On Fri, J=
ul 21, 2017 at 7:32 PM, Dan Brown <span dir=3D"ltr">&lt;<a href=3D"mailto:d=
anibrown@blackberry.com" target=3D"_blank">danibrown@blackberry.com</a>&gt;=
</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px=
 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">




<div lang=3D"EN-US">
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
Answering myself below: VRFs have been around since 1999, so are not so new=
. =C2=A0=E2=80=8EStill don&#39;t like the name, and still have trouble seei=
ng the value.</div>
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
<span style=3D"font-family:Calibri,&quot;Slate Pro&quot;,sans-serif,sans-se=
rif;font-size:initial;line-height:initial;text-align:initial"><br>
</span></div>
<table style=3D"background-color:white" width=3D"100%">
<tbody>
<tr>
<td colspan=3D"2" style=3D"font-size:initial;text-align:initial;background-=
color:rgb(255,255,255)">
<div style=3D"border-style:solid none none;border-top-color:rgb(181,196,223=
);border-top-width:1pt;padding:3pt 0in 0in;font-family:Tahoma,&quot;BB Alph=
a Sans&quot;,&quot;Slate Pro&quot;;font-size:10pt">
<div><b>From: </b>Dan Brown</div>
<div><b>Sent: </b>Tuesday, July 18, 2017 2:29 PM</div>
<div><b>To: </b>Sharon Goldberg; <a href=3D"mailto:cfrg@irtf.org" target=3D=
"_blank">cfrg@irtf.org</a></div>
<div><b>Cc: </b><a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.co=
m</a>; Leonid Reyzin; Dimitrios Papadopoulos</div>
<div><b>Subject: </b>Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functio=
ns</div>
</div>
</td>
</tr>
</tbody>
</table><div><div class=3D"m_-5638161815282581577m_2913212881139340244gmail=
-m_4922457647511857001m_-6153101734044142155m_4165835283928257204gmail-h5">
<div style=3D"border-style:solid none none;border-top-color:rgb(186,188,209=
);border-top-width:1pt;font-size:initial;text-align:initial;background-colo=
r:rgb(255,255,255)">
</div>
<br>
<div>
<div class=3D"m_-5638161815282581577m_2913212881139340244gmail-m_4922457647=
511857001m_-6153101734044142155m_4165835283928257204gmail-m_635874924274820=
2832WordSection1">
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Hi Sharon and CFRG,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">On VRFs, my uncertain comments to consider at your leisure:</span=
></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Is it fair to say VRFs are relatively new?=C2=A0 If so, then mayb=
e a little more caution is needed about their use.=C2=A0 It seems a tad has=
ty that it is being used already.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">To me, it seems that VRFs are basically signatures, with an extra=
 feature.=C2=A0 My concern is that this extra feature might get overused, b=
efore it is thoroughly reviewed.=C2=A0
</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">It is unsurprising to me that random oracle model proof can prove=
 the output of a hash to be random.=C2=A0 My intuitive concern is that at l=
east informally, this is kind of circular.=C2=A0
 Hashes often have some non-random-ish properties that might affect the ext=
ra security (over signatures) that VRFs are aiming for.=C2=A0 I guess I wou=
ld much prefer a proof saying if the hash has (well-studied) properties XYZ=
, then your construction are VRFs.=C2=A0 (Maybe
 you have this already?=C2=A0 If so, then tell me so.)</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the w=
ire, I find it hard to see how it could be used to prevent dictionary attac=
ks.=C2=A0 I assume that you are saying the proofs must
 be encrypted when one needs to avoid dictionary models?=C2=A0 I suppose al=
l the details are there in I-D and papers, but for now, I am confused about=
 the threat model (which parties have keys, etc., if they require a secure =
channel and mutual trust, why just use
 plain old hash,=E2=80=A6). To resist dictionary attacks, were already have=
 PAKEs and PBHashing.=C2=A0 Now this?</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Finally, on a bikeshed-coloring note, I object to the name =E2=80=
=9Cverifiable random function=E2=80=9D, on several grounds.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<ol start=3D"1" style=3D"margin-top:0in" type=3D"1">
<li class=3D"m_-5638161815282581577m_2913212881139340244gmail-m_49224576475=
11857001m_-6153101734044142155m_4165835283928257204gmail-m_6358749242748202=
832MsoListParagraph" style=3D"margin-left:0in"><span style=3D"font-size:11p=
t;font-family:Calibri,sans-serif">It is not a function.=C2=A0 It is at leas=
t four functions, keygen, sign, verify, and hashify.</span></li><li class=
=3D"m_-5638161815282581577m_2913212881139340244gmail-m_4922457647511857001m=
_-6153101734044142155m_4165835283928257204gmail-m_6358749242748202832MsoLis=
tParagraph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;font-fa=
mily:Calibri,sans-serif">If you make it into a keyed function F_sk(m), as i=
n prooftohash(sign_sk(m)), it is not verifiable.=C2=A0
</span></li><li class=3D"m_-5638161815282581577m_2913212881139340244gmail-m=
_4922457647511857001m_-6153101734044142155m_4165835283928257204gmail-m_6358=
749242748202832MsoListParagraph" style=3D"margin-left:0in"><span style=3D"f=
ont-size:11pt;font-family:Calibri,sans-serif">Verification requires the int=
ermediate proof, which is certainly not even pseudorandom (it is easy to di=
stinguish valid signatures from random).</span></li><li class=3D"m_-5638161=
815282581577m_2913212881139340244gmail-m_4922457647511857001m_-615310173404=
4142155m_4165835283928257204gmail-m_6358749242748202832MsoListParagraph" st=
yle=3D"margin-left:0in"><span style=3D"font-size:11pt;font-family:Calibri,s=
ans-serif">It is pseudorandom, not random.=C2=A0 (The keys are random, but =
many crypto has keys, without having =E2=80=9Crandom=E2=80=9D in its name: =
encryption, MAC, signatures,
 key exchange, =E2=80=A6, they also don=E2=80=99t verifiable or random in t=
heir names either.)</span></li><li class=3D"m_-5638161815282581577m_2913212=
881139340244gmail-m_4922457647511857001m_-6153101734044142155m_416583528392=
8257204gmail-m_6358749242748202832MsoListParagraph" style=3D"margin-left:0i=
n"><span style=3D"font-size:11pt;font-family:Calibri,sans-serif">The simila=
r phrase =E2=80=9Cverifiably random=E2=80=9D, albeit as a misnomer, has pas=
t precedents, see NIST P-256 and Brainpool, etc.=C2=A0 When I see VRF, I th=
ink
 a function, that aims to VR in that sense, and great, now we can improve o=
n Brainpool, etc.</span></li><li class=3D"m_-5638161815282581577m_291321288=
1139340244gmail-m_4922457647511857001m_-6153101734044142155m_41658352839282=
57204gmail-m_6358749242748202832MsoListParagraph" style=3D"margin-left:0in"=
><span style=3D"font-size:11pt;font-family:Calibri,sans-serif">=E2=80=9CRan=
dom function=E2=80=9D should be reserved for the ideal random mapping conce=
pt, for example, as studied by Flajolet-Odlyzko (ok they only studied
 the case of equal size domain and range).=C2=A0 The random oracle model, i=
s the idea of approximating this ideal, etc.=C2=A0 An actual approximation =
should not be name as the ideal (sorry, I=E2=80=99m kind of repeating my po=
int 4).</span></li></ol>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Please forgive the fact that my comments above are not very const=
ructive (or if the tone is wrong).=C2=A0 This is a new topic for me, so I a=
m reluctant too many suggestions.=C2=A0 Nonetheless,
 I suggest (0) waiting a little, (1) a non-random-oracle security proof (if=
 you don=E2=80=99t have it yet), (2) re-naming the scheme to something like=
 re-hashable (or digestible) signatures (and re-name the various parts, i.e=
. proof -&gt; signature, etc.).</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Best regards,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Dan</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><b><span style=3D"font-size:11pt;font-family:Calibri=
,sans-serif">From:</span></b><span style=3D"font-size:11pt;font-family:Cali=
bri,sans-serif"> Cfrg [mailto:<a href=3D"mailto:cfrg-bounces@irtf.org" targ=
et=3D"_blank">cfrg-bounces@irtf.org</a>]
<b>On Behalf Of </b>Sharon Goldberg<br>
<b>Sent:</b> Wednesday, July 12, 2017 5:42 AM<br>
<b>To:</b> <a href=3D"mailto:cfrg@irtf.org" target=3D"_blank">cfrg@irtf.org=
</a><br>
<b>Cc:</b> <a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.com</a>=
; Dimitrios Papadopoulos &lt;<a href=3D"mailto:dipapado@umd.edu" target=3D"=
_blank">dipapado@umd.edu</a>&gt;; Leonid Reyzin &lt;<a href=3D"mailto:reyzi=
n@cs.bu.edu" target=3D"_blank">reyzin@cs.bu.edu</a>&gt;<br>
<b>Subject:</b> [Cfrg] draft-goldbe-vrf: Verifiable Random Functions</span>=
</p>
<p class=3D"MsoNormal">=C2=A0</p>
<div>
<p class=3D"MsoNormal">Dear CFRG,<br>
<br>
I&#39;m presenting at next week&#39;s meeting on Verifiable Random Function=
s. A VRF is the public-key version of keyed cryptographic hash. Only the ho=
lder of the VRF secret key can compute the hash, but anyone with the public=
 key can verify it.=C2=A0 VRFs can be used to
 prevent dictionary attacks on hash-based data structures, and have applica=
tions to key transparency (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (A=
lgorand).<br>
<br>
In advance of the meeting, please see:<br>
<br>
1) Our substantially updated -01 draft:<br>
<a href=3D"https://datatracker.ietf.org/doc/draft-goldbe-vrf/" target=3D"_b=
lank">https://datatracker.ietf.org/d<wbr>oc/draft-goldbe-vrf/</a><br>
<br>
2) Our project page, with links to various VRF implementations:<br>
<a href=3D"https://www.cs.bu.edu/~goldbe/projects/vrf" target=3D"_blank">ht=
tps://www.cs.bu.edu/~goldbe/<wbr>projects/vrf</a><br>
<br>
Comments welcome.=C2=A0 Thanks,<br>
<br>
Sharon<br>
<br>
--<br>
Sharon Goldberg<br>
Computer Science, Boston University<br>
<a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu=
.edu/~goldbe</a></p>
</div>
</div>
</div>
</div></div></div>

</blockquote></div><br><br clear=3D"all"><div><br></div></div></div>-- <br>=
<div class=3D"m_-5638161815282581577m_2913212881139340244gmail-m_4922457647=
511857001m_-6153101734044142155m_4165835283928257204gmail_signature">---<sp=
an><br>Sharon Goldberg<br>Computer Science, Boston University<br><a href=3D=
"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu.edu/~gold=
be</a></span></div>
</div></div>
<br></div></div><span class=3D"m_-5638161815282581577m_2913212881139340244g=
mail-">______________________________<wbr>_________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/l<wbr>istinfo/cfrg</a><br>
<br></span></blockquote></div><br></div>
</blockquote></div></div></div><div><div class=3D"m_-5638161815282581577h5"=
><br><br clear=3D"all"><div><br></div>-- <br><div class=3D"m_-5638161815282=
581577m_2913212881139340244gmail_signature">---<br>Sharon Goldberg<br>Compu=
ter Science, Boston University<br><a href=3D"http://www.cs.bu.edu/~goldbe" =
target=3D"_blank">http://www.cs.bu.edu/~goldbe</a></div>
</div></div></div></div>
</blockquote></div><br></div>
</div></div><br>______________________________<wbr>_________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/<wbr>listinfo/cfrg</a><br>
<br></blockquote></div><br></div>

--001a114fab7ed0eced05558be18f--


From nobody Mon Jul 31 02:04:57 2017
Return-Path: <sharon.goldbe@gmail.com>
X-Original-To: cfrg@ietfa.amsl.com
Delivered-To: cfrg@ietfa.amsl.com
Received: from localhost (localhost [127.0.0.1]) by ietfa.amsl.com (Postfix) with ESMTP id 23E7E129AD3 for <cfrg@ietfa.amsl.com>; Mon, 31 Jul 2017 02:04:55 -0700 (PDT)
X-Virus-Scanned: amavisd-new at amsl.com
X-Spam-Flag: NO
X-Spam-Score: -1.998
X-Spam-Level: 
X-Spam-Status: No, score=-1.998 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_PASS=-0.001, URIBL_BLOCKED=0.001] autolearn=ham autolearn_force=no
Authentication-Results: ietfa.amsl.com (amavisd-new); dkim=pass (2048-bit key) header.d=gmail.com
Received: from mail.ietf.org ([4.31.198.44]) by localhost (ietfa.amsl.com [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id u_hjDZ5kEHfh for <cfrg@ietfa.amsl.com>; Mon, 31 Jul 2017 02:04:51 -0700 (PDT)
Received: from mail-io0-x230.google.com (mail-io0-x230.google.com [IPv6:2607:f8b0:4001:c06::230]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256 (128/128 bits)) (No client certificate requested) by ietfa.amsl.com (Postfix) with ESMTPS id A9185131F6A for <cfrg@irtf.org>; Mon, 31 Jul 2017 02:04:51 -0700 (PDT)
Received: by mail-io0-x230.google.com with SMTP id g35so75932059ioi.3 for <cfrg@irtf.org>; Mon, 31 Jul 2017 02:04:51 -0700 (PDT)
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025;  h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=xToRZDDGXz4e98F4Iwb4Z21cTP7o/2592zg9utqxr48=; b=mXBzxLPXHLCnqeIcm7X/KpEH+xjdFXzekjz1m7J5id3lXlLmhgPhoEdL/qSb5b3QXh XoXl9oiFdYqOczzLc8QmKv2/u4Y4SVmMkdoM3Bq2bvtiWe/5JjAba5aUHSGNT3Vgtg9X AhlmqPYkv8/qsBhXghckDwi/MipPPbT6LaRXknIdryOPDKom1cuwOMG2WKA24huUoCn7 ue4a4NJrnTnv2KC4dCzyJr4M/FHFYF6Dfpea1aO/WT1VWgKVG8+YtEzBd/flTi+GBKQn z1Xr7Kq7rIHfm5EA84SVNQtO8kTqkiJ2igrHObQMQdfvjf+iYWpZ79rd2OE40URL3d3s EHNQ==
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=xToRZDDGXz4e98F4Iwb4Z21cTP7o/2592zg9utqxr48=; b=rLFCeKBXlePRE6y2PvY8PZq3voTHXZHfDcOgkw0INyeGoYUfS6vyDzlSCYglU0WscH E9+/BSWKkTXQEnzPmbTIiIsSx/2TsMkxZte61muuoK/8zpeACCKie1klmUKj8oQQD+fa RqCp9qflag0FgIkA3jOF/RhEpJtYi7NHH9y9/vs9cWmFGSDe7wErMsPw2+Se55KZ3n0a wNLbQKOhbv81oFtK0ctDnZjyDifzBwROaBU8fe7tN/+lb4X7M2SWv6T9L1uBROLgZq5p VkNwJXkw1vwRQqWHOM1EqXFc8GEw/js49pwIQpqaydnRw3hBdl/Lw4NVEurM7DBTQPRB 1VrA==
X-Gm-Message-State: AIVw1108KfMKMMACDyY1lE081ctewsXHDv2zQ4QkoWY2qTioo94shl6z PlzipP7nqHMxpsTSL6RBXI8UIEnlEQ==
X-Received: by 10.107.147.66 with SMTP id v63mr18692320iod.126.1501491890929;  Mon, 31 Jul 2017 02:04:50 -0700 (PDT)
MIME-Version: 1.0
Received: by 10.107.39.83 with HTTP; Mon, 31 Jul 2017 02:04:10 -0700 (PDT)
In-Reply-To: <CANQLCQTn27qjJ5-cpgu_nAPjaE6FOu34LCtG=iV7MPRrrmdTHg@mail.gmail.com>
References: <CAJHGrrROHxR6WLQFO4+tL7N6DGKSAbwSzQZP-x3es+iy2O6TDg@mail.gmail.com> <810C31990B57ED40B2062BA10D43FBF501B63B22@XMB116CNC.rim.net> <20170721163204.8573013.1016.15939@blackberry.com> <CAJHGrrTbjL3rd_XU9tx28g3QcBe9tJBOxs2t1OebfvZR_c7epA@mail.gmail.com> <CAFTSWvfwf34uH1AjzQq7zCMEARGH8rH310pSRe7kkYCZ3TMNeQ@mail.gmail.com> <CAJHGrrSh27DFzuGDmTD_GuBF7tCtNQsCJ42XTjZWO1LqqAm3wQ@mail.gmail.com> <CAFTSWvd5GR_WsesCrfs3QNR1hPNtN-GW7-yn9PwC4GUiq0AxKw@mail.gmail.com> <CANQLCQTn27qjJ5-cpgu_nAPjaE6FOu34LCtG=iV7MPRrrmdTHg@mail.gmail.com>
From: Sharon Goldberg <sharon.goldbe@gmail.com>
Date: Mon, 31 Jul 2017 12:04:10 +0300
Message-ID: <CAJHGrrRqMf8upGO5KEKuLAKFYpivQatJYnZbZjY88aQE8=CvEQ@mail.gmail.com>
To: Philip L <philippl.lee@gmail.com>
Cc: Thomas Garcia <tgarcia.3141@gmail.com>, "cfrg@irtf.org" <cfrg@irtf.org>, "jan@ns1.com" <jan@ns1.com>,  Leonid Reyzin <reyzin@cs.bu.edu>, Dimitrios Papadopoulos <dipapado@umd.edu>
Content-Type: multipart/alternative; boundary="001a1148e222cad5c105559952ab"
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/4O9FHdiXYYcGMlZqG6i0EYHo9JI>
Subject: Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
X-BeenThere: cfrg@irtf.org
X-Mailman-Version: 2.1.22
Precedence: list
List-Id: Crypto Forum Research Group <cfrg.irtf.org>
List-Unsubscribe: <https://www.irtf.org/mailman/options/cfrg>, <mailto:cfrg-request@irtf.org?subject=unsubscribe>
List-Archive: <https://mailarchive.ietf.org/arch/browse/cfrg/>
List-Post: <mailto:cfrg@irtf.org>
List-Help: <mailto:cfrg-request@irtf.org?subject=help>
List-Subscribe: <https://www.irtf.org/mailman/listinfo/cfrg>, <mailto:cfrg-request@irtf.org?subject=subscribe>
X-List-Received-Date: Mon, 31 Jul 2017 09:04:55 -0000

--001a1148e222cad5c105559952ab
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

It is "verifiable pseudorandomness". (Not true randomness.)
Think of a pseudorandom function (PRF) that comes with a public key that
allows anyone to check that the output of the PRF was computed correctly.

Sharon

On Sun, Jul 30, 2017 at 8:02 PM, Philip L <philippl.lee@gmail.com> wrote:

> Please excuse the spam. I thought for just a moment somehow that the
> function was verifiably random... like one of those hard problems (for
> decidability?).
>
> Just a random thought...
>
> On Thu, Jul 27, 2017 at 4:51 AM, Thomas Garcia <tgarcia.3141@gmail.com>
> wrote:
>
>>
>> Thanks for helping me clear those things up!
>>
>> Thomas G.
>>
>> On Wed, Jul 26, 2017 at 12:42 PM, Sharon Goldberg <
>> sharon.goldbe@gmail.com> wrote:
>>
>>> Hi Thomas,
>>>
>>> 1. It seems that one of the properties that you are interested that the
>>>> VRF will have is determinism. On the other hand, the EC-VRF value is
>>>> dependent on the choice of some random number k. How are these two fac=
ts
>>>> compatible? Am I missing something?
>>>>
>>>
>>> We require determinism from the VRF hash output, which is obtained from
>>> the VRF proof via the "proof2hash" function.
>>>
>>> The EC-VRF proof has 3 values: gamma, c, s
>>> Values c and s depends on the choice of random number k
>>> But value gamma does not depend on k.
>>>
>>> We get determinism because the VRF hash output (derived using
>>> "proof2hash") depends only on gamma, but not on c and s.
>>>
>>> Slide 28 from my CFRG presentations gives a pictorial explanation of
>>> this:
>>> http://www.cs.bu.edu/~goldbe/papers/VRF_ietf99_print.pdf
>>>
>>> 2. The value c calculated in EC-VRF is only 128 bits long for Ed25519.
>>>> In normal usage of Ed25519 the signature uses the full length of the h=
ash
>>>> output. Doesn't this expose the signature to collision attacks?
>>>>
>>>> No. We worked this out in our proofs of security.  Section B.2.1 of
>>> this paper explains why this works.
>>>
>>> https://eprint.iacr.org/2017/099.pdf
>>>
>>> Thanks,
>>> Sharon
>>>
>>>
>>>
>>>> Thank you for your comments. Indeed, VRFs have been around since 1999.
>>>>> They are really "verifiable PRFs" but the name is by now standard in =
the
>>>>> crypto literature, and changing it will cause more confusion than kee=
ping
>>>>> it.
>>>>>
>>>>> In terms of the VRF's security properties, there are three:
>>>>>  uniqueness, collision resistance, and pseudorandomness. These are de=
fined
>>>>> in our draft (https://tools.ietf.org/html/d
>>>>> raft-goldbe-vrf-01#section-3).
>>>>>
>>>>> How VRFs prevent dictionary attacks: a public hash is subject to a
>>>>> dictionary attack because, given the output, an adversary can evaluat=
e the
>>>>> hash on different inputs and see what hits the outputs. In a VRF, the
>>>>> adversary can't evaluate the hash on different inputs.
>>>>>
>>>>> You say it's not surprising that "random oracle model proof can prove
>>>>> the output of a hash to be random". But actually, the output of a has=
h is
>>>>> NOT random if the input and the hash function are known. This is beca=
use
>>>>> the output of a hash is deterministic (every input maps to a unique
>>>>> output). That's exactly what enables dictionary attacks. This is in
>>>>> contrast to a VRF, where the output is (pseudo)random even given know=
ledge
>>>>> of the input. Only once the VRF proof is given, does the VRF output s=
top
>>>>> looking random. Note that random oracles are not essential for VRFs, =
and
>>>>> non-random-oracles constructions exist (but are less efficient than w=
hat we
>>>>> propose to standardize).
>>>>>
>>>>> As far as use cases, here are a few:
>>>>>
>>>>> In the NSEC5 use case for DNSSEC, you have sensitive data (domain
>>>>> names) and you sign consecutive pairs of hashes of domain names in or=
der to
>>>>> be able to prove absence of a name. If you just use standard hashing,
>>>>> whenever signed hash values are disclosed, your sensitive data is sub=
ject
>>>>> to dictionary attacks. VRFs solve that problem, and sensitive names d=
on't
>>>>> have to be disclosed at all. More details are in
>>>>> https://eprint.iacr.org/2017/099.pdf
>>>>>
>>>>> In CONIKS (also Google Key Transparency, Signal secure messaging,
>>>>> Yahoo! Coname) you also have some sensitive data (user names) that ar=
e put
>>>>> into a Merkle-like authenticated data structure. If you just use stan=
dard
>>>>> hashing, whenever hash values are disclosed, sensitive data is subjec=
t to
>>>>> dictionary attacks. If you use VRFs, sensitive data again can be disc=
losed
>>>>> only on an as-needed basis. More details are in
>>>>> https://eprint.iacr.org/2014/1004.pdf.
>>>>>
>>>>> In a cryptocurrency use case, you wish perform a coin flip that is
>>>>> deterministic and provably correct, but cannot be done by just anyone=
.
>>>>> More details are in https://people.csail.mit.ed
>>>>> u/nickolai/papers/gilad-algorand-eprint.pdf and possibly other
>>>>> cryptocurrency papers.
>>>>>
>>>>> Bryan Ford mentioned an additional usecase at the mic on Tuesday:
>>>>> distributed password protection protocols
>>>>>
>>>>> Many of these use case are already putting VRFs into production use
>>>>> (esp. the CONIKS one).  You can see a list of the various implementat=
ions
>>>>> we have found in the "implementation status" section of our draft.  O=
ne of
>>>>> the reasons we think this spec is so important is that we found flaws=
 in
>>>>> several of the implementations that can be used to trivially break
>>>>> uniqueness.  (See eg: https://github.com/google/
>>>>> keytransparency/issues/567)
>>>>>
>>>>> Thanks,
>>>>> Sharon
>>>>>
>>>>> On Fri, Jul 21, 2017 at 7:32 PM, Dan Brown <danibrown@blackberry.com>
>>>>> wrote:
>>>>>
>>>>>> Answering myself below: VRFs have been around since 1999, so are not
>>>>>> so new.  =E2=80=8EStill don't like the name, and still have trouble =
seeing the
>>>>>> value.
>>>>>>
>>>>>> *From: *Dan Brown
>>>>>> *Sent: *Tuesday, July 18, 2017 2:29 PM
>>>>>> *To: *Sharon Goldberg; cfrg@irtf.org
>>>>>> *Cc: *jan@ns1.com; Leonid Reyzin; Dimitrios Papadopoulos
>>>>>> *Subject: *Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>>>>>
>>>>>> Hi Sharon and CFRG,
>>>>>>
>>>>>>
>>>>>>
>>>>>> On VRFs, my uncertain comments to consider at your leisure:
>>>>>>
>>>>>>
>>>>>>
>>>>>> Is it fair to say VRFs are relatively new?  If so, then maybe a
>>>>>> little more caution is needed about their use.  It seems a tad hasty=
 that
>>>>>> it is being used already.
>>>>>>
>>>>>>
>>>>>>
>>>>>> To me, it seems that VRFs are basically signatures, with an extra
>>>>>> feature.  My concern is that this extra feature might get overused, =
before
>>>>>> it is thoroughly reviewed.
>>>>>>
>>>>>>
>>>>>>
>>>>>> It is unsurprising to me that random oracle model proof can prove th=
e
>>>>>> output of a hash to be random.  My intuitive concern is that at leas=
t
>>>>>> informally, this is kind of circular.  Hashes often have some
>>>>>> non-random-ish properties that might affect the extra security (over
>>>>>> signatures) that VRFs are aiming for.  I guess I would much prefer a=
 proof
>>>>>> saying if the hash has (well-studied) properties XYZ, then your
>>>>>> construction are VRFs.  (Maybe you have this already?  If so, then t=
ell me
>>>>>> so.)
>>>>>>
>>>>>>
>>>>>>
>>>>>> Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the wire=
, I find it hard
>>>>>> to see how it could be used to prevent dictionary attacks.  I assume=
 that
>>>>>> you are saying the proofs must be encrypted when one needs to avoid
>>>>>> dictionary models?  I suppose all the details are there in I-D and p=
apers,
>>>>>> but for now, I am confused about the threat model (which parties hav=
e keys,
>>>>>> etc., if they require a secure channel and mutual trust, why just us=
e plain
>>>>>> old hash,=E2=80=A6). To resist dictionary attacks, were already have=
 PAKEs and
>>>>>> PBHashing.  Now this?
>>>>>>
>>>>>>
>>>>>>
>>>>>> Finally, on a bikeshed-coloring note, I object to the name
>>>>>> =E2=80=9Cverifiable random function=E2=80=9D, on several grounds.
>>>>>>
>>>>>>
>>>>>>
>>>>>>    1. It is not a function.  It is at least four functions, keygen,
>>>>>>    sign, verify, and hashify.
>>>>>>    2. If you make it into a keyed function F_sk(m), as in
>>>>>>    prooftohash(sign_sk(m)), it is not verifiable.
>>>>>>    3. Verification requires the intermediate proof, which is
>>>>>>    certainly not even pseudorandom (it is easy to distinguish valid =
signatures
>>>>>>    from random).
>>>>>>    4. It is pseudorandom, not random.  (The keys are random, but
>>>>>>    many crypto has keys, without having =E2=80=9Crandom=E2=80=9D in =
its name: encryption, MAC,
>>>>>>    signatures, key exchange, =E2=80=A6, they also don=E2=80=99t veri=
fiable or random in their
>>>>>>    names either.)
>>>>>>    5. The similar phrase =E2=80=9Cverifiably random=E2=80=9D, albeit=
 as a misnomer,
>>>>>>    has past precedents, see NIST P-256 and Brainpool, etc.  When I s=
ee VRF, I
>>>>>>    think a function, that aims to VR in that sense, and great, now w=
e can
>>>>>>    improve on Brainpool, etc.
>>>>>>    6. =E2=80=9CRandom function=E2=80=9D should be reserved for the i=
deal random
>>>>>>    mapping concept, for example, as studied by Flajolet-Odlyzko (ok =
they only
>>>>>>    studied the case of equal size domain and range).  The random ora=
cle model,
>>>>>>    is the idea of approximating this ideal, etc.  An actual approxim=
ation
>>>>>>    should not be name as the ideal (sorry, I=E2=80=99m kind of repea=
ting my point 4).
>>>>>>
>>>>>>
>>>>>>
>>>>>> Please forgive the fact that my comments above are not very
>>>>>> constructive (or if the tone is wrong).  This is a new topic for me,=
 so I
>>>>>> am reluctant too many suggestions.  Nonetheless, I suggest (0) waiti=
ng a
>>>>>> little, (1) a non-random-oracle security proof (if you don=E2=80=99t=
 have it yet),
>>>>>> (2) re-naming the scheme to something like re-hashable (or digestibl=
e)
>>>>>> signatures (and re-name the various parts, i.e. proof -> signature, =
etc.).
>>>>>>
>>>>>>
>>>>>>
>>>>>> Best regards,
>>>>>>
>>>>>>
>>>>>>
>>>>>> Dan
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> *From:* Cfrg [mailto:cfrg-bounces@irtf.org] *On Behalf Of *Sharon
>>>>>> Goldberg
>>>>>> *Sent:* Wednesday, July 12, 2017 5:42 AM
>>>>>> *To:* cfrg@irtf.org
>>>>>> *Cc:* jan@ns1.com; Dimitrios Papadopoulos <dipapado@umd.edu>; Leonid
>>>>>> Reyzin <reyzin@cs.bu.edu>
>>>>>> *Subject:* [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>>>>>
>>>>>>
>>>>>>
>>>>>> Dear CFRG,
>>>>>>
>>>>>> I'm presenting at next week's meeting on Verifiable Random Functions=
.
>>>>>> A VRF is the public-key version of keyed cryptographic hash. Only th=
e
>>>>>> holder of the VRF secret key can compute the hash, but anyone with t=
he
>>>>>> public key can verify it.  VRFs can be used to prevent dictionary at=
tacks
>>>>>> on hash-based data structures, and have applications to key transpar=
ency
>>>>>> (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (Algorand).
>>>>>>
>>>>>> In advance of the meeting, please see:
>>>>>>
>>>>>> 1) Our substantially updated -01 draft:
>>>>>> https://datatracker.ietf.org/doc/draft-goldbe-vrf/
>>>>>>
>>>>>> 2) Our project page, with links to various VRF implementations:
>>>>>> https://www.cs.bu.edu/~goldbe/projects/vrf
>>>>>>
>>>>>> Comments welcome.  Thanks,
>>>>>>
>>>>>> Sharon
>>>>>>
>>>>>> --
>>>>>> Sharon Goldberg
>>>>>> Computer Science, Boston University
>>>>>> http://www.cs.bu.edu/~goldbe
>>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> ---
>>>>> Sharon Goldberg
>>>>> Computer Science, Boston University
>>>>> http://www.cs.bu.edu/~goldbe
>>>>>
>>>>> _______________________________________________
>>>>> Cfrg mailing list
>>>>> Cfrg@irtf.org
>>>>> https://www.irtf.org/mailman/listinfo/cfrg
>>>>>
>>>>>
>>>>
>>>
>>>
>>> --
>>> ---
>>> Sharon Goldberg
>>> Computer Science, Boston University
>>> http://www.cs.bu.edu/~goldbe
>>>
>>
>>
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org
>> https://www.irtf.org/mailman/listinfo/cfrg
>>
>>
>


--=20
---
Sharon Goldberg
Computer Science, Boston University
http://www.cs.bu.edu/~goldbe

--001a1148e222cad5c105559952ab
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div><div>It is &quot;verifiable pseudorandomness&quot;. (=
Not true randomness.)<br></div>Think of a pseudorandom function (PRF) that =
comes with a public key that allows anyone to check that the output of the =
PRF was computed correctly.<br><br></div>Sharon<br><div class=3D"gmail_extr=
a"><br><div class=3D"gmail_quote">On Sun, Jul 30, 2017 at 8:02 PM, Philip L=
 <span dir=3D"ltr">&lt;<a href=3D"mailto:philippl.lee@gmail.com" target=3D"=
_blank">philippl.lee@gmail.com</a>&gt;</span> wrote:<br><blockquote class=
=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padd=
ing-left:1ex"><div dir=3D"ltr">Please excuse the spam. I thought for just a=
 moment somehow that the function was verifiably random... like one of thos=
e hard problems (for decidability?).<br><br>Just a random thought...<br></d=
iv><div class=3D"m_2212788026349419488HOEnZb"><div class=3D"m_2212788026349=
419488h5"><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">On Thu,=
 Jul 27, 2017 at 4:51 AM, Thomas Garcia <span dir=3D"ltr">&lt;<a href=3D"ma=
ilto:tgarcia.3141@gmail.com" target=3D"_blank">tgarcia.3141@gmail.com</a>&g=
t;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0=
 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir=3D"ltr"><div><b=
r></div><div>Thanks for helping me clear those things up!</div><div><br></d=
iv><div>Thomas G.</div></div><div class=3D"m_2212788026349419488m_850783251=
8487412230HOEnZb"><div class=3D"m_2212788026349419488m_8507832518487412230h=
5"><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">On Wed, Jul 26=
, 2017 at 12:42 PM, Sharon Goldberg <span dir=3D"ltr">&lt;<a href=3D"mailto=
:sharon.goldbe@gmail.com" target=3D"_blank">sharon.goldbe@gmail.com</a>&gt;=
</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .=
8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir=3D"ltr">Hi Thomas=
,<div><br></div><div class=3D"gmail_extra"><div class=3D"gmail_quote"><span=
><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border=
-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir=3D"ltr"><div>1.=
 It seems that one of the properties that you are interested that the VRF w=
ill have is determinism. On the other hand, the EC-VRF value is dependent o=
n the choice of some random number k. How are these two facts compatible? A=
m I missing something?</div></div></blockquote><div><br></div></span><div>W=
e require determinism from the VRF hash output, which is obtained from the =
VRF proof via the &quot;proof2hash&quot; function.</div><div><br></div><div=
>The EC-VRF proof has 3 values: gamma, c, s</div><div>Values c and s depend=
s on the choice of random number k</div><div>But value gamma does not depen=
d on k.</div><div><br></div><div>We get determinism because the VRF hash ou=
tput (derived using &quot;proof2hash&quot;) depends only on gamma, but not =
on c and s.</div><div>=C2=A0</div><div>Slide 28 from my CFRG presentations =
gives a pictorial explanation of this:</div><div><a href=3D"http://www.cs.b=
u.edu/~goldbe/papers/VRF_ietf99_print.pdf" target=3D"_blank">http://www.cs.=
bu.edu/~goldbe/p<wbr>apers/VRF_ietf99_print.pdf</a><br></div><span><div><br=
></div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;=
border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir=3D"ltr"><=
div>2. The value c calculated in EC-VRF is only 128 bits long for Ed25519. =
In normal usage of Ed25519 the signature uses the full length of the hash o=
utput. Doesn&#39;t this expose the signature to collision attacks?</div><di=
v><br></div></div></blockquote></span><div>No. We worked this out in our pr=
oofs of security.=C2=A0 Section B.2.1 of this paper explains why this works=
.</div><div><br></div><div><a href=3D"https://eprint.iacr.org/2017/099.pdf"=
 target=3D"_blank">https://eprint.iacr.org/2017/0<wbr>99.pdf</a><br></div><=
div><br></div><div>Thanks,</div><div>Sharon</div><div><div class=3D"m_22127=
88026349419488m_8507832518487412230m_-5638161815282581577h5"><div><br></div=
><div>=C2=A0</div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px=
 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div cl=
ass=3D"gmail_extra"><div class=3D"gmail_quote"><blockquote class=3D"gmail_q=
uote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,2=
04);padding-left:1ex"><div><div class=3D"m_2212788026349419488m_85078325184=
87412230m_-5638161815282581577m_2913212881139340244gmail-h5"><div dir=3D"lt=
r"><div style=3D"font-size:12.8px"></div><div style=3D"font-size:12.8px">Th=
ank you for your comments. Indeed, VRFs have been around since 1999. They a=
re really &quot;verifiable PRFs&quot; but the name is by now standard in th=
e crypto literature, and changing it will cause more confusion than keeping=
 it.</div><div style=3D"font-size:12.8px"><br></div><div style=3D"font-size=
:12.8px">In terms of the VRF&#39;s security properties, there are three: =
=C2=A0uniqueness, collision resistance, and pseudorandomness. These are def=
ined in our draft (<span style=3D"font-size:12.8px"><a href=3D"https://tool=
s.ietf.org/html/draft-goldbe-vrf-01#section-3" target=3D"_blank">https://to=
ols.ietf.org/html/d<wbr>raft-goldbe-vrf-01#section-3</a></span><span style=
=3D"font-size:12.8px">).<wbr>=C2=A0</span></div><div style=3D"font-size:12.=
8px"><br></div><div style=3D"font-size:12.8px">How VRFs prevent dictionary =
attacks: a public hash is subject to a dictionary attack because, given the=
 output, an adversary can evaluate the hash on different inputs and see wha=
t hits the outputs. In a VRF, the adversary can&#39;t evaluate the hash on =
different inputs.=C2=A0</div><div style=3D"font-size:12.8px"><br></div><div=
 style=3D"font-size:12.8px">You say it&#39;s not surprising that &quot;rand=
om oracle model proof can prove the output of a hash to be random&quot;. Bu=
t actually, the output of a hash is NOT random if the input and the hash fu=
nction are known. This is because the output of a hash is deterministic (ev=
ery input maps to a unique output). That&#39;s exactly what enables diction=
ary attacks. This is in contrast to a VRF, where the output is (pseudo)rand=
om even given knowledge of the input. Only once the VRF proof is given, doe=
s the VRF output stop looking random. Note that random oracles are not esse=
ntial for VRFs, and non-random-oracles constructions exist (but are less ef=
ficient than what we propose to standardize).</div><div style=3D"font-size:=
12.8px"><br></div><div style=3D"font-size:12.8px">As far as use cases, here=
 are a few:=C2=A0</div><div style=3D"font-size:12.8px"><br></div><div style=
=3D"font-size:12.8px">In the NSEC5 use case for DNSSEC, you have sensitive =
data (domain names) and you sign consecutive pairs of hashes of domain name=
s in order to be able to prove absence of a name. If you just use standard =
hashing, whenever signed hash values are disclosed, your sensitive data is =
subject to dictionary attacks. VRFs solve that problem, and sensitive names=
 don&#39;t have to be disclosed at all. More details are in=C2=A0<a href=3D=
"https://eprint.iacr.org/2017/099.pdf" target=3D"_blank">https://eprint.iac=
r.org/201<wbr>7/099.pdf</a></div><div style=3D"font-size:12.8px"><br></div>=
<div style=3D"font-size:12.8px">In CONIKS (also Google Key Transparency, Si=
gnal secure messaging, Yahoo! Coname) you also have some sensitive data (us=
er names) that are put into a Merkle-like authenticated data structure. If =
you just use standard hashing, whenever hash values are disclosed, sensitiv=
e data is subject to dictionary attacks. If you use VRFs, sensitive data ag=
ain can be disclosed only on an as-needed basis. More details are in =C2=A0=
<a href=3D"https://eprint.iacr.org/2014/1004.pdf" target=3D"_blank">https:/=
/eprint.iacr.org/2014/<wbr>1004.pdf</a>.</div><div style=3D"font-size:12.8p=
x"><br></div><div style=3D"font-size:12.8px">In a cryptocurrency use case, =
you wish perform a coin flip that is deterministic and provably correct, bu=
t cannot be done by just anyone.=C2=A0 More details are in=C2=A0<a href=3D"=
https://people.csail.mit.edu/nickolai/papers/gilad-algorand-eprint.pdf" tar=
get=3D"_blank">https://people.csail.mit.ed<wbr>u/nickolai/papers/gilad-algo=
ra<wbr>nd-eprint.pdf</a>=C2=A0and possibly other cryptocurrency papers.</di=
v><div style=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8px"=
>Bryan Ford mentioned an additional usecase at the mic on Tuesday: distribu=
ted password protection protocols</div><div style=3D"font-size:12.8px"><br>=
</div><div style=3D"font-size:12.8px">Many of these use case are already pu=
tting VRFs into production use (esp. the CONIKS one).=C2=A0 You can see a l=
ist of the various implementations we have found in the &quot;implementatio=
n status&quot; section of our draft.=C2=A0 One of the reasons we think this=
 spec is so important is that we found flaws in several of the implementati=
ons that can be used to trivially break uniqueness. =C2=A0(See eg:=C2=A0<a =
href=3D"https://github.com/google/keytransparency/issues/567" target=3D"_bl=
ank">https://github.com/google/<wbr>keytransparency/issues/567</a>)</div><d=
iv style=3D"font-size:12.8px"><br></div><div style=3D"font-size:12.8px"><sp=
an style=3D"font-size:12.8px">Thanks,</span><br></div><div style=3D"font-si=
ze:12.8px">Sharon=C2=A0</div><div class=3D"gmail_extra"><div><div class=3D"=
m_2212788026349419488m_8507832518487412230m_-5638161815282581577m_291321288=
1139340244gmail-m_4922457647511857001h5"><br><div class=3D"gmail_quote">On =
Fri, Jul 21, 2017 at 7:32 PM, Dan Brown <span dir=3D"ltr">&lt;<a href=3D"ma=
ilto:danibrown@blackberry.com" target=3D"_blank">danibrown@blackberry.com</=
a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0=
px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">




<div lang=3D"EN-US">
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
Answering myself below: VRFs have been around since 1999, so are not so new=
. =C2=A0=E2=80=8EStill don&#39;t like the name, and still have trouble seei=
ng the value.</div>
<div style=3D"width:100%;font-size:initial;font-family:Calibri,&quot;Slate =
Pro&quot;,sans-serif,sans-serif;color:rgb(31,73,125);text-align:initial;bac=
kground-color:rgb(255,255,255)">
<span style=3D"font-family:Calibri,&quot;Slate Pro&quot;,sans-serif,sans-se=
rif;font-size:initial;line-height:initial;text-align:initial"><br>
</span></div>
<table style=3D"background-color:white" width=3D"100%">
<tbody>
<tr>
<td colspan=3D"2" style=3D"font-size:initial;text-align:initial;background-=
color:rgb(255,255,255)">
<div style=3D"border-style:solid none none;border-top-color:rgb(181,196,223=
);border-top-width:1pt;padding:3pt 0in 0in;font-family:Tahoma,&quot;BB Alph=
a Sans&quot;,&quot;Slate Pro&quot;;font-size:10pt">
<div><b>From: </b>Dan Brown</div>
<div><b>Sent: </b>Tuesday, July 18, 2017 2:29 PM</div>
<div><b>To: </b>Sharon Goldberg; <a href=3D"mailto:cfrg@irtf.org" target=3D=
"_blank">cfrg@irtf.org</a></div>
<div><b>Cc: </b><a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.co=
m</a>; Leonid Reyzin; Dimitrios Papadopoulos</div>
<div><b>Subject: </b>Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functio=
ns</div>
</div>
</td>
</tr>
</tbody>
</table><div><div class=3D"m_2212788026349419488m_8507832518487412230m_-563=
8161815282581577m_2913212881139340244gmail-m_4922457647511857001m_-61531017=
34044142155m_4165835283928257204gmail-h5">
<div style=3D"border-style:solid none none;border-top-color:rgb(186,188,209=
);border-top-width:1pt;font-size:initial;text-align:initial;background-colo=
r:rgb(255,255,255)">
</div>
<br>
<div>
<div class=3D"m_2212788026349419488m_8507832518487412230m_-5638161815282581=
577m_2913212881139340244gmail-m_4922457647511857001m_-6153101734044142155m_=
4165835283928257204gmail-m_6358749242748202832WordSection1">
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Hi Sharon and CFRG,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">On VRFs, my uncertain comments to consider at your leisure:</span=
></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Is it fair to say VRFs are relatively new?=C2=A0 If so, then mayb=
e a little more caution is needed about their use.=C2=A0 It seems a tad has=
ty that it is being used already.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">To me, it seems that VRFs are basically signatures, with an extra=
 feature.=C2=A0 My concern is that this extra feature might get overused, b=
efore it is thoroughly reviewed.=C2=A0
</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">It is unsurprising to me that random oracle model proof can prove=
 the output of a hash to be random.=C2=A0 My intuitive concern is that at l=
east informally, this is kind of circular.=C2=A0
 Hashes often have some non-random-ish properties that might affect the ext=
ra security (over signatures) that VRFs are aiming for.=C2=A0 I guess I wou=
ld much prefer a proof saying if the hash has (well-studied) properties XYZ=
, then your construction are VRFs.=C2=A0 (Maybe
 you have this already?=C2=A0 If so, then tell me so.)</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Since, VRFs require sending the =E2=80=9Cproofs=E2=80=9D on the w=
ire, I find it hard to see how it could be used to prevent dictionary attac=
ks.=C2=A0 I assume that you are saying the proofs must
 be encrypted when one needs to avoid dictionary models?=C2=A0 I suppose al=
l the details are there in I-D and papers, but for now, I am confused about=
 the threat model (which parties have keys, etc., if they require a secure =
channel and mutual trust, why just use
 plain old hash,=E2=80=A6). To resist dictionary attacks, were already have=
 PAKEs and PBHashing.=C2=A0 Now this?</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Finally, on a bikeshed-coloring note, I object to the name =E2=80=
=9Cverifiable random function=E2=80=9D, on several grounds.</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<ol start=3D"1" style=3D"margin-top:0in" type=3D"1">
<li class=3D"m_2212788026349419488m_8507832518487412230m_-56381618152825815=
77m_2913212881139340244gmail-m_4922457647511857001m_-6153101734044142155m_4=
165835283928257204gmail-m_6358749242748202832MsoListParagraph" style=3D"mar=
gin-left:0in"><span style=3D"font-size:11pt;font-family:Calibri,sans-serif"=
>It is not a function.=C2=A0 It is at least four functions, keygen, sign, v=
erify, and hashify.</span></li><li class=3D"m_2212788026349419488m_85078325=
18487412230m_-5638161815282581577m_2913212881139340244gmail-m_4922457647511=
857001m_-6153101734044142155m_4165835283928257204gmail-m_635874924274820283=
2MsoListParagraph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;=
font-family:Calibri,sans-serif">If you make it into a keyed function F_sk(m=
), as in prooftohash(sign_sk(m)), it is not verifiable.=C2=A0
</span></li><li class=3D"m_2212788026349419488m_8507832518487412230m_-56381=
61815282581577m_2913212881139340244gmail-m_4922457647511857001m_-6153101734=
044142155m_4165835283928257204gmail-m_6358749242748202832MsoListParagraph" =
style=3D"margin-left:0in"><span style=3D"font-size:11pt;font-family:Calibri=
,sans-serif">Verification requires the intermediate proof, which is certain=
ly not even pseudorandom (it is easy to distinguish valid signatures from r=
andom).</span></li><li class=3D"m_2212788026349419488m_8507832518487412230m=
_-5638161815282581577m_2913212881139340244gmail-m_4922457647511857001m_-615=
3101734044142155m_4165835283928257204gmail-m_6358749242748202832MsoListPara=
graph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;font-family:=
Calibri,sans-serif">It is pseudorandom, not random.=C2=A0 (The keys are ran=
dom, but many crypto has keys, without having =E2=80=9Crandom=E2=80=9D in i=
ts name: encryption, MAC, signatures,
 key exchange, =E2=80=A6, they also don=E2=80=99t verifiable or random in t=
heir names either.)</span></li><li class=3D"m_2212788026349419488m_85078325=
18487412230m_-5638161815282581577m_2913212881139340244gmail-m_4922457647511=
857001m_-6153101734044142155m_4165835283928257204gmail-m_635874924274820283=
2MsoListParagraph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;=
font-family:Calibri,sans-serif">The similar phrase =E2=80=9Cverifiably rand=
om=E2=80=9D, albeit as a misnomer, has past precedents, see NIST P-256 and =
Brainpool, etc.=C2=A0 When I see VRF, I think
 a function, that aims to VR in that sense, and great, now we can improve o=
n Brainpool, etc.</span></li><li class=3D"m_2212788026349419488m_8507832518=
487412230m_-5638161815282581577m_2913212881139340244gmail-m_492245764751185=
7001m_-6153101734044142155m_4165835283928257204gmail-m_6358749242748202832M=
soListParagraph" style=3D"margin-left:0in"><span style=3D"font-size:11pt;fo=
nt-family:Calibri,sans-serif">=E2=80=9CRandom function=E2=80=9D should be r=
eserved for the ideal random mapping concept, for example, as studied by Fl=
ajolet-Odlyzko (ok they only studied
 the case of equal size domain and range).=C2=A0 The random oracle model, i=
s the idea of approximating this ideal, etc.=C2=A0 An actual approximation =
should not be name as the ideal (sorry, I=E2=80=99m kind of repeating my po=
int 4).</span></li></ol>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Please forgive the fact that my comments above are not very const=
ructive (or if the tone is wrong).=C2=A0 This is a new topic for me, so I a=
m reluctant too many suggestions.=C2=A0 Nonetheless,
 I suggest (0) waiting a little, (1) a non-random-oracle security proof (if=
 you don=E2=80=99t have it yet), (2) re-naming the scheme to something like=
 re-hashable (or digestible) signatures (and re-name the various parts, i.e=
. proof -&gt; signature, etc.).</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Best regards,</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">Dan</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><span style=3D"font-size:11pt;font-family:Calibri,sa=
ns-serif">=C2=A0</span></p>
<p class=3D"MsoNormal"><b><span style=3D"font-size:11pt;font-family:Calibri=
,sans-serif">From:</span></b><span style=3D"font-size:11pt;font-family:Cali=
bri,sans-serif"> Cfrg [mailto:<a href=3D"mailto:cfrg-bounces@irtf.org" targ=
et=3D"_blank">cfrg-bounces@irtf.org</a>]
<b>On Behalf Of </b>Sharon Goldberg<br>
<b>Sent:</b> Wednesday, July 12, 2017 5:42 AM<br>
<b>To:</b> <a href=3D"mailto:cfrg@irtf.org" target=3D"_blank">cfrg@irtf.org=
</a><br>
<b>Cc:</b> <a href=3D"mailto:jan@ns1.com" target=3D"_blank">jan@ns1.com</a>=
; Dimitrios Papadopoulos &lt;<a href=3D"mailto:dipapado@umd.edu" target=3D"=
_blank">dipapado@umd.edu</a>&gt;; Leonid Reyzin &lt;<a href=3D"mailto:reyzi=
n@cs.bu.edu" target=3D"_blank">reyzin@cs.bu.edu</a>&gt;<br>
<b>Subject:</b> [Cfrg] draft-goldbe-vrf: Verifiable Random Functions</span>=
</p>
<p class=3D"MsoNormal">=C2=A0</p>
<div>
<p class=3D"MsoNormal">Dear CFRG,<br>
<br>
I&#39;m presenting at next week&#39;s meeting on Verifiable Random Function=
s. A VRF is the public-key version of keyed cryptographic hash. Only the ho=
lder of the VRF secret key can compute the hash, but anyone with the public=
 key can verify it.=C2=A0 VRFs can be used to
 prevent dictionary attacks on hash-based data structures, and have applica=
tions to key transparency (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (A=
lgorand).<br>
<br>
In advance of the meeting, please see:<br>
<br>
1) Our substantially updated -01 draft:<br>
<a href=3D"https://datatracker.ietf.org/doc/draft-goldbe-vrf/" target=3D"_b=
lank">https://datatracker.ietf.org/d<wbr>oc/draft-goldbe-vrf/</a><br>
<br>
2) Our project page, with links to various VRF implementations:<br>
<a href=3D"https://www.cs.bu.edu/~goldbe/projects/vrf" target=3D"_blank">ht=
tps://www.cs.bu.edu/~goldbe/<wbr>projects/vrf</a><br>
<br>
Comments welcome.=C2=A0 Thanks,<br>
<br>
Sharon<br>
<br>
--<br>
Sharon Goldberg<br>
Computer Science, Boston University<br>
<a href=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu=
.edu/~goldbe</a></p>
</div>
</div>
</div>
</div></div></div>

</blockquote></div><br><br clear=3D"all"><div><br></div></div></div>-- <br>=
<div class=3D"m_2212788026349419488m_8507832518487412230m_-5638161815282581=
577m_2913212881139340244gmail-m_4922457647511857001m_-6153101734044142155m_=
4165835283928257204gmail_signature">---<span><br>Sharon Goldberg<br>Compute=
r Science, Boston University<br><a href=3D"http://www.cs.bu.edu/~goldbe" ta=
rget=3D"_blank">http://www.cs.bu.edu/~goldbe</a></span></div>
</div></div>
<br></div></div><span class=3D"m_2212788026349419488m_8507832518487412230m_=
-5638161815282581577m_2913212881139340244gmail-">__________________________=
____<wbr>_________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/l<wbr>istinfo/cfrg</a><br>
<br></span></blockquote></div><br></div>
</blockquote></div></div></div><div><div class=3D"m_2212788026349419488m_85=
07832518487412230m_-5638161815282581577h5"><br><br clear=3D"all"><div><br><=
/div>-- <br><div class=3D"m_2212788026349419488m_8507832518487412230m_-5638=
161815282581577m_2913212881139340244gmail_signature">---<br>Sharon Goldberg=
<br>Computer Science, Boston University<br><a href=3D"http://www.cs.bu.edu/=
~goldbe" target=3D"_blank">http://www.cs.bu.edu/~goldbe</a></div>
</div></div></div></div>
</blockquote></div><br></div>
</div></div><br>______________________________<wbr>_________________<br>
Cfrg mailing list<br>
<a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank">Cfrg@irtf.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferrer" t=
arget=3D"_blank">https://www.irtf.org/mailman/l<wbr>istinfo/cfrg</a><br>
<br></blockquote></div><br></div>
</div></div></blockquote></div><br><br clear=3D"all"><br>-- <br><div class=
=3D"m_2212788026349419488gmail_signature" data-smartmail=3D"gmail_signature=
">---<br>Sharon Goldberg<br>Computer Science, Boston University<br><a href=
=3D"http://www.cs.bu.edu/~goldbe" target=3D"_blank">http://www.cs.bu.edu/~g=
oldbe</a></div>
</div></div>

--001a1148e222cad5c105559952ab--

