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   New version of the PKEX protocol... changes include cleaning up of how
proof-of-possession is accomplished and some new role-specific (SPAKE2)
elements for some popular FFC groups from RFC 3256.

   This protocol allows for the establishment of trust in "raw" public keys
to be used, subsequently, in protocols like IPsec or TLS.

   Comments are solicited!

   regards,

   Dan.

-------- Forwarded Message --------
Subject: 	New Version Notification for draft-harkins-pkex-03.txt
Date: 	Mon, 02 Jan 2017 21:00:19 -0800
From: 	internet-drafts@ietf.org
To: 	Dan Harkins <dharkins@lounge.org>



A new version of I-D, draft-harkins-pkex-03.txt
has been successfully submitted by Dan Harkins and posted to the
IETF repository.

Name:		draft-harkins-pkex
Revision:	03
Title:		Public Key Exchange
Document date:	2017-01-02
Group:		Individual Submission
Pages:		30
URL:            https://www.ietf.org/internet-drafts/draft-harkins-pkex-03.txt
Status:         https://datatracker.ietf.org/doc/draft-harkins-pkex/
Htmlized:       https://tools.ietf.org/html/draft-harkins-pkex-03
Diff:           https://www.ietf.org/rfcdiff?url2=draft-harkins-pkex-03

Abstract:
    This memo describes a password-authenticated protocol to allow two
    devices to exchange "raw" (uncertified) public keys and establish
    trust that the keys belong to their respective identities.

                                                                                   


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.

The IETF Secretariat


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<html>
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    <meta http-equiv="content-type" content="text/html; charset=utf-8">
  </head>
  <body bgcolor="#FFFFFF" text="#000000">
    <br>
    <div class="moz-forward-container">  New version of the PKEX
      protocol... changes include cleaning up of how<br>
      proof-of-possession is accomplished and some new role-specific
      (SPAKE2)<br>
      elements for some popular FFC groups from RFC 3256.<br>
      <br>
        This protocol allows for the establishment of trust in "raw"
      public keys<br>
      to be used, subsequently, in protocols like IPsec or TLS. <br>
      <br>
        Comments are solicited!<br>
      <br>
        regards,<br>
      <br>
        Dan.<br>
      <br>
      -------- Forwarded Message --------
      <table class="moz-email-headers-table" border="0" cellpadding="0"
        cellspacing="0">
        <tbody>
          <tr>
            <th align="RIGHT" valign="BASELINE" nowrap="nowrap">Subject:
            </th>
            <td>New Version Notification for draft-harkins-pkex-03.txt</td>
          </tr>
          <tr>
            <th align="RIGHT" valign="BASELINE" nowrap="nowrap">Date: </th>
            <td>Mon, 02 Jan 2017 21:00:19 -0800</td>
          </tr>
          <tr>
            <th align="RIGHT" valign="BASELINE" nowrap="nowrap">From: </th>
            <td><a class="moz-txt-link-abbreviated" href="mailto:internet-drafts@ietf.org">internet-drafts@ietf.org</a></td>
          </tr>
          <tr>
            <th align="RIGHT" valign="BASELINE" nowrap="nowrap">To: </th>
            <td>Dan Harkins <a class="moz-txt-link-rfc2396E" href="mailto:dharkins@lounge.org">&lt;dharkins@lounge.org&gt;</a></td>
          </tr>
        </tbody>
      </table>
      <br>
      <br>
      <pre>A new version of I-D, draft-harkins-pkex-03.txt
has been successfully submitted by Dan Harkins and posted to the
IETF repository.

Name:		draft-harkins-pkex
Revision:	03
Title:		Public Key Exchange
Document date:	2017-01-02
Group:		Individual Submission
Pages:		30
URL:            <a class="moz-txt-link-freetext" href="https://www.ietf.org/internet-drafts/draft-harkins-pkex-03.txt">https://www.ietf.org/internet-drafts/draft-harkins-pkex-03.txt</a>
Status:         <a class="moz-txt-link-freetext" href="https://datatracker.ietf.org/doc/draft-harkins-pkex/">https://datatracker.ietf.org/doc/draft-harkins-pkex/</a>
Htmlized:       <a class="moz-txt-link-freetext" href="https://tools.ietf.org/html/draft-harkins-pkex-03">https://tools.ietf.org/html/draft-harkins-pkex-03</a>
Diff:           <a class="moz-txt-link-freetext" href="https://www.ietf.org/rfcdiff?url2=draft-harkins-pkex-03">https://www.ietf.org/rfcdiff?url2=draft-harkins-pkex-03</a>

Abstract:
   This memo describes a password-authenticated protocol to allow two
   devices to exchange "raw" (uncertified) public keys and establish
   trust that the keys belong to their respective identities.

                                                                                  


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.

The IETF Secretariat

</pre>
    </div>
  </body>
</html>

--------------DEED00776CC2543121A26FCA--


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From: Sean Turner <sean@sn3rd.com>
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Date: Wed, 4 Jan 2017 16:55:44 -0500
To: IRTF CFRG <cfrg@irtf.org>
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Subject: [Cfrg] Help with the use of contexts
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Hi CFRG,

The TLS WG is nearing the end of our journey moving EC-based algorithms =
for TLS 1.2 (and earlier) from Informational to Standards track [0].  =
While we were doing that we also added in 25519 and x448 as well as =
EdDSA.

I=E2=80=99d like to get some input from the CFRG on the use of contexts; =
the "context label" is a way to provide domain separation between =
signatures made in different contexts, avoiding cross-protocol attacks.  =
s10.3 of draft-irtf-cfrg-eddsa includes the following:

Contexts SHOULD NOT be used opportunistically, as that kind of use
is very error-prone.  If contexts are used, one SHOULD require all
signature schemes available for use in that purpose support
contexts.

This is great advice for new protocols because it=E2=80=99s easy to make =
all the schemes the same, but for existing protocols like TLS where =
there=E2=80=99s zero chance of obsoleting the existing signature schemes =
and defining new signature schemes with contexts it makes you wonder =
what =E2=80=9Copportunistically=E2=80=9D means. I.e., would setting a =
context parameter for Ed448 and no other already defined signature =
scheme be considered opportunistic?

spt
(as document Shepherd for draft-ietf-tls-rfc4492bis)

[0] https://datatracker.ietf.org/doc/draft-ietf-tls-rfc4492bis/=


From nobody Thu Jan  5 06:04:42 2017
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From: Mike Hamburg <mike@shiftleft.org>
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Subject: Re: [Cfrg] Removing the magic constants from SPAKE2
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> On Jan 8, 2014, at 6:19 PM, Michael Hamburg <mike@shiftleft.org> =
wrote:
>=20
> =E2=80=A6 The goal of this post is to suggest that a SPAKE2 variant =
might be a suitable standardized PAKE now that SPAKE2 itself is out of =
patent=E2=80=A6

I have been reminded that I am not a patent lawyer, that I am not aware =
of all patents in existence, and in general that I should shut up about =
patents.  If you are thinking of deploying SPAKE2, a variant of it, or =
some other PAKE, please consult your legal team to do a patent search.  =
Please do not rely on my statement from 2014.

Also, the "Elligator version of SPAKE2=E2=80=9D that I=E2=80=99d hoped =
to deploy is actually something very old: it is an elliptic curve =
instantiation of PAK:

http://www.iacr.org/archive/eurocrypt2000/1807/18070157-new.pdf =
<http://www.iacr.org/archive/eurocrypt2000/1807/18070157-new.pdf>

Happy 2017,
=E2=80=94 Mike


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<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""><br class=3D""><div><blockquote type=3D"cite" class=3D""><div =
class=3D"">On Jan 8, 2014, at 6:19 PM, Michael Hamburg &lt;<a =
href=3D"mailto:mike@shiftleft.org" class=3D"">mike@shiftleft.org</a>&gt; =
wrote:</div><br class=3D"Apple-interchange-newline"><div class=3D""><div =
class=3D"">=E2=80=A6 The goal of this post is to suggest that a SPAKE2 =
variant might be a suitable standardized PAKE now that SPAKE2 itself is =
out of patent=E2=80=A6</div></div></blockquote><br class=3D""></div><div>I=
 have been reminded that I am not a patent lawyer, that I am not aware =
of all patents in existence, and in general that I should shut up about =
patents. &nbsp;If you are thinking of deploying SPAKE2, a variant of it, =
or some other PAKE, please consult your legal team to do a patent =
search. &nbsp;Please do not rely on my statement from =
2014.</div><div><br class=3D""></div><div>Also, the "Elligator version =
of SPAKE2=E2=80=9D that I=E2=80=99d hoped to deploy is actually =
something very old: it is an elliptic curve instantiation of =
PAK:</div><div><br class=3D""></div><div><a =
href=3D"http://www.iacr.org/archive/eurocrypt2000/1807/18070157-new.pdf" =
class=3D"">http://www.iacr.org/archive/eurocrypt2000/1807/18070157-new.pdf=
</a></div><div><br class=3D""></div><div>Happy 2017,</div><div>=E2=80=94 =
Mike</div><div><br class=3D""></div></body></html>=

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From nobody Tue Jan 10 16:22:27 2017
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From: Dan Harkins <dharkins@lounge.org>
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Subject: Re: [Cfrg] AES-GCM-SIV with a new key hierarchy
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   Hello,

On 6/24/16 10:10 AM, Gueron, Shay wrote:
> Hello everyone,
>
> I start a new tread.
>
> It is a branch off the one entitled "AES-GCM-SIV security of the 
> additional data" and initiated by Daniel.
>
> It combine Kenny's inputs about having two separate keys and the AEADE 
> interface (which he raised at the CFRG meeting in
> Vienna in May and also mentioned, in the previous thread, that 
> concatenating 2 separate keys does not solve the problem that Daniel 
> raised).
>
> It also address a comment that Bart Preneel made at that CFRG meeting.
>
> ****
>
> It is possible to define AES-GCM-SIV with a standard interface that 
> has a single key (say, MK for "Master Key"), which can be 128 or 256 
> bits. Basically, by adding the following key derivation step:
>
>     Using MK, derive two new keys K and H: K for encryption and H for 
> authentication.
>     From that point on, apply AES-GCM-SIV as it is defined now, where 
> (K, H) are the keys.
>
> Note that K and H are derived statically from MK. The "record 
> encryption key" for the encryption depends on the nonce N, via another 
> derivation, as it is currently defined in AES-GCM-SIV.
>
> Note: the derivations are different for the 128 and the 256 bit keys, 
> but such derivations are already in use by AES-GCM-SIV.
> With this, AES-GM-SIV could be used with the protocol Daniel 
> described, and would address Kenny's comment on the AEAD interface.
> (I guess that it could be better viewed as a drop in replacement to 
> AES-GCM)
>
> The cost is the additional key derivation. this cost could be low if 
> the message is long, or if many messages are encrypted (so that K, H 
> can be cached).
>
> An alternative would be to incorporate the nonce from the beginning, 
> during the derivation of K, H from MK. This will modify the record 
> encryption key and also the hash key per each nonce. In that case the 
> extra derivation of the record encryption key (per nonce) could be 
> skipped (but also could be not done).
>
> I would appreciate any comments on this.

   Why not just have a single double-wide key the way AES-SIV (RFC 5297) 
does?
It's 256 bits or 512 bits. KDFs are good at generating streams of any 
length so
why not just let the KDF give you all that you need instead of doing 
additional
derivations inside?

   regards,

   Dan.

>
> Thanks, Shay
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg


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From: Shay Gueron <shay.gueron@gmail.com>
Date: Thu, 12 Jan 2017 12:01:16 +0200
Message-ID: <CAHP81y-SJZRANmSXsvABD3Gw0aRv+ZKm8uy0B6XNYp_f=0cE2w@mail.gmail.com>
To: Dan Harkins <dharkins@lounge.org>
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Cc: Yehuda Lindell <Yehuda.Lindell@biu.ac.il>, cfrg@irtf.org
Subject: Re: [Cfrg] AES-GCM-SIV with a new key hierarchy
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--94eb2c0327c46417830545e2cc8c
Content-Type: text/plain; charset=UTF-8

Hi Dan,

Thanks for your question.

In general, some KDF is needed, in order to increase the number of times
that the algorithm can be used with a given key. So, we start with a KDF
that has a master key and derives a new key(s)  per nonce.

The "cascade" method we use now is also some kind of a KDF, and there can
be others.

However, your timing with this question is fantastic. Indeed, we were not
satisfied with the serialized nature of the current KDF, and are working on
a different (better) one. This work is coming to an end, and we expect to
post the revision of AES-GCM-SIV next week.

Thanks, Shay


2017-01-10 16:22 GMT-08:00 Dan Harkins <dharkins@lounge.org>:

>
>   Hello,
>
> On 6/24/16 10:10 AM, Gueron, Shay wrote:
>
>> Hello everyone,
>>
>> I start a new tread.
>>
>> It is a branch off the one entitled "AES-GCM-SIV security of the
>> additional data" and initiated by Daniel.
>>
>> It combine Kenny's inputs about having two separate keys and the AEADE
>> interface (which he raised at the CFRG meeting in
>> Vienna in May and also mentioned, in the previous thread, that
>> concatenating 2 separate keys does not solve the problem that Daniel
>> raised).
>>
>> It also address a comment that Bart Preneel made at that CFRG meeting.
>>
>> ****
>>
>> It is possible to define AES-GCM-SIV with a standard interface that has a
>> single key (say, MK for "Master Key"), which can be 128 or 256 bits.
>> Basically, by adding the following key derivation step:
>>
>>     Using MK, derive two new keys K and H: K for encryption and H for
>> authentication.
>>     From that point on, apply AES-GCM-SIV as it is defined now, where (K,
>> H) are the keys.
>>
>> Note that K and H are derived statically from MK. The "record encryption
>> key" for the encryption depends on the nonce N, via another derivation, as
>> it is currently defined in AES-GCM-SIV.
>>
>> Note: the derivations are different for the 128 and the 256 bit keys, but
>> such derivations are already in use by AES-GCM-SIV.
>> With this, AES-GM-SIV could be used with the protocol Daniel described,
>> and would address Kenny's comment on the AEAD interface.
>> (I guess that it could be better viewed as a drop in replacement to
>> AES-GCM)
>>
>> The cost is the additional key derivation. this cost could be low if the
>> message is long, or if many messages are encrypted (so that K, H can be
>> cached).
>>
>> An alternative would be to incorporate the nonce from the beginning,
>> during the derivation of K, H from MK. This will modify the record
>> encryption key and also the hash key per each nonce. In that case the extra
>> derivation of the record encryption key (per nonce) could be skipped (but
>> also could be not done).
>>
>> I would appreciate any comments on this.
>>
>
>   Why not just have a single double-wide key the way AES-SIV (RFC 5297)
> does?
> It's 256 bits or 512 bits. KDFs are good at generating streams of any
> length so
> why not just let the KDF give you all that you need instead of doing
> additional
> derivations inside?
>
>   regards,
>
>   Dan.
>
>
>> Thanks, Shay
>>
>> _______________________________________________
>> 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
>

--94eb2c0327c46417830545e2cc8c
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

<div dir=3D"rtl"><div dir=3D"ltr">Hi Dan,=C2=A0</div><div dir=3D"ltr"><br><=
/div><div dir=3D"ltr">Thanks for your question.=C2=A0</div><div dir=3D"ltr"=
><br></div><div dir=3D"ltr">In general, some KDF is needed, in order to inc=
rease the number of times that the algorithm can be used with a given key. =
So, we start with a KDF that has a master key and derives a new key(s) =C2=
=A0per nonce.=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">The &q=
uot;cascade&quot; method we use now is also some kind of a KDF, and there c=
an be others.=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">Howeve=
r, your timing with this question is fantastic. Indeed, we were not satisfi=
ed with the serialized nature of the current KDF, and are working on a diff=
erent (better) one. This work is coming to an end, and we expect to post th=
e revision of AES-GCM-SIV next week.=C2=A0</div><div dir=3D"ltr"><br></div>=
<div dir=3D"ltr">Thanks, Shay</div><div dir=3D"ltr"><br></div></div><div cl=
ass=3D"gmail_extra"><br><div class=3D"gmail_quote"><div dir=3D"ltr">2017-01=
-10 16:22 GMT-08:00 Dan Harkins <span dir=3D"ltr">&lt;<a href=3D"mailto:dha=
rkins@lounge.org" target=3D"_blank">dharkins@lounge.org</a>&gt;</span>:</di=
v><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:=
1px #ccc solid;padding-left:1ex"><br>
=C2=A0 Hello,<span class=3D""><br>
<br>
On 6/24/16 10:10 AM, Gueron, Shay wrote:<br>
<blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p=
x #ccc solid;padding-left:1ex">
Hello everyone,<br>
<br>
I start a new tread.<br>
<br>
It is a branch off the one entitled &quot;AES-GCM-SIV security of the addit=
ional data&quot; and initiated by Daniel.<br>
<br>
It combine Kenny&#39;s inputs about having two separate keys and the AEADE =
interface (which he raised at the CFRG meeting in<br>
Vienna in May and also mentioned, in the previous thread, that concatenatin=
g 2 separate keys does not solve the problem that Daniel raised).<br>
<br>
It also address a comment that Bart Preneel made at that CFRG meeting.<br>
<br>
****<br>
<br>
It is possible to define AES-GCM-SIV with a standard interface that has a s=
ingle key (say, MK for &quot;Master Key&quot;), which can be 128 or 256 bit=
s. Basically, by adding the following key derivation step:<br>
<br>
=C2=A0 =C2=A0 Using MK, derive two new keys K and H: K for encryption and H=
 for authentication.<br>
=C2=A0 =C2=A0 From that point on, apply AES-GCM-SIV as it is defined now, w=
here (K, H) are the keys.<br>
<br>
Note that K and H are derived statically from MK. The &quot;record encrypti=
on key&quot; for the encryption depends on the nonce N, via another derivat=
ion, as it is currently defined in AES-GCM-SIV.<br>
<br>
Note: the derivations are different for the 128 and the 256 bit keys, but s=
uch derivations are already in use by AES-GCM-SIV.<br>
With this, AES-GM-SIV could be used with the protocol Daniel described, and=
 would address Kenny&#39;s comment on the AEAD interface.<br>
(I guess that it could be better viewed as a drop in replacement to AES-GCM=
)<br>
<br>
The cost is the additional key derivation. this cost could be low if the me=
ssage is long, or if many messages are encrypted (so that K, H can be cache=
d).<br>
<br>
An alternative would be to incorporate the nonce from the beginning, during=
 the derivation of K, H from MK. This will modify the record encryption key=
 and also the hash key per each nonce. In that case the extra derivation of=
 the record encryption key (per nonce) could be skipped (but also could be =
not done).<br>
<br>
I would appreciate any comments on this.<br>
</blockquote>
<br></span>
=C2=A0 Why not just have a single double-wide key the way AES-SIV (RFC 5297=
) does?<br>
It&#39;s 256 bits or 512 bits. KDFs are good at generating streams of any l=
ength so<br>
why not just let the KDF give you all that you need instead of doing additi=
onal<br>
derivations inside?<br>
<br>
=C2=A0 regards,<br>
<br>
=C2=A0 Dan.<br>
<br>
<blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p=
x #ccc solid;padding-left:1ex">
<br>
Thanks, Shay<span class=3D""><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>
</span></blockquote><div class=3D"HOEnZb"><div class=3D"h5">
<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>
</div></div></blockquote></div><br></div>

--94eb2c0327c46417830545e2cc8c--


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To: IRTF CFRG <cfrg@irtf.org>
Date: Thu, 12 Jan 2017 08:24:44 +0200
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Subject: [Cfrg] Fwd:  Rev RFC 7539?
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Reminder.

Is there interest in pushing this forward?

Yoav

> Begin forwarded message:
>=20
> From: Yoav Nir <ynir.ietf@gmail.com>
> Subject: Re: [Cfrg] Rev RFC 7539?
> Date: 16 November 2016 at 9:09:11 GMT+2
> To: Sean Turner <sean@sn3rd.com>
> Cc: IRTF CFRG <cfrg@irtf.org>
>=20
> Cycles found.
>=20
> Attached please find two files:
>   1. rfc7539_long.txt is RFC 7539 with page breaks and page numbers =
removed.=20
>  2. draft-nir-cfrg-rfc7539bis-00.raw.txt is the unpaginated form of =
the new draft.
>=20
> Couldn=E2=80=99t do much about the boilerplate, but this makes it easy =
to compare.
>=20
> Yoav
>=20
>=20
>=20
>> On 16 Nov 2016, at 10:06, Sean Turner <sean@sn3rd.com =
<mailto:sean@sn3rd.com>> wrote:
>>=20
>> +1 - if you got the cycles.
>>=20
>> spt
>>=20
>>> On Nov 14, 2016, at 15:55, Eric Rescorla <ekr@rtfm.com =
<mailto:ekr@rtfm.com>> wrote:
>>>=20
>>> This seems like a good plan.
>>>=20
>>> -Ekr
>>>=20
>>>=20
>>> On Mon, Nov 14, 2016 at 3:32 PM, Yoav Nir <ynir.ietf@gmail.com =
<mailto:ynir.ietf@gmail.com>> wrote:
>>> Hi
>>>=20
>>> RFC 7539 (=E2=80=9CChaCha20 and Poly1305 for IETF Protocols=E2=80=9D)[=
1] is now implemented in many places and referenced by 3 RFCs and 8 =
Internet Drafts ([2])
>>>=20
>>> However, the quality of the document is not where we=E2=80=99d like =
it to be. There have been 7 errata filed against it. Most of it is =
editorial or insignificant, but still no errata is better than some =
errata.
>>>=20
>>> So what do the participants and chairs think about spinning up a =
quick[4] rfc7539bis that has the same text, except that the errata will =
be merged in?
>>>=20
>>> I think such a document should be fairly easy and quick.
>>>=20
>>> Yoav
>>>=20
>>> P.S: and yes, of course I=E2=80=99m volunteering to write it.
>>>=20
>>> [1] https://tools.ietf.org/html/rfc7539 =
<https://tools.ietf.org/html/rfc7539>
>>> [2] https://datatracker.ietf.org/doc/rfc7539/referencedby/ =
<https://datatracker.ietf.org/doc/rfc7539/referencedby/>
>>> [3] https://www.rfc-editor.org/errata_search.php?rfc=3D7539 =
<https://www.rfc-editor.org/errata_search.php?rfc=3D7539>
>>> [4] My spell check actually corrected =E2=80=9Cquick=E2=80=9D to =
=E2=80=9Cquic=E2=80=9D. The contents of my mails are veering far away =
from regular English.
>>>=20
>>>=20
>>> _______________________________________________
>>> Cfrg mailing list
>>> Cfrg@irtf.org <mailto:Cfrg@irtf.org>
>>> https://www.irtf.org/mailman/listinfo/cfrg
>>>=20
>>>=20
>>> _______________________________________________
>>> Cfrg mailing list
>>> Cfrg@irtf.org
>>> https://www.irtf.org/mailman/listinfo/cfrg
>>=20
>=20


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<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"">Reminder.<div class=3D""><br class=3D""></div><div =
class=3D"">Is there interest in pushing this forward?</div><div =
class=3D""><br class=3D""></div><div class=3D"">Yoav<br =
class=3D""><div><br class=3D""><blockquote type=3D"cite" class=3D""><div =
class=3D"">Begin forwarded message:</div><br =
class=3D"Apple-interchange-newline"><div style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=3D""><span=
 style=3D"font-family: -webkit-system-font, Helvetica Neue, Helvetica, =
sans-serif; color:rgba(0, 0, 0, 1.0);" class=3D""><b class=3D"">From: =
</b></span><span style=3D"font-family: -webkit-system-font, Helvetica =
Neue, Helvetica, sans-serif;" class=3D"">Yoav Nir &lt;<a =
href=3D"mailto:ynir.ietf@gmail.com" =
class=3D"">ynir.ietf@gmail.com</a>&gt;<br class=3D""></span></div><div =
style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; =
margin-left: 0px;" class=3D""><span style=3D"font-family: =
-webkit-system-font, Helvetica Neue, Helvetica, sans-serif; =
color:rgba(0, 0, 0, 1.0);" class=3D""><b class=3D"">Subject: =
</b></span><span style=3D"font-family: -webkit-system-font, Helvetica =
Neue, Helvetica, sans-serif;" class=3D""><b class=3D"">Re: [Cfrg] Rev =
RFC 7539?</b><br class=3D""></span></div><div style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=3D""><span=
 style=3D"font-family: -webkit-system-font, Helvetica Neue, Helvetica, =
sans-serif; color:rgba(0, 0, 0, 1.0);" class=3D""><b class=3D"">Date: =
</b></span><span style=3D"font-family: -webkit-system-font, Helvetica =
Neue, Helvetica, sans-serif;" class=3D"">16 November 2016 at 9:09:11 =
GMT+2<br class=3D""></span></div><div style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=3D""><span=
 style=3D"font-family: -webkit-system-font, Helvetica Neue, Helvetica, =
sans-serif; color:rgba(0, 0, 0, 1.0);" class=3D""><b class=3D"">To: =
</b></span><span style=3D"font-family: -webkit-system-font, Helvetica =
Neue, Helvetica, sans-serif;" class=3D"">Sean Turner &lt;<a =
href=3D"mailto:sean@sn3rd.com" class=3D"">sean@sn3rd.com</a>&gt;<br =
class=3D""></span></div><div style=3D"margin-top: 0px; margin-right: =
0px; margin-bottom: 0px; margin-left: 0px;" class=3D""><span =
style=3D"font-family: -webkit-system-font, Helvetica Neue, Helvetica, =
sans-serif; color:rgba(0, 0, 0, 1.0);" class=3D""><b class=3D"">Cc: =
</b></span><span style=3D"font-family: -webkit-system-font, Helvetica =
Neue, Helvetica, sans-serif;" class=3D"">IRTF CFRG &lt;<a =
href=3D"mailto:cfrg@irtf.org" class=3D"">cfrg@irtf.org</a>&gt;<br =
class=3D""></span></div><br class=3D""><div class=3D""><meta =
http-equiv=3D"Content-Type" content=3D"text/html charset=3Dutf-8" =
class=3D""><div style=3D"word-wrap: break-word; -webkit-nbsp-mode: =
space; -webkit-line-break: after-white-space;" class=3D"">Cycles =
found.<div class=3D""><br class=3D""></div><div class=3D"">Attached =
please find two files:</div><div class=3D"">&nbsp; 1.&nbsp;<span =
style=3D"font-family: Menlo; font-size: 11px; background-color: rgb(255, =
255, 255);" class=3D"">rfc7539_long.txt is RFC 7539 with page breaks and =
page numbers removed.</span><font face=3D"Menlo" class=3D""><span =
style=3D"font-size: 11px; background-color: rgb(255, 255, 255);" =
class=3D"">&nbsp;</span></font></div><div class=3D""><font face=3D"Menlo" =
class=3D""><span style=3D"font-size: 11px; background-color: rgb(255, =
255, 255);" class=3D"">&nbsp;2.&nbsp;</span></font><span =
style=3D"font-family: Menlo; font-size: 11px; background-color: rgb(255, =
255, 255);" class=3D"">draft-nir-cfrg-rfc7539bis-00.raw.txt is the =
unpaginated form of the new draft.</span></div><div class=3D""><span =
style=3D"font-family: Menlo; font-size: 11px; background-color: rgb(255, =
255, 255);" class=3D""><br class=3D""></span></div><div class=3D""><span =
style=3D"background-color: rgb(255, 255, 255);" class=3D""><font =
face=3D"Menlo" class=3D""><span style=3D"font-size: 11px;" =
class=3D"">Couldn=E2=80=99t do much about the boilerplate, but this =
makes it easy to compare.</span></font></span></div><div class=3D""><span =
style=3D"background-color: rgb(255, 255, 255);" class=3D""><font =
face=3D"Menlo" class=3D""><span style=3D"font-size: 11px;" class=3D""><br =
class=3D""></span></font></span></div><div class=3D""><span =
style=3D"background-color: rgb(255, 255, 255);" class=3D""><font =
face=3D"Menlo" class=3D""><span style=3D"font-size: 11px;" =
class=3D"">Yoav</span></font></span></div><div =
class=3D""></div></div></div></blockquote></div></div></body></html>=

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Crypto Forum                                                      Y. Nir
Internet-Draft                                               Check Point
Obsoletes: 7539 (if approved)                                 A. Langley
Intended status: Informational                              Google, Inc.
Expires: May 20, 2017                                  November 16, 2016


                ChaCha20 and Poly1305 for IETF Protocols
                      draft-nir-cfrg-rfc7539bis-00

Abstract

   This document defines the ChaCha20 stream cipher as well as the use
   of the Poly1305 authenticator, both as stand-alone algorithms and as
   a "combined mode", or Authenticated Encryption with Associated Data
   (AEAD) algorithm.

   RFC 7539, The predecessor of this document, did not introduce any new
   crypto, but was meant to serve as a stable reference and an
   implementation guide.  It was a product of the Crypto Forum Research
   Group (CFRG).  This document merges the errata filed against RFC 7539
   and adds a little text to the Security Considerations section.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on May 20, 2017.

Copyright Notice

   Copyright (c) 2016 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction
     1.1.  Conventions Used in This Document
   2.  The Algorithms
     2.1.  The ChaCha Quarter Round
       2.1.1.  Test Vector for the ChaCha Quarter Round
     2.2.  A Quarter Round on the ChaCha State
       2.2.1.  Test Vector for the Quarter Round on the ChaCha State
     2.3.  The ChaCha20 Block Function
       2.3.1.  The ChaCha20 Block Function in Pseudocode
       2.3.2.  Test Vector for the ChaCha20 Block Function
     2.4.  The ChaCha20 Encryption Algorithm
       2.4.1.  The ChaCha20 Encryption Algorithm in Pseudocode
       2.4.2.  Example and Test Vector for the ChaCha20 Cipher
     2.5.  The Poly1305 Algorithm
       2.5.1.  The Poly1305 Algorithms in Pseudocode
       2.5.2.  Poly1305 Example and Test Vector
     2.6.  Generating the Poly1305 Key Using ChaCha20
       2.6.1.  Poly1305 Key Generation in Pseudocode
       2.6.2.  Poly1305 Key Generation Test Vector
     2.7.  A Pseudorandom Function for Crypto Suites based on
           ChaCha/Poly1305
     2.8.  AEAD Construction
       2.8.1.  Pseudocode for the AEAD Construction
       2.8.2.  Example and Test Vector for AEAD_CHACHA20_POLY1305
   3.  Implementation Advice
   4.  Security Considerations
   5.  IANA Considerations
   6.  References
     6.1.  Normative References
     6.2.  Informative References
   Appendix A.  Additional Test Vectors
     A.1.  The ChaCha20 Block Functions
     A.2.  ChaCha20 Encryption
     A.3.  Poly1305 Message Authentication Code
     A.4.  Poly1305 Key Generation Using ChaCha20
     A.5.  ChaCha20-Poly1305 AEAD Decryption
   Appendix B.  Performance Measurements of ChaCha20
   Acknowledgements
   Authors' Addresses

1.  Introduction

   The Advanced Encryption Standard (AES -- [FIPS-197]) has become the
   gold standard in encryption.  Its efficient design, widespread
   implementation, and hardware support allow for high performance in
   many areas.  On most modern platforms, AES is anywhere from four to
   ten times as fast as the previous most-used cipher, Triple Data
   Encryption Standard (3DES -- [SP800-67]), which makes it not only the
   best choice, but the only practical choice.

   There are several problems with this.  If future advances in
   cryptanalysis reveal a weakness in AES, users will be in an
   unenviable position.  With the only other widely supported cipher
   being the much slower 3DES, it is not feasible to reconfigure
   deployments to use 3DES.  [Standby-Cipher] describes this issue and
   the need for a standby cipher in greater detail.  Another problem is
   that while AES is very fast on dedicated hardware, its performance on
   platforms that lack such hardware is considerably lower.  Yet another
   problem is that many AES implementations are vulnerable to cache-
   collision timing attacks ([Cache-Collisions]).

   This document provides a definition and implementation guide for
   three algorithms:

   1.  The ChaCha20 cipher.  This is a high-speed cipher first described
       in [ChaCha].  It is considerably faster than AES in software-only
       implementations, making it around three times as fast on
       platforms that lack specialized AES hardware.  See Appendix B for
       some hard numbers.  ChaCha20 is also not sensitive to timing
       attacks (see the security considerations in Section 4).  This
       algorithm is described in Section 2.4

   2.  The Poly1305 authenticator.  This is a high-speed message
       authentication code.  Implementation is also straightforward and
       easy to get right.  The algorithm is described in Section 2.5.

   3.  The CHACHA20-POLY1305 Authenticated Encryption with Associated
       Data (AEAD) construction, described in Section 2.8.

   This document does not introduce these new algorithms for the first
   time.  They have been defined in scientific papers by
   D. J. Bernstein, which are referenced by this document.  The purpose
   of this document is to serve as a stable reference for IETF documents
   making use of these algorithms.

   These algorithms have undergone rigorous analysis.  Several papers
   discuss the security of Salsa and ChaCha ([LatinDances],
   [LatinDances2], [Zhenqing2012]).

   This document represents the consensus of the Crypto Forum Research
   Group (CFRG).  It replaces [RFC7539].

1.1.  Conventions Used in This Document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].

   The description of the ChaCha algorithm will at various time refer to
   the ChaCha state as a "vector" or as a "matrix".  This follows the
   use of these terms in Professor Bernstein's paper.  The matrix
   notation is more visually convenient and gives a better notion as to
   why some rounds are called "column rounds" while others are called
   "diagonal rounds".  Here's a diagram of how the matrices relate to
   vectors (using the C language convention of zero being the index
   origin).

      0   1   2   3
      4   5   6   7
      8   9  10  11
     12  13  14  15

   The elements in this vector or matrix are 32-bit unsigned integers.

   The algorithm name is "ChaCha".  "ChaCha20" is a specific instance
   where 20 "rounds" (or 80 quarter rounds -- see Section 2.1) are used.
   Other variations are defined, with 8 or 12 rounds, but in this
   document we only describe the 20-round ChaCha, so the names "ChaCha"
   and "ChaCha20" will be used interchangeably.

2.  The Algorithms

   The subsections below describe the algorithms used and the AEAD
   construction.

2.1.  The ChaCha Quarter Round

   The basic operation of the ChaCha algorithm is the quarter round.  It
   operates on four 32-bit unsigned integers, denoted a, b, c, and d.
   The operation is as follows (in C-like notation):

   1.  a += b; d ^= a; d <<<= 16;
   2.  c += d; b ^= c; b <<<= 12;
   3.  a += b; d ^= a; d <<<= 8;
   4.  c += d; b ^= c; b <<<= 7;

   Where "+" denotes integer addition modulo 2^32, "^" denotes a bitwise
   Exclusive OR (XOR), and "<<< n" denotes an n-bit left rotation
   (towards the high bits).

   For example, let's see the add, XOR, and roll operations from the
   fourth line with sample numbers:

   o  a = 0x11111111
   o  b = 0x01020304
   o  c = 0x77777777
   o  d = 0x01234567
   o  c = c + d = 0x77777777 + 0x01234567 = 0x789abcde
   o  b = b ^ c = 0x01020304 ^ 0x789abcde = 0x7998bfda
   o  b = b <<< 7 = 0x7998bfda <<< 7 = 0xcc5fed3c

2.1.1.  Test Vector for the ChaCha Quarter Round

   For a test vector, we will use the same numbers as in the example,
   adding something random for c.

   o  a = 0x11111111
   o  b = 0x01020304
   o  c = 0x9b8d6f43
   o  d = 0x01234567

   After running a Quarter Round on these four numbers, we get these:

   o  a = 0xea2a92f4
   o  b = 0xcb1cf8ce
   o  c = 0x4581472e
   o  d = 0x5881c4bb

2.2.  A Quarter Round on the ChaCha State

   The ChaCha state does not have four integer numbers: it has 16.  So
   the quarter-round operation works on only four of them -- hence the
   name.  Each quarter round operates on four predetermined numbers in
   the ChaCha state.  We will denote by QUARTERROUND(x,y,z,w) a quarter-
   round operation on the numbers at indices x, y, z, and w of the
   ChaCha state when viewed as a vector.  For example, if we apply
   QUARTERROUND(1,5,9,13) to a state, this means running the quarter-
   round operation on the elements marked with an asterisk, while
   leaving the others alone:

      0  *a   2   3
      4  *b   6   7
      8  *c  10  11
     12  *d  14  15

   Note that this run of quarter round is part of what is called a
   "column round".

2.2.1.  Test Vector for the Quarter Round on the ChaCha State

   For a test vector, we will use a ChaCha state that was generated
   randomly:

   Sample ChaCha State

       879531e0  c5ecf37d  516461b1  c9a62f8a
       44c20ef3  3390af7f  d9fc690b  2a5f714c
       53372767  b00a5631  974c541a  359e9963
       5c971061  3d631689  2098d9d6  91dbd320

   We will apply the QUARTERROUND(2,7,8,13) operation to this state.
   For obvious reasons, this one is part of what is called a "diagonal
   round":

   After applying QUARTERROUND(2,7,8,13)

       879531e0  c5ecf37d *bdb886dc  c9a62f8a
       44c20ef3  3390af7f  d9fc690b *cfacafd2
      *e46bea80  b00a5631  974c541a  359e9963
       5c971061 *ccc07c79  2098d9d6  91dbd320

   Note that only the numbers in positions 2, 7, 8, and 13 changed.

2.3.  The ChaCha20 Block Function

   The ChaCha block function transforms a ChaCha state by running
   multiple quarter rounds.

   The inputs to ChaCha20 are:

   o  A 256-bit key, treated as a concatenation of eight 32-bit little-
      endian integers.

   o  A 96-bit nonce, treated as a concatenation of three 32-bit little-
      endian integers.

   o  A 32-bit block count parameter, treated as a 32-bit little-endian
      integer.

   The output is 64 random-looking bytes.

   The ChaCha algorithm described here uses a 256-bit key.  The original
   algorithm also specified 128-bit keys and 8- and 12-round variants,
   but these are out of scope for this document.  In this section, we
   describe the ChaCha block function.

   Note also that the original ChaCha had a 64-bit nonce and 64-bit
   block count.  We have modified this here to be more consistent with
   recommendations in Section 3.2 of [RFC5116].  This limits the use of
   a single (key,nonce) combination to 2^32 blocks, or 256 GB, but that
   is enough for most uses.  In cases where a single key is used by
   multiple senders, it is important to make sure that they don't use
   the same nonces.  This can be assured by partitioning the nonce space
   so that the first 32 bits are unique per sender, while the other 64
   bits come from a counter.

   The ChaCha20 state is initialized as follows:

   o  The first four words (0-3) are constants: 0x61707865, 0x3320646e,
      0x79622d32, 0x6b206574.

   o  The next eight words (4-11) are taken from the 256-bit key by
      reading the bytes in little-endian order, in 4-byte chunks.

   o  Word 12 is a block counter.  Since each block is 64-byte, a 32-bit
      word is enough for 256 gigabytes of data.

   o  Words 13-15 are a nonce, which should not be repeated for the same
      key.  The 13th word is the first 32 bits of the input nonce taken
      as a little-endian integer, while the 15th word is the last 32
      bits.

       cccccccc  cccccccc  cccccccc  cccccccc
       kkkkkkkk  kkkkkkkk  kkkkkkkk  kkkkkkkk
       kkkkkkkk  kkkkkkkk  kkkkkkkk  kkkkkkkk
       bbbbbbbb  nnnnnnnn  nnnnnnnn  nnnnnnnn

   c=constant k=key b=blockcount n=nonce

   ChaCha20 runs 20 rounds, alternating between "column rounds" and
   "diagonal rounds".  Each round consists of four quarter-rounds, and
   they are run as follows.  Quarter rounds 1-4 are part of a "column"
   round, while 5-8 are part of a "diagonal" round:

   1.  QUARTERROUND ( 0, 4, 8,12)
   2.  QUARTERROUND ( 1, 5, 9,13)
   3.  QUARTERROUND ( 2, 6,10,14)
   4.  QUARTERROUND ( 3, 7,11,15)
   5.  QUARTERROUND ( 0, 5,10,15)
   6.  QUARTERROUND ( 1, 6,11,12)
   7.  QUARTERROUND ( 2, 7, 8,13)
   8.  QUARTERROUND ( 3, 4, 9,14)

   At the end of 20 rounds (or 10 iterations of the above list), we add
   the original input words to the output words, and serialize the
   result by sequencing the words one-by-one in little-endian order.

   Note: "addition" in the above paragraph is done modulo 2^32.  In some
   machine languages, this is called carryless addition on a 32-bit
   word.

2.3.1.  The ChaCha20 Block Function in Pseudocode

   Note: This section and a few others contain pseudocode for the
   algorithm explained in a previous section.  Every effort was made for
   the pseudocode to accurately reflect the algorithm as described in
   the preceding section.  If a conflict is still present, the textual
   explanation and the test vectors are normative.

      inner_block (state):
         Qround(state, 0, 4, 8,12)
         Qround(state, 1, 5, 9,13)
         Qround(state, 2, 6,10,14)
         Qround(state, 3, 7,11,15)
         Qround(state, 0, 5,10,15)
         Qround(state, 1, 6,11,12)
         Qround(state, 2, 7, 8,13)
         Qround(state, 3, 4, 9,14)
         end

      chacha20_block(key, counter, nonce):
         state = constants | key | counter | nonce
         working_state = state
         for i=1 upto 10
            inner_block(working_state)
            end
         state += working_state
         return serialize(state)
         end

2.3.2.  Test Vector for the ChaCha20 Block Function

   For a test vector, we will use the following inputs to the ChaCha20
   block function:

   o  Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13:
      14:15:16:17:18:19:1a:1b:1c:1d:1e:1f.  The key is a sequence of
      octets with no particular structure before we copy it into the
      ChaCha state.

   o  Nonce = (00:00:00:09:00:00:00:4a:00:00:00:00)

   o  Block Count = 1.

   After setting up the ChaCha state, it looks like this:

   ChaCha state with the key setup.

       61707865  3320646e  79622d32  6b206574
       03020100  07060504  0b0a0908  0f0e0d0c
       13121110  17161514  1b1a1918  1f1e1d1c
       00000001  09000000  4a000000  00000000

   After running 20 rounds (10 column rounds interleaved with 10
   "diagonal rounds"), the ChaCha state looks like this:

   ChaCha state after 20 rounds

       837778ab  e238d763  a67ae21e  5950bb2f
       c4f2d0c7  fc62bb2f  8fa018fc  3f5ec7b7
       335271c2  f29489f3  eabda8fc  82e46ebd
       d19c12b4  b04e16de  9e83d0cb  4e3c50a2

   Finally, we add the original state to the result (simple vector or
   matrix addition), giving this:

   ChaCha state at the end of the ChaCha20 operation

       e4e7f110  15593bd1  1fdd0f50  c47120a3
       c7f4d1c7  0368c033  9aaa2204  4e6cd4c3
       466482d2  09aa9f07  05d7c214  a2028bd9
       d19c12b5  b94e16de  e883d0cb  4e3c50a2

   After we serialize the state, we get this:

  Serialized Block:
  000  10 f1 e7 e4 d1 3b 59 15 50 0f dd 1f a3 20 71 c4  .....;Y.P.... q.
  016  c7 d1 f4 c7 33 c0 68 03 04 22 aa 9a c3 d4 6c 4e  ....3.h.."....lN
  032  d2 82 64 46 07 9f aa 09 14 c2 d7 05 d9 8b 02 a2  ..dF............
  048  b5 12 9c d1 de 16 4e b9 cb d0 83 e8 a2 50 3c 4e  ......N......P<N

2.4.  The ChaCha20 Encryption Algorithm

   ChaCha20 is a stream cipher designed by D. J. Bernstein.  It is a
   refinement of the Salsa20 algorithm, and it uses a 256-bit key.

   ChaCha20 successively calls the ChaCha20 block function, with the
   same key and nonce, and with successively increasing block counter
   parameters.  ChaCha20 then serializes the resulting state by writing
   the numbers in little-endian order, creating a keystream block.
   Concatenating the keystream blocks from the successive blocks forms a
   keystream.  The ChaCha20 function then performs an XOR of this
   keystream with the plaintext.  Alternatively, each keystream block
   can be XORed with a plaintext block before proceeding to create the
   next block, saving some memory.  There is no requirement for the
   plaintext to be an integral multiple of 512 bits.  If there is extra
   keystream from the last block, it is discarded.  Specific protocols
   MAY require that the plaintext and ciphertext have certain length.
   Such protocols need to specify how the plaintext is padded and how
   much padding it receives.

   The inputs to ChaCha20 are:

   o  A 256-bit key

   o  A 32-bit initial counter.  This can be set to any number, but will
      usually be zero or one.  It makes sense to use one if we use the
      zero block for something else, such as generating a one-time
      authenticator key as part of an AEAD algorithm.

   o  A 96-bit nonce.  In some protocols, this is known as the
      Initialization Vector.

   o  An arbitrary-length plaintext

   The output is an encrypted message, or "ciphertext", of the same
   length.

   Decryption is done in the same way.  The ChaCha20 block function is
   used to expand the key into a keystream, which is XORed with the
   ciphertext giving back the plaintext.

2.4.1.  The ChaCha20 Encryption Algorithm in Pseudocode

     chacha20_encrypt(key, counter, nonce, plaintext):
        for j = 0 upto floor(len(plaintext)/64)-1
           key_stream = chacha20_block(key, counter+j, nonce)
           block = plaintext[(j*64)..(j*64+63)]
           encrypted_message +=  block ^ key_stream
           end
        if ((len(plaintext) % 64) != 0)
           j = floor(len(plaintext)/64)
           key_stream = chacha20_block(key, counter+j, nonce)
           block = plaintext[(j*64)..len(plaintext)-1]
           encrypted_message += (block^key_stream)[0..len(plaintext)%64]
           end
        return encrypted_message
        end

2.4.2.  Example and Test Vector for the ChaCha20 Cipher

   For a test vector, we will use the following inputs to the ChaCha20
   block function:

   o  Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13:
      14:15:16:17:18:19:1a:1b:1c:1d:1e:1f.

   o  Nonce = (00:00:00:00:00:00:00:4a:00:00:00:00).

   o  Initial Counter = 1.

   We use the following for the plaintext.  It was chosen to be long
   enough to require more than one block, but not so long that it would
   make this example cumbersome (so, less than 3 blocks):

  Plaintext Sunscreen:
  000  4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c  Ladies and Gentl
  016  65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73  emen of the clas
  032  73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63  s of '99: If I c
  048  6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f  ould offer you o
  064  6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20  nly one tip for
  080  74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73  the future, suns
  096  63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69  creen would be i
  112  74 2e                                            t.

   The following figure shows four ChaCha state matrices:

   1.  First block as it is set up.

   2.  Second block as it is set up.  Note that these blocks are only
       two bits apart -- only the counter in position 12 is different.

   3.  Third block is the first block after the ChaCha20 block
       operation.

   4.  Final block is the second block after the ChaCha20 block
       operation was applied.

   After that, we show the keystream.

   First block setup:
       61707865  3320646e  79622d32  6b206574
       03020100  07060504  0b0a0908  0f0e0d0c
       13121110  17161514  1b1a1918  1f1e1d1c
       00000001  00000000  4a000000  00000000

   Second block setup:
       61707865  3320646e  79622d32  6b206574
       03020100  07060504  0b0a0908  0f0e0d0c
       13121110  17161514  1b1a1918  1f1e1d1c
       00000002  00000000  4a000000  00000000

   First block after block operation:
       f3514f22  e1d91b40  6f27de2f  ed1d63b8
       821f138c  e2062c3d  ecca4f7e  78cff39e
       a30a3b8a  920a6072  cd7479b5  34932bed
       40ba4c79  cd343ec6  4c2c21ea  b7417df0

   Second block after block operation:
       9f74a669  410f633f  28feca22  7ec44dec
       6d34d426  738cb970  3ac5e9f3  45590cc4
       da6e8b39  892c831a  cdea67c1  2b7e1d90
       037463f3  a11a2073  e8bcfb88  edc49139

   Keystream:
   22:4f:51:f3:40:1b:d9:e1:2f:de:27:6f:b8:63:1d:ed:8c:13:1f:82:3d:2c:06
   e2:7e:4f:ca:ec:9e:f3:cf:78:8a:3b:0a:a3:72:60:0a:92:b5:79:74:cd:ed:2b
   93:34:79:4c:ba:40:c6:3e:34:cd:ea:21:2c:4c:f0:7d:41:b7:69:a6:74:9f:3f
   63:0f:41:22:ca:fe:28:ec:4d:c4:7e:26:d4:34:6d:70:b9:8c:73:f3:e9:c5:3a
   c4:0c:59:45:39:8b:6e:da:1a:83:2c:89:c1:67:ea:cd:90:1d:7e:2b:f3:63

   Finally, we XOR the keystream with the plaintext, yielding the
   ciphertext:

  Ciphertext Sunscreen:
  000  6e 2e 35 9a 25 68 f9 80 41 ba 07 28 dd 0d 69 81  n.5.%h..A..(..i.
  016  e9 7e 7a ec 1d 43 60 c2 0a 27 af cc fd 9f ae 0b  .~z..C`..'......
  032  f9 1b 65 c5 52 47 33 ab 8f 59 3d ab cd 62 b3 57  ..e.RG3..Y=..b.W
  048  16 39 d6 24 e6 51 52 ab 8f 53 0c 35 9f 08 61 d8  .9.$.QR..S.5..a.
  064  07 ca 0d bf 50 0d 6a 61 56 a3 8e 08 8a 22 b6 5e  ....P.jaV....".^
  080  52 bc 51 4d 16 cc f8 06 81 8c e9 1a b7 79 37 36  R.QM.........y76
  096  5a f9 0b bf 74 a3 5b e6 b4 0b 8e ed f2 78 5e 42  Z...t.[......x^B
  112  87 4d                                            .M

2.5.  The Poly1305 Algorithm

   Poly1305 is a one-time authenticator designed by D. J. Bernstein.
   Poly1305 takes a 32-byte one-time key and a message and produces a
   16-byte tag.  This tag is used to authenticate the message.

   The original article ([Poly1305]) is titled "The Poly1305-AES
   message-authentication code", and the MAC function there requires a
   128-bit AES key, a 128-bit "additional key", and a 128-bit (non-
   secret) nonce.  AES is used there for encrypting the nonce, so as to
   get a unique (and secret) 128-bit string, but as the paper states,
   "There is nothing special about AES here.  One can replace AES with
   an arbitrary keyed function from an arbitrary set of nonces to
   16-byte strings."

   Regardless of how the key is generated, the key is partitioned into
   two parts, called "r" and "s".  The pair (r,s) should be unique, and
   MUST be unpredictable for each invocation (that is why it was
   originally obtained by encrypting a nonce), while "r" MAY be
   constant, but needs to be modified as follows before being used: ("r"
   is treated as a 16-octet little-endian number):

   o  r[3], r[7], r[11], and r[15] are required to have their top four
      bits clear (be smaller than 16)

   o  r[4], r[8], and r[12] are required to have their bottom two bits
      clear (be divisible by 4)

   The following sample code clamps "r" to be appropriate:

   /*
   Adapted from poly1305aes_test_clamp.c version 20050207
   D. J. Bernstein
   Public domain.
   */

   #include "poly1305aes_test.h"

   void poly1305aes_test_clamp(unsigned char r[16])
   {
     r[3] &= 15;
     r[7] &= 15;
     r[11] &= 15;
     r[15] &= 15;
     r[4] &= 252;
     r[8] &= 252;
     r[12] &= 252;
   }

   The "s" should be unpredictable, but it is perfectly acceptable to
   generate both "r" and "s" uniquely each time.  Because each of them
   is 128 bits, pseudorandomly generating them (see Section 2.6) is also
   acceptable.

   The inputs to Poly1305 are:

   o  A 256-bit one-time key

   o  An arbitrary length message

   The output is a 128-bit tag.

   First, the "r" value should be clamped.

   Next, set the constant prime "P" be 2^130-5:
   3fffffffffffffffffffffffffffffffb.  Also set a variable "accumulator"
   to zero.

   Next, divide the message into 16-byte blocks.  The last one might be
   shorter:

   o  Read the block as a little-endian number.

   o  Add one bit beyond the number of octets.  For a 16-byte block,
      this is equivalent to adding 2^128 to the number.  For the shorter
      block, it can be 2^120, 2^112, or any power of two that is evenly
      divisible by 8, all the way down to 2^8.

   o  If the block is not 17 bytes long (the last block), pad it with
      zeros.  This is meaningless if you are treating the blocks as
      numbers.

   o  Add this number to the accumulator.

   o  Multiply by "r".

   o  Set the accumulator to the result modulo p.  To summarize: Acc =
      ((Acc+block)*r) % p.

   Finally, the value of the secret key "s" is added to the accumulator,
   and the 128 least significant bits are serialized in little-endian
   order to form the tag.

2.5.1.  The Poly1305 Algorithms in Pseudocode

      clamp(r): r &= 0x0ffffffc0ffffffc0ffffffc0fffffff
      poly1305_mac(msg, key):
         r = (le_bytes_to_num(key[0..15])
         clamp(r)
         s = le_bytes_to_num(key[16..31])
         a = 0  /* a is the accumulator */
         p = (1<<130)-5
         for i=1 upto ceil(msg length in bytes / 16)
            n = le_bytes_to_num(msg[((i-1)*16)..(i*16)] | [0x01])
            a += n
            a = (r * a) % p
            end
         a += s
         return num_to_16_le_bytes(a)
         end

2.5.2.  Poly1305 Example and Test Vector

   For our example, we will dispense with generating the one-time key
   using AES, and assume that we got the following keying material:

   o  Key Material: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8:01:0
      3:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:f5:1b

   o  s as an octet string:
      01:03:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:f5:1b

   o  s as a 128-bit number: 1bf54941aff6bf4afdb20dfb8a800301

   o  r before clamping: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8

   o  Clamped r as a number: 806d5400e52447c036d555408bed685

   For our message, we'll use a short text:

  Message to be Authenticated:
  000  43 72 79 70 74 6f 67 72 61 70 68 69 63 20 46 6f  Cryptographic Fo
  016  72 75 6d 20 52 65 73 65 61 72 63 68 20 47 72 6f  rum Research Gro
  032  75 70                                            up

   Since Poly1305 works in 16-byte chunks, the 34-byte message divides
   into three blocks.  In the following calculation, "Acc" denotes the
   accumulator and "Block" the current block:

   Block #1

   Acc = 00
   Block = 6f4620636968706172676f7470797243
   Block with 0x01 byte = 016f4620636968706172676f7470797243
   Acc + block = 016f4620636968706172676f7470797243
   (Acc+Block) * r =
        b83fe991ca66800489155dcd69e8426ba2779453994ac90ed284034da565ecf
   Acc = ((Acc+Block)*r) % P = 2c88c77849d64ae9147ddeb88e69c83fc

   Block #2

   Acc = 2c88c77849d64ae9147ddeb88e69c83fc
   Block = 6f7247206863726165736552206d7572
   Block with 0x01 byte = 016f7247206863726165736552206d7572
   Acc + block = 437febea505c820f2ad5150db0709f96e
   (Acc+Block) * r =
        21dcc992d0c659ba4036f65bb7f88562ae59b32c2b3b8f7efc8b00f78e548a26
   Acc = ((Acc+Block)*r) % P = 2d8adaf23b0337fa7cccfb4ea344b30de

   Last Block

   Acc = 2d8adaf23b0337fa7cccfb4ea344b30de
   Block = 7075
   Block with 0x01 byte = 017075
   Acc + block = 2d8adaf23b0337fa7cccfb4ea344ca153
   (Acc + Block) * r =
        16d8e08a0f3fe1de4fe4a15486aca7a270a29f1e6c849221e4a6798b8e45321f
   ((Acc + Block) * r) % P = 28d31b7caff946c77c8844335369d03a7

   Adding s, we get this number, and serialize if to get the tag:

   Acc + s = 2a927010caf8b2bc2c6365130c11d06a8

   Tag: a8:06:1d:c1:30:51:36:c6:c2:2b:8b:af:0c:01:27:a9

2.6.  Generating the Poly1305 Key Using ChaCha20

   As said in Section 2.5, it is acceptable to generate the one-time
   Poly1305 pseudorandomly.  This section defines such a method.

   To generate such a key pair (r,s), we will use the ChaCha20 block
   function described in Section 2.3.  This assumes that we have a
   256-bit session key for the Message Authentication Code (MAC)
   function, such as SK_ai and SK_ar in Internet Key Exchange Protocol
   version 2 (IKEv2) ([RFC7296]), the integrity key in the Encapsulating
   Security Payload (ESP) and Authentication Header (AH), or the
   client_write_MAC_key and server_write_MAC_key in TLS.  Any document
   that specifies the use of Poly1305 as a MAC algorithm for some
   protocol must specify that 256 bits are allocated for the integrity
   key.  Note that in the AEAD construction defined in Section 2.8, the
   same key is used for encryption and key generation, so the use of
   SK_a* or *_write_MAC_key is only for stand-alone Poly1305.

   The method is to call the block function with the following
   parameters:

   o  The 256-bit session integrity key is used as the ChaCha20 key.

   o  The block counter is set to zero.

   o  The protocol will specify a 96-bit or 64-bit nonce.  This MUST be
      unique per invocation with the same key, so it MUST NOT be
      randomly generated.  A counter is a good way to implement this,
      but other methods, such as a Linear Feedback Shift Register (LFSR)
      are also acceptable.  ChaCha20 as specified here requires a 96-bit
      nonce.  So if the provided nonce is only 64-bit, then the first 32
      bits of the nonce will be set to a constant number.  This will
      usually be zero, but for protocols with multiple senders it may be
      different for each sender, but should be the same for all
      invocations of the function with the same key by a particular
      sender.

   After running the block function, we have a 512-bit state.  We take
   the first 256 bits of the serialized state, and use those as the one-
   time Poly1305 key: the first 128 bits are clamped and form "r", while
   the next 128 bits become "s".  The other 256 bits are discarded.

   Note that while many protocols have provisions for a nonce for
   encryption algorithms (often called Initialization Vectors, or IVs),
   they usually don't have such a provision for the MAC function.  In
   that case, the per-invocation nonce will have to come from somewhere
   else, such as a message counter.

2.6.1.  Poly1305 Key Generation in Pseudocode

      poly1305_key_gen(key,nonce):
         counter = 0
         block = chacha20_block(key,counter,nonce)
         return block[0..31]
         end

2.6.2.  Poly1305 Key Generation Test Vector

   For this example, we'll set:

  Key:
  000  80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f  ................
  016  90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f  ................

   Nonce:
   000  00 00 00 00 00 01 02 03 04 05 06 07              ............

   The ChaCha state setup with key, nonce, and block counter zero:
         61707865  3320646e  79622d32  6b206574
         83828180  87868584  8b8a8988  8f8e8d8c
         93929190  97969594  9b9a9998  9f9e9d9c
         00000000  00000000  03020100  07060504

   The ChaCha state after 20 rounds:
         8ba0d58a  cc815f90  27405081  7194b24a
         37b633a8  a50dfde3  e2b8db08  46a6d1fd
         7da03782  9183a233  148ad271  b46773d1
         3cc1875a  8607def1  ca5c3086  7085eb87

  Output bytes:
  000  8a d5 a0 8b 90 5f 81 cc 81 50 40 27 4a b2 94 71  ....._...P@'J..q
  016  a8 33 b6 37 e3 fd 0d a5 08 db b8 e2 fd d1 a6 46  .3.7...........F

   And that output is also the 32-byte one-time key used for Poly1305.

2.7.  A Pseudorandom Function for Crypto Suites based on ChaCha/Poly1305

   Some protocols, such as IKEv2 ([RFC7296]), require a Pseudorandom
   Function (PRF), mostly for key derivation.  In the IKEv2 definition,
   a PRF is a function that accepts a variable-length key and a
   variable-length input, and returns a fixed-length output.  Most
   commonly, Hashed MAC (HMAC) constructions are used for this purpose,
   and often the same function is used for both message authentication
   and PRF.

   Poly1305 is not a suitable choice for a PRF.  Poly1305 prohibits
   using the same key twice, whereas the PRF in IKEv2 is used multiple
   times with the same key.  Additionally, unlike HMAC, Poly1305 is
   biased, so using it for key derivation would reduce the security of
   the symmetric encryption.

   Chacha20 could be used as a key-derivation function, by generating an
   arbitrarily long keystream.  However, that is not what protocols such
   as IKEv2 require.

   For this reason, this document does not specify a PRF and recommends
   that crypto suites use some other PRF such as PRF_HMAC_SHA2_256 (see
   Section 2.1.2 of [RFC4868]).

2.8.  AEAD Construction

   AEAD_CHACHA20_POLY1305 is an authenticated encryption with additional
   data algorithm.  The inputs to AEAD_CHACHA20_POLY1305 are:

   o  A 256-bit key

   o  A 96-bit nonce -- different for each invocation with the same key

   o  An arbitrary length plaintext

   o  Arbitrary length additional authenticated data (AAD)

   Some protocols may have unique per-invocation inputs that are not 96
   bits in length.  For example, IPsec may specify a 64-bit nonce.  In
   such a case, it is up to the protocol document to define how to
   transform the protocol nonce into a 96-bit nonce, for example, by
   concatenating a constant value.

   The ChaCha20 and Poly1305 primitives are combined into an AEAD that
   takes a 256-bit key and 96-bit nonce as follows:

   o  First, a Poly1305 one-time key is generated from the 256-bit key
      and nonce using the procedure described in Section 2.6.

   o  Next, the ChaCha20 encryption function is called to encrypt the
      plaintext, using the same key and nonce, and with the initial
      counter set to 1.

   o  Finally, the Poly1305 function is called with the Poly1305 key
      calculated above, and a message constructed as a concatenation of
      the following:

      *  The AAD

      *  padding1 -- the padding is up to 15 zero bytes, and it brings
         the total length so far to an integral multiple of 16.  If the
         length of the AAD was already an integral multiple of 16 bytes,
         this field is zero-length.

      *  The ciphertext

      *  padding2 -- the padding is up to 15 zero bytes, and it brings
         the total length so far to an integral multiple of 16.  If the
         length of the ciphertext was already an integral multiple of 16
         bytes, this field is zero-length.

      *  The length of the additional data in octets (as a 64-bit
         little-endian integer).

      *  The length of the ciphertext in octets (as a 64-bit little-
         endian integer).

   The output from the AEAD is the concatenation of:

   o  A ciphertext of the same length as the plaintext.

   o  A 128-bit tag, which is the output of the Poly1305 function.

   Decryption is similar with the following differences:

   o  The roles of ciphertext and plaintext are reversed, so the
      ChaCha20 encryption function is applied to the ciphertext,
      producing the plaintext.

   o  The Poly1305 function is still run on the AAD and the ciphertext,
      not the plaintext.

   o  The calculated tag is bitwise compared to the received tag.  The
      message is authenticated if and only if the tags match.

   A few notes about this design:

   1.  The amount of encrypted data possible in a single invocation is
       2^32-1 blocks of 64 bytes each, because of the size of the block
       counter field in the ChaCha20 block function.  This gives a total
       of 274,877,906,880 bytes, or nearly 256 GB.  This should be
       enough for traffic protocols such as IPsec and TLS, but may be
       too small for file and/or disk encryption.  For such uses, we can
       return to the original design, reduce the nonce to 64 bits, and
       use the integer at position 13 as the top 32 bits of a 64-bit
       block counter, increasing the total message size to over a
       million petabytes (1,180,591,620,717,411,303,360 bytes to be
       exact).

   2.  Despite the previous item, the ciphertext length field in the
       construction of the buffer on which Poly1305 runs limits the
       ciphertext (and hence, the plaintext) size to 2^64 bytes, or
       sixteen thousand petabytes (18,446,744,073,709,551,616 bytes to
       be exact).

   The AEAD construction in this section is a novel composition of
   ChaCha20 and Poly1305.  A security analysis of this composition is
   given in [Procter].

   Here is a list of the parameters for this construction as defined in
   Section 4 of RFC 5116:

   o  K_LEN (key length) is 32 octets.

   o  P_MAX (maximum size of the plaintext) is 247,877,906,880 bytes, or
      nearly 256 GB.

   o  A_MAX (maximum size of the associated data) is set to 2^64-1
      octets by the length field for associated data.

   o  N_MIN = N_MAX = 12 octets.

   o  C_MAX = P_MAX + tag length = 274,877,906,896 octets.

   Distinct AAD inputs (as described in Section 3.3 of RFC 5116) shall
   be concatenated into a single input to AEAD_CHACHA20_POLY1305.  It is
   up to the application to create a structure in the AAD input if it is
   needed.

2.8.1.  Pseudocode for the AEAD Construction

      pad16(x):
         if (len(x) % 16)==0
            then return NULL
            else return copies(0, 16-(len(x)%16))
         end

      chacha20_aead_encrypt(aad, key, iv, constant, plaintext):
         nonce = constant | iv
         otk = poly1305_key_gen(key, nonce)
         ciphertext = chacha20_encrypt(key, 1, nonce, plaintext)
         mac_data = aad | pad16(aad)
         mac_data |= ciphertext | pad16(ciphertext)
         mac_data |= num_to_8_le_bytes(aad.length)
         mac_data |= num_to_8_le_bytes(ciphertext.length)
         tag = poly1305_mac(mac_data, otk)
         return (ciphertext, tag)

2.8.2.  Example and Test Vector for AEAD_CHACHA20_POLY1305

   For a test vector, we will use the following inputs to the
   AEAD_CHACHA20_POLY1305 function:

  Plaintext:
  000  4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c  Ladies and Gentl
  016  65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73  emen of the clas
  032  73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63  s of '99: If I c
  048  6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f  ould offer you o
  064  6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20  nly one tip for
  080  74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73  the future, suns
  096  63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69  creen would be i
  112  74 2e                                            t.

   AAD:
   000  50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7              PQRS........

  Key:
  000  80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f  ................
  016  90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f  ................

   IV:
   000  40 41 42 43 44 45 46 47                          @ABCDEFG

   32-bit fixed-common part:
   000  07 00 00 00                                      ....

   Setup for generating Poly1305 one-time key (sender id=7):
       61707865  3320646e  79622d32  6b206574
       83828180  87868584  8b8a8988  8f8e8d8c
       93929190  97969594  9b9a9998  9f9e9d9c
       00000000  00000007  43424140  47464544

   After generating Poly1305 one-time key:
       252bac7b  af47b42d  557ab609  8455e9a4
       73d6e10a  ebd97510  7875932a  ff53d53e
       decc7ea2  b44ddbad  e49c17d1  d8430bc9
       8c94b7bc  8b7d4b4b  3927f67d  1669a432

  Poly1305 Key:
  000  7b ac 2b 25 2d b4 47 af 09 b6 7a 55 a4 e9 55 84  {.+%-.G...zU..U.
  016  0a e1 d6 73 10 75 d9 eb 2a 93 75 78 3e d5 53 ff  ...s.u..*.ux>.S.

  Poly1305 r =  455e9a4057ab6080f47b42c052bac7b
  Poly1305 s = ff53d53e7875932aebd9751073d6e10a

   keystream bytes:
   9f:7b:e9:5d:01:fd:40:ba:15:e2:8f:fb:36:81:0a:ae:
   c1:c0:88:3f:09:01:6e:de:dd:8a:d0:87:55:82:03:a5:
   4e:9e:cb:38:ac:8e:5e:2b:b8:da:b2:0f:fa:db:52:e8:
   75:04:b2:6e:be:69:6d:4f:60:a4:85:cf:11:b8:1b:59:
   fc:b1:c4:5f:42:19:ee:ac:ec:6a:de:c3:4e:66:69:78:
   8e:db:41:c4:9c:a3:01:e1:27:e0:ac:ab:3b:44:b9:cf:
   5c:86:bb:95:e0:6b:0d:f2:90:1a:b6:45:e4:ab:e6:22:
   15:38

  Ciphertext:
  000  d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2  ...4d.`.{...S.~.
  016  a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6  ...Q)n......6.b.
  032  3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b  =..^..g....i..r.
  048  1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36  .q.....)....~.;6
  064  92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58  ....-w......(..X
  080  fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc  ..$...u.U...H1..
  096  3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b  ?....Kz..v.e...K
  112  61 16                                            a.

  AEAD Construction for Poly1305:
  000  50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7 00 00 00 00  PQRS............
  016  d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2  ...4d.`.{...S.~.
  032  a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6  ...Q)n......6.b.
  048  3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b  =..^..g....i..r.
  064  1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36  .q.....)....~.;6
  080  92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58  ....-w......(..X
  096  fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc  ..$...u.U...H1..
  112  3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b  ?....Kz..v.e...K
  128  61 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00  a...............
  144  0c 00 00 00 00 00 00 00 72 00 00 00 00 00 00 00  ........r.......

   Note the four zero bytes in line 000 and the 14 zero bytes in line
   128

   Tag:
   1a:e1:0b:59:4f:09:e2:6a:7e:90:2e:cb:d0:60:06:91

3.  Implementation Advice

   Each block of ChaCha20 involves 16 move operations and one increment
   operation for loading the state, 80 each of XOR, addition and Roll
   operations for the rounds, 16 more add operations and 16 XOR
   operations for protecting the plaintext.  Section 2.3 describes the
   ChaCha block function as "adding the original input words".  This
   implies that before starting the rounds on the ChaCha state, we copy
   it aside, only to add it in later.  This is correct, but we can save
   a few operations if we instead copy the state and do the work on the
   copy.  This way, for the next block you don't need to recreate the
   state, but only to increment the block counter.  This saves
   approximately 5.5% of the cycles.

   It is not recommended to use a generic big number library such as the
   one in OpenSSL for the arithmetic operations in Poly1305.  Such
   libraries use dynamic allocation to be able to handle an integer of
   any size, but that flexibility comes at the expense of performance as
   well as side-channel security.  More efficient implementations that
   run in constant time are available, one of them in D. J. Bernstein's
   own library, NaCl ([NaCl]).  A constant-time but not optimal approach
   would be to naively implement the arithmetic operations for 288-bit
   integers, because even a naive implementation will not exceed 2^288
   in the multiplication of (acc+block) and r.  An efficient constant-
   time implementation can be found in the public domain library
   poly1305-donna ([Poly1305_Donna]).

4.  Security Considerations

   The ChaCha20 cipher is designed to provide 256-bit security.

   The Poly1305 authenticator is designed to ensure that forged messages
   are rejected with a probability of 1-(n/(2^102)) for a 16n-byte
   message, even after sending 2^64 legitimate messages, so it is
   SUF-CMA (strong unforgeability against chosen-message attacks) in the
   terminology of [AE].

   Proving the security of either of these is beyond the scope of this
   document.  Such proofs are available in the referenced academic
   papers ([ChaCha], [Poly1305], [LatinDances], [LatinDances2], and
   [Zhenqing2012]).

   The most important security consideration in implementing this
   document is the uniqueness of the nonce used in ChaCha20.  Counters
   and LFSRs are both acceptable ways of generating unique nonces, as is
   encrypting a counter using a 64-bit cipher such as DES.  Note that it
   is not acceptable to use a truncation of a counter encrypted with a
   128-bit or 256-bit cipher, because such a truncation may repeat after
   a short time.

   Consequences of repeating a nonce: If a nonce is repeated, then both
   the one-time Poly1305 key and the keystream are identical between the
   messages.  This reveals the XOR of the plaintexts, because the XOR of
   the plaintexts is equal to the XOR of the ciphertexts.

   The Poly1305 key MUST be unpredictable to an attacker.  Randomly
   generating the key would fulfill this requirement, except that
   Poly1305 is often used in communications protocols, so the receiver
   should know the key.  Pseudorandom number generation such as by
   encrypting a counter is acceptable.  Using ChaCha with a secret key
   and a nonce is also acceptable.

   The algorithms presented here were designed to be easy to implement
   in constant time to avoid side-channel vulnerabilities.  The
   operations used in ChaCha20 are all additions, XORs, and fixed
   rotations.  All of these can and should be implemented in constant
   time.  Access to offsets into the ChaCha state and the number of
   operations do not depend on any property of the key, eliminating the
   chance of information about the key leaking through the timing of
   cache misses.

   For Poly1305, the operations are addition, multiplication. and
   modulus, all on numbers with greater than 128 bits.  This can be done
   in constant time, but a naive implementation (such as using some
   generic big number library) will not be constant time.  For example,
   if the multiplication is performed as a separate operation from the
   modulus, the result will sometimes be under 2^256 and sometimes be
   above 2^256.  Implementers should be careful about timing side-
   channels for Poly1305 by using the appropriate implementation of
   these operations.

   Validating the authenticity of a message involves a bitwise
   comparison of the calculated tag with the received tag.  In most use
   cases, nonces and AAD contents are not "used up" until a valid
   message is received.  This allows an attacker to send multiple
   identical messages with different tags until one passes the tag
   comparison.  This is hard if the attacker has to try all 2^128
   possible tags one by one.  However, if the timing of the tag
   comparison operation reveals how long a prefix of the calculated and
   received tags is identical, the number of messages can be reduced
   significantly.  For this reason, with online protocols,
   implementation MUST use a constant-time comparison function rather
   than relying on optimized but insecure library functions such as the
   C language's memcmp().

5.  IANA Considerations

   IANA has assigned an entry in the "Authenticated Encryption with
   Associated Data (AEAD) Parameters" registry with 29 as the Numeric
   ID, "AEAD_CHACHA20_POLY1305" as the name, and RFC 7539 as reference.

   IANA is requested to modify the registry by using this document as
   reference.

6.  References

6.1.  Normative References

   [ChaCha]   Bernstein, D., "ChaCha, a variant of Salsa20", January
              2008, <http://cr.yp.to/chacha/chacha-20080128.pdf>.

   [Poly1305]
              Bernstein, D., "The Poly1305-AES message-authentication
              code", March 2005,
              <http://cr.yp.to/mac/poly1305-20050329.pdf>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <http://www.rfc-editor.org/info/rfc2119>.

6.2.  Informative References

   [AE]       Bellare, M. and C. Namprempre, "Authenticated Encryption:
              Relations among notions and analysis of the generic
              composition paradigm", September 2008,
              <http://dl.acm.org/citation.cfm?id=1410269>.

   [Cache-Collisions]
              Bonneau, J. and I. Mironov, "Cache-Collision Timing
              Attacks Against AES", 2006,
              <http://research.microsoft.com/pubs/64024/aes-timing.pdf>.

   [FIPS-197]
              National Institute of Standards and Technology, "Advanced
              Encryption Standard (AES)", FIPS PUB 197, November 2001,
              <http://csrc.nist.gov/publications/fips/fips197/
              fips-197.pdf>.

   [LatinDances]
              Aumasson, J., Fischer, S., Khazaei, S., Meier, W., and C.
              Rechberger, "New Features of Latin Dances: Analysis of
              Salsa, ChaCha, and Rumba", December 2007,
              <http://cr.yp.to/rumba20/newfeatures-20071218.pdf>.

   [LatinDances2]
              Ishiguro, T., Kiyomoto, S., and Y. Miyake, "Modified
              version of 'Latin Dances Revisited: New Analytic Results
              of Salsa20 and ChaCha'", February 2012,
              <https://eprint.iacr.org/2012/065.pdf>.

   [NaCl]     Bernstein, D., Lange, T., and P. Schwabe, "NaCl:
              Networking and Cryptography library", July 2012,
              <http://nacl.cr.yp.to>.

   [Poly1305_Donna]
              Floodyberry, A., "poly1305-donna", February 2014,
              <https://github.com/floodyberry/poly1305-donna>.

   [Procter]  Procter, G., "A Security Analysis of the Composition of
              ChaCha20 and Poly1305", August 2014,
              <http://eprint.iacr.org/2014/613.pdf>.

   [RFC4868]  Kelly, S. and S. Frankel, "Using HMAC-SHA-256, HMAC-SHA-
              384, and HMAC-SHA-512 with IPsec", RFC 4868,
              DOI 10.17487/RFC4868, May 2007,
              <http://www.rfc-editor.org/info/rfc4868>.

   [RFC5116]  McGrew, D., "An Interface and Algorithms for Authenticated
              Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008,
              <http://www.rfc-editor.org/info/rfc5116>.

   [RFC7296]  Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T.
              Kivinen, "Internet Key Exchange Protocol Version 2
              (IKEv2)", STD 79, RFC 7296, DOI 10.17487/RFC7296, October
              2014, <http://www.rfc-editor.org/info/rfc7296>.

   [RFC7539]  Nir, Y. and A. Langley, "ChaCha20 and Poly1305 for IETF
              Protocols", RFC 7539, DOI 10.17487/RFC7539, May 2015,
              <http://www.rfc-editor.org/info/rfc7539>.

   [SP800-67]
              National Institute of Standards and Technology,
              "Recommendation for the Triple Data Encryption Algorithm
              (TDEA) Block Cipher", NIST 800-67, January 2012,
              <http://csrc.nist.gov/publications/nistpubs/800-67-Rev1/
              SP-800-67-Rev1.pdf>.

   [Standby-Cipher]
              McGrew, D., Grieco, A., and Y. Sheffer, "Selection of
              Future Cryptographic Standards", Work in Progress, draft-
              mcgrew-standby-cipher-00, January 2013.

   [Zhenqing2012]
              Zhenqing, S., Bin, Z., Dengguo, F., and W. Wenling,
              "Improved Key Recovery Attacks on Reduced-Round Salsa20
              and ChaCha*", 2012.

Appendix A.  Additional Test Vectors

   The subsections of this appendix contain more test vectors for the
   algorithms in the sub-sections of Section 2.

A.1.  The ChaCha20 Block Functions

  Test Vector #1:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Block Counter = 0

    ChaCha state at the end
        ade0b876  903df1a0  e56a5d40  28bd8653
        b819d2bd  1aed8da0  ccef36a8  c70d778b
        7c5941da  8d485751  3fe02477  374ad8b8
        f4b8436a  1ca11815  69b687c3  8665eeb2

  Keystream:
  000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
  016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..
  032  da 41 59 7c 51 57 48 8d 77 24 e0 3f b8 d8 4a 37  .AY|QWH.w$.?..J7
  048  6a 43 b8 f4 15 18 a1 1c c3 87 b6 69 b2 ee 65 86  jC.........i..e.

  Test Vector #2:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Block Counter = 1

    ChaCha state at the end
        bee7079f  7a385155  7c97ba98  0d082d73
        a0290fcb  6965e348  3e53c612  ed7aee32
        7621b729  434ee69c  b03371d5  d539d874
        281fed31  45fb0a51  1f0ae1ac  6f4d794b

  Keystream:
  000  9f 07 e7 be 55 51 38 7a 98 ba 97 7c 73 2d 08 0d  ....UQ8z...|s-..
  016  cb 0f 29 a0 48 e3 65 69 12 c6 53 3e 32 ee 7a ed  ..).H.ei..S>2.z.
  032  29 b7 21 76 9c e6 4e 43 d5 71 33 b0 74 d8 39 d5  ).!v..NC.q3.t.9.
  048  31 ed 1f 28 51 0a fb 45 ac e1 0a 1f 4b 79 4d 6f  1..(Q..E....KyMo

  Test Vector #3:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Block Counter = 1

    ChaCha state at the end
        2452eb3a  9249f8ec  8d829d9b  ddd4ceb1
        e8252083  60818b01  f38422b8  5aaa49c9
        bb00ca8e  da3ba7b4  c4b592d1  fdf2732f
        4436274e  2561b3c8  ebdd4aa6  a0136c00

  Keystream:
  000  3a eb 52 24 ec f8 49 92 9b 9d 82 8d b1 ce d4 dd  :.R$..I.........
  016  83 20 25 e8 01 8b 81 60 b8 22 84 f3 c9 49 aa 5a  . %....`."...I.Z
  032  8e ca 00 bb b4 a7 3b da d1 92 b5 c4 2f 73 f2 fd  ......;...../s..
  048  4e 27 36 44 c8 b3 61 25 a6 4a dd eb 00 6c 13 a0  N'6D..a%.J...l..

  Test Vector #4:
  ==============

  Key:
  000  00 ff 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Block Counter = 2

    ChaCha state at the end
        fb4dd572  4bc42ef1  df922636  327f1394
        a78dea8f  5e269039  a1bebbc1  caf09aae
        a25ab213  48a6b46c  1b9d9bcb  092c5be6
        546ca624  1bec45d5  87f47473  96f0992e

  Keystream:
  000  72 d5 4d fb f1 2e c4 4b 36 26 92 df 94 13 7f 32  r.M....K6&.....2
  016  8f ea 8d a7 39 90 26 5e c1 bb be a1 ae 9a f0 ca  ....9.&^........
  032  13 b2 5a a2 6c b4 a6 48 cb 9b 9d 1b e6 5b 2c 09  ..Z.l..H.....[,.
  048  24 a6 6c 54 d5 45 ec 1b 73 74 f4 87 2e 99 f0 96  $.lT.E..st......

  Test Vector #5:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

  Block Counter = 0

    ChaCha state at the end
        374dc6c2  3736d58c  b904e24a  cd3f93ef
        88228b1a  96a4dfb3  5b76ab72  c727ee54
        0e0e978a  f3145c95  1b748ea8  f786c297
        99c28f5f  628314e8  398a19fa  6ded1b53

  Keystream:
  000  c2 c6 4d 37 8c d5 36 37 4a e2 04 b9 ef 93 3f cd  ..M7..67J.....?.
  016  1a 8b 22 88 b3 df a4 96 72 ab 76 5b 54 ee 27 c7  ..".....r.v[T.'.
  032  8a 97 0e 0e 95 5c 14 f3 a8 8e 74 1b 97 c2 86 f7  .....\....t.....
  048  5f 8f c2 99 e8 14 83 62 fa 19 8a 39 53 1b ed 6d  _......b...9S..m

A.2.  ChaCha20 Encryption

  Test Vector #1:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Initial Block Counter = 0

  Plaintext:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  032  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  048  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Ciphertext:
  000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
  016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..
  032  da 41 59 7c 51 57 48 8d 77 24 e0 3f b8 d8 4a 37  .AY|QWH.w$.?..J7
  048  6a 43 b8 f4 15 18 a1 1c c3 87 b6 69 b2 ee 65 86  jC.........i..e.

  Test Vector #2:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

  Initial Block Counter = 1

  Plaintext:
  000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
  016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
  032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
  048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
  064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
  080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
  096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
  112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
  128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
  144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
  160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
  176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
  192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
  208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
  224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
  240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
  256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
  272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
  288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
  304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
  320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
  336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
  352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
  368  73 73 65 64 20 74 6f                             ssed to

  Ciphertext:
  000  a3 fb f0 7d f3 fa 2f de 4f 37 6c a2 3e 82 73 70  ...}../.O7l.>.sp
  016  41 60 5d 9f 4f 4f 57 bd 8c ff 2c 1d 4b 79 55 ec  A`].OOW...,.KyU.
  032  2a 97 94 8b d3 72 29 15 c8 f3 d3 37 f7 d3 70 05  *....r)....7..p.
  048  0e 9e 96 d6 47 b7 c3 9f 56 e0 31 ca 5e b6 25 0d  ....G...V.1.^.%.
  064  40 42 e0 27 85 ec ec fa 4b 4b b5 e8 ea d0 44 0e  @B.'....KK....D.
  080  20 b6 e8 db 09 d8 81 a7 c6 13 2f 42 0e 52 79 50   ........./B.RyP
  096  42 bd fa 77 73 d8 a9 05 14 47 b3 29 1c e1 41 1c  B..ws....G.)..A.
  112  68 04 65 55 2a a6 c4 05 b7 76 4d 5e 87 be a8 5a  h.eU*....vM^...Z
  128  d0 0f 84 49 ed 8f 72 d0 d6 62 ab 05 26 91 ca 66  ...I..r..b..&..f
  144  42 4b c8 6d 2d f8 0e a4 1f 43 ab f9 37 d3 25 9d  BK.m-....C..7.%.
  160  c4 b2 d0 df b4 8a 6c 91 39 dd d7 f7 69 66 e9 28  ......l.9...if.(
  176  e6 35 55 3b a7 6c 5c 87 9d 7b 35 d4 9e b2 e6 2b  .5U;.l\..{5....+
  192  08 71 cd ac 63 89 39 e2 5e 8a 1e 0e f9 d5 28 0f  .q..c.9.^.....(.
  208  a8 ca 32 8b 35 1c 3c 76 59 89 cb cf 3d aa 8b 6c  ..2.5.<vY...=..l
  224  cc 3a af 9f 39 79 c9 2b 37 20 fc 88 dc 95 ed 84  .:..9y.+7 ......
  240  a1 be 05 9c 64 99 b9 fd a2 36 e7 e8 18 b0 4b 0b  ....d....6....K.
  256  c3 9c 1e 87 6b 19 3b fe 55 69 75 3f 88 12 8c c0  ....k.;.Uiu?....
  272  8a aa 9b 63 d1 a1 6f 80 ef 25 54 d7 18 9c 41 1f  ...c..o..%T...A.
  288  58 69 ca 52 c5 b8 3f a3 6f f2 16 b9 c1 d3 00 62  Xi.R..?.o......b
  304  be bc fd 2d c5 bc e0 91 19 34 fd a7 9a 86 f6 e6  ...-.....4......
  320  98 ce d7 59 c3 ff 9b 64 77 33 8f 3d a4 f9 cd 85  ...Y...dw3.=....
  336  14 ea 99 82 cc af b3 41 b2 38 4d d9 02 f3 d1 ab  .......A.8M.....
  352  7a c6 1d d2 9c 6f 21 ba 5b 86 2f 37 30 e3 7c fd  z....o!.[./70.|.
  368  c4 fd 80 6c 22 f2 21                             ...l".!

  Test Vector #3:
  ==============

  Key:
  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

  Initial Block Counter = 42

  Plaintext:
  000  27 54 77 61 73 20 62 72 69 6c 6c 69 67 2c 20 61  'Twas brillig, a
  016  6e 64 20 74 68 65 20 73 6c 69 74 68 79 20 74 6f  nd the slithy to
  032  76 65 73 0a 44 69 64 20 67 79 72 65 20 61 6e 64  ves.Did gyre and
  048  20 67 69 6d 62 6c 65 20 69 6e 20 74 68 65 20 77   gimble in the w
  064  61 62 65 3a 0a 41 6c 6c 20 6d 69 6d 73 79 20 77  abe:.All mimsy w
  080  65 72 65 20 74 68 65 20 62 6f 72 6f 67 6f 76 65  ere the borogove
  096  73 2c 0a 41 6e 64 20 74 68 65 20 6d 6f 6d 65 20  s,.And the mome
  112  72 61 74 68 73 20 6f 75 74 67 72 61 62 65 2e     raths outgrabe.

  Ciphertext:
  000  62 e6 34 7f 95 ed 87 a4 5f fa e7 42 6f 27 a1 df  b.4....._..Bo'..
  016  5f b6 91 10 04 4c 0d 73 11 8e ff a9 5b 01 e5 cf  _....L.s....[...
  032  16 6d 3d f2 d7 21 ca f9 b2 1e 5f b1 4c 61 68 71  .m=..!...._.Lahq
  048  fd 84 c5 4f 9d 65 b2 83 19 6c 7f e4 f6 05 53 eb  ...O.e...l....S.
  064  f3 9c 64 02 c4 22 34 e3 2a 35 6b 3e 76 43 12 a6  ..d.."4.*5k>vC..
  080  1a 55 32 05 57 16 ea d6 96 25 68 f8 7d 3f 3f 77  .U2.W....%h.}??w
  096  04 c6 a8 d1 bc d1 bf 4d 50 d6 15 4b 6d a7 31 b1  .......MP..Km.1.
  112  87 b5 8d fd 72 8a fa 36 75 7a 79 7a c1 88 d1     ....r..6uzyz...

A.3.  Poly1305 Message Authentication Code

   Notice how, in test vector #2, r is equal to zero.  The part of the
   Poly1305 algorithm where the accumulator is multiplied by r means
   that with r equal zero, the tag will be equal to s regardless of the
   content of the text.  Fortunately, all the proposed methods of
   generating r are such that getting this particular weak key is very
   unlikely.

  Test Vector #1:
  ==============

  One-time Poly1305 Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Text to MAC:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  032  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  048  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Tag:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Test Vector #2:
  ==============

  One-time Poly1305 Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>

  Text to MAC:
  000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
  016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
  032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
  048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
  064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
  080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
  096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
  112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
  128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
  144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
  160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
  176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
  192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
  208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
  224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
  240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
  256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
  272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
  288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
  304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
  320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
  336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
  352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
  368  73 73 65 64 20 74 6f                             ssed to

  Tag:
  000  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>

  Test Vector #3:
  ==============

  One-time Poly1305 Key:
  000  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Text to MAC:
  000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
  016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
  032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
  048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
  064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
  080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
  096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
  112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
  128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
  144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
  160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
  176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
  192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
  208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
  224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
  240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
  256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
  272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
  288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
  304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
  320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
  336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
  352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
  368  73 73 65 64 20 74 6f                             ssed to

  Tag:
  000  f3 47 7e 7c d9 54 17 af 89 a6 b8 79 4c 31 0c f0  .G~|.T.....yL1..

  Test Vector #4:
  ==============

  One-time Poly1305 Key:
  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

  Text to MAC:
  000  27 54 77 61 73 20 62 72 69 6c 6c 69 67 2c 20 61  'Twas brillig, a
  016  6e 64 20 74 68 65 20 73 6c 69 74 68 79 20 74 6f  nd the slithy to
  032  76 65 73 0a 44 69 64 20 67 79 72 65 20 61 6e 64  ves.Did gyre and
  048  20 67 69 6d 62 6c 65 20 69 6e 20 74 68 65 20 77   gimble in the w
  064  61 62 65 3a 0a 41 6c 6c 20 6d 69 6d 73 79 20 77  abe:.All mimsy w
  080  65 72 65 20 74 68 65 20 62 6f 72 6f 67 6f 76 65  ere the borogove
  096  73 2c 0a 41 6e 64 20 74 68 65 20 6d 6f 6d 65 20  s,.And the mome
  112  72 61 74 68 73 20 6f 75 74 67 72 61 62 65 2e     raths outgrabe.

  Tag:
  000  45 41 66 9a 7e aa ee 61 e7 08 dc 7c bc c5 eb 62  EAf.~..a...|...b

   Test Vector #5: If one uses 130-bit partial reduction, does the code
   handle the case where partially reduced final result is not fully
   reduced?

   R:
   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   tag:
   03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   Test Vector #6: What happens if addition of s overflows modulo 2^128?

   R:
   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   S:
   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   data:
   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   tag:
   03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   Test Vector #7: What happens if data limb is all ones and there is
   carry from lower limb?

   R:
   01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   F0 FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   tag:
   05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   Test Vector #8: What happens if final result from polynomial part is
   exactly 2^130-5?

   R:
   01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   FB FE FE FE FE FE FE FE FE FE FE FE FE FE FE FE
   01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
   tag:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   Test Vector #9: What happens if final result from polynomial part is
   exactly 2^130-6?

   R:
   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   FD FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   tag:
   FA FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF

   Test Vector #10: What happens if 5*H+L-type reduction produces
   131-bit intermediate result?

   R:
   01 00 00 00 00 00 00 00 04 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   E3 35 94 D7 50 5E 43 B9 00 00 00 00 00 00 00 00
   33 94 D7 50 5E 43 79 CD 01 00 00 00 00 00 00 00
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   tag:
   14 00 00 00 00 00 00 00 55 00 00 00 00 00 00 00

   Test Vector #11: What happens if 5*H+L-type reduction produces
   131-bit final result?

   R:
   01 00 00 00 00 00 00 00 04 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   E3 35 94 D7 50 5E 43 B9 00 00 00 00 00 00 00 00
   33 94 D7 50 5E 43 79 CD 01 00 00 00 00 00 00 00
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   tag:
   13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

A.4.  Poly1305 Key Generation Using ChaCha20

  Test Vector #1:
  ==============

  The key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  The nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Poly1305 one-time key:
  000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
  016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..

  Test Vector #2:
  ==============

  The key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

  The nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

  Poly1305 one-time key:
  000  ec fa 25 4f 84 5f 64 74 73 d3 cb 14 0d a9 e8 76  ..%O._dts......v
  016  06 cb 33 06 6c 44 7b 87 bc 26 66 dd e3 fb b7 39  ..3.lD{..&f....9

  Test Vector #3:
  ==============

  The key:
  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

  The nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

  Poly1305 one-time key:
  000  96 5e 3b c6 f9 ec 7e d9 56 08 08 f4 d2 29 f9 4b  .^;...~.V....).K
  016  13 7f f2 75 ca 9b 3f cb dd 59 de aa d2 33 10 ae  ...u..?..Y...3..

A.5.  ChaCha20-Poly1305 AEAD Decryption

   Below we see decrypting a message.  We receive a ciphertext, a nonce,
   and a tag.  We know the key.  We will check the tag and then
   (assuming that it validates) decrypt the ciphertext.  In this
   particular protocol, we'll assume that there is no padding of the
   plaintext.

  The key:
  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

  Ciphertext:
  000  64 a0 86 15 75 86 1a f4 60 f0 62 c7 9b e6 43 bd  d...u...`.b...C.
  016  5e 80 5c fd 34 5c f3 89 f1 08 67 0a c7 6c 8c b2  ^.\.4\....g..l..
  032  4c 6c fc 18 75 5d 43 ee a0 9e e9 4e 38 2d 26 b0  Ll..u]C....N8-&.
  048  bd b7 b7 3c 32 1b 01 00 d4 f0 3b 7f 35 58 94 cf  ...<2.....;.5X..
  064  33 2f 83 0e 71 0b 97 ce 98 c8 a8 4a bd 0b 94 81  3/..q......J....
  080  14 ad 17 6e 00 8d 33 bd 60 f9 82 b1 ff 37 c8 55  ...n..3.`....7.U
  096  97 97 a0 6e f4 f0 ef 61 c1 86 32 4e 2b 35 06 38  ...n...a..2N+5.8
  112  36 06 90 7b 6a 7c 02 b0 f9 f6 15 7b 53 c8 67 e4  6..{j|.....{S.g.
  128  b9 16 6c 76 7b 80 4d 46 a5 9b 52 16 cd e7 a4 e9  ..lv{.MF..R.....
  144  90 40 c5 a4 04 33 22 5e e2 82 a1 b0 a0 6c 52 3e  .@...3"^.....lR>
  160  af 45 34 d7 f8 3f a1 15 5b 00 47 71 8c bc 54 6a  .E4..?..[.Gq..Tj
  176  0d 07 2b 04 b3 56 4e ea 1b 42 22 73 f5 48 27 1a  ..+..VN..B"s.H'.
  192  0b b2 31 60 53 fa 76 99 19 55 eb d6 31 59 43 4e  ..1`S.v..U..1YCN
  208  ce bb 4e 46 6d ae 5a 10 73 a6 72 76 27 09 7a 10  ..NFm.Z.s.rv'.z.
  224  49 e6 17 d9 1d 36 10 94 fa 68 f0 ff 77 98 71 30  I....6...h..w.q0
  240  30 5b ea ba 2e da 04 df 99 7b 71 4d 6c 6f 2c 29  0[.......{qMlo,)
  256  a6 ad 5c b4 02 2b 02 70 9b                       ..\..+.p.

  The nonce:
  000  00 00 00 00 01 02 03 04 05 06 07 08              ............

  The AAD:
  000  f3 33 88 86 00 00 00 00 00 00 4e 91              .3........N.

  Received Tag:
  000  ee ad 9d 67 89 0c bb 22 39 23 36 fe a1 85 1f 38  ...g..."9#6....8

   First, we calculate the one-time Poly1305 key

  @@@  ChaCha state with key setup
        61707865  3320646e  79622d32  6b206574
        a540921c  8ad355eb  868833f3  f0b5f604
        c1173947  09802b40  bc5cca9d  c0757020
        00000000  00000000  04030201  08070605

  @@@  ChaCha state after 20 rounds
        a94af0bd  89dee45c  b64bb195  afec8fa1
        508f4726  63f554c0  1ea2c0db  aa721526
        11b1e514  a0bacc0f  828a6015  d7825481
        e8a4a850  d9dcbbd6  4c2de33a  f8ccd912

  @@@ out bytes:
  bd:f0:4a:a9:5c:e4:de:89:95:b1:4b:b6:a1:8f:ec:af:
  26:47:8f:50:c0:54:f5:63:db:c0:a2:1e:26:15:72:aa

  Poly1305 one-time key:
  000  bd f0 4a a9 5c e4 de 89 95 b1 4b b6 a1 8f ec af  ..J.\.....K.....
  016  26 47 8f 50 c0 54 f5 63 db c0 a2 1e 26 15 72 aa  &G.P.T.c....&.r.

   Next, we construct the AEAD buffer

  Poly1305 Input:
  000  f3 33 88 86 00 00 00 00 00 00 4e 91 00 00 00 00  .3........N.....
  016  64 a0 86 15 75 86 1a f4 60 f0 62 c7 9b e6 43 bd  d...u...`.b...C.
  032  5e 80 5c fd 34 5c f3 89 f1 08 67 0a c7 6c 8c b2  ^.\.4\....g..l..
  048  4c 6c fc 18 75 5d 43 ee a0 9e e9 4e 38 2d 26 b0  Ll..u]C....N8-&.
  064  bd b7 b7 3c 32 1b 01 00 d4 f0 3b 7f 35 58 94 cf  ...<2.....;.5X..
  080  33 2f 83 0e 71 0b 97 ce 98 c8 a8 4a bd 0b 94 81  3/..q......J....
  096  14 ad 17 6e 00 8d 33 bd 60 f9 82 b1 ff 37 c8 55  ...n..3.`....7.U
  112  97 97 a0 6e f4 f0 ef 61 c1 86 32 4e 2b 35 06 38  ...n...a..2N+5.8
  128  36 06 90 7b 6a 7c 02 b0 f9 f6 15 7b 53 c8 67 e4  6..{j|.....{S.g.
  144  b9 16 6c 76 7b 80 4d 46 a5 9b 52 16 cd e7 a4 e9  ..lv{.MF..R.....
  160  90 40 c5 a4 04 33 22 5e e2 82 a1 b0 a0 6c 52 3e  .@...3"^.....lR>
  176  af 45 34 d7 f8 3f a1 15 5b 00 47 71 8c bc 54 6a  .E4..?..[.Gq..Tj
  192  0d 07 2b 04 b3 56 4e ea 1b 42 22 73 f5 48 27 1a  ..+..VN..B"s.H'.
  208  0b b2 31 60 53 fa 76 99 19 55 eb d6 31 59 43 4e  ..1`S.v..U..1YCN
  224  ce bb 4e 46 6d ae 5a 10 73 a6 72 76 27 09 7a 10  ..NFm.Z.s.rv'.z.
  240  49 e6 17 d9 1d 36 10 94 fa 68 f0 ff 77 98 71 30  I....6...h..w.q0
  256  30 5b ea ba 2e da 04 df 99 7b 71 4d 6c 6f 2c 29  0[.......{qMlo,)
  272  a6 ad 5c b4 02 2b 02 70 9b 00 00 00 00 00 00 00  ..\..+.p........
  288  0c 00 00 00 00 00 00 00 09 01 00 00 00 00 00 00  ................

   We calculate the Poly1305 tag and find that it matches

  Calculated Tag:
  000  ee ad 9d 67 89 0c bb 22 39 23 36 fe a1 85 1f 38  ...g..."9#6....8

   Finally, we decrypt the ciphertext

  Plaintext::
  000  49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 73 20  Internet-Drafts
  016  61 72 65 20 64 72 61 66 74 20 64 6f 63 75 6d 65  are draft docume
  032  6e 74 73 20 76 61 6c 69 64 20 66 6f 72 20 61 20  nts valid for a
  048  6d 61 78 69 6d 75 6d 20 6f 66 20 73 69 78 20 6d  maximum of six m
  064  6f 6e 74 68 73 20 61 6e 64 20 6d 61 79 20 62 65  onths and may be
  080  20 75 70 64 61 74 65 64 2c 20 72 65 70 6c 61 63   updated, replac
  096  65 64 2c 20 6f 72 20 6f 62 73 6f 6c 65 74 65 64  ed, or obsoleted
  112  20 62 79 20 6f 74 68 65 72 20 64 6f 63 75 6d 65   by other docume
  128  6e 74 73 20 61 74 20 61 6e 79 20 74 69 6d 65 2e  nts at any time.
  144  20 49 74 20 69 73 20 69 6e 61 70 70 72 6f 70 72   It is inappropr
  160  69 61 74 65 20 74 6f 20 75 73 65 20 49 6e 74 65  iate to use Inte
  176  72 6e 65 74 2d 44 72 61 66 74 73 20 61 73 20 72  rnet-Drafts as r
  192  65 66 65 72 65 6e 63 65 20 6d 61 74 65 72 69 61  eference materia
  208  6c 20 6f 72 20 74 6f 20 63 69 74 65 20 74 68 65  l or to cite the
  224  6d 20 6f 74 68 65 72 20 74 68 61 6e 20 61 73 20  m other than as
  240  2f e2 80 9c 77 6f 72 6b 20 69 6e 20 70 72 6f 67  /...work in prog
  256  72 65 73 73 2e 2f e2 80 9d                       ress./...

Appendix B.  Performance Measurements of ChaCha20

   The following measurements were made by Adam Langley for a blog post
   published on February 27th, 2014.  The original blog post was
   available at the time of this writing at
   <https://www.imperialviolet.org/2014/02/27/tlssymmetriccrypto.html>.

     +----------------------------+-------------+-------------------+
     | Chip                       | AES-128-GCM | ChaCha20-Poly1305 |
     +----------------------------+-------------+-------------------+
     | OMAP 4460                  |  24.1 MB/s  |     75.3 MB/s     |
     | Snapdragon S4 Pro          |  41.5 MB/s  |     130.9 MB/s    |
     | Sandy Bridge Xeon (AES-NI) |   900 MB/s  |      500 MB/s     |
     +----------------------------+-------------+-------------------+

                         Table 1: Speed Comparison

Acknowledgements

   ChaCha20 and Poly1305 were invented by Daniel J. Bernstein.  The AEAD
   construction and the method of creating the one-time Poly1305 key
   were invented by Adam Langley.

   Thanks to Robert Ransom, Watson Ladd, Stefan Buhler, Dan Harkins, and
   Kenny Paterson for their helpful comments and explanations.  Thanks
   to Niels Moller for suggesting the more efficient AEAD construction
   in this document.  Special thanks to Ilari Liusvaara for providing
   extra test vectors, helpful comments, and for being the first to
   attempt an implementation from this document.  Thanks to Sean
   Parkinson for suggesting improvements to the examples and the
   pseudocode.  Thanks to David Ireland for pointing out a bug in the
   pseudocode, and to Stephen Farrell and Alyssa Rowan for pointing out
   missing advise in the security considerations.

   Special thanks goes to Gordon Procter for performing a security
   analysis of the composition and publishing [Procter].

Authors' Addresses

   Yoav Nir
   Check Point Software Technologies, Ltd.
   5 Hasolelim st.
   Tel Aviv  6789735
   Israel

   EMail: ynir.ietf@gmail.com


   Adam Langley
   Google, Inc.

   EMail: agl@google.com


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Internet Research Task Force (IRTF)                               Y. Nir
Request for Comments: 7539                                   Check Point
Category: Informational                                       A. Langley
ISSN: 2070-1721                                             Google, Inc.
                                                                May 2015


                ChaCha20 and Poly1305 for IETF Protocols

Abstract

   This document defines the ChaCha20 stream cipher as well as the use
   of the Poly1305 authenticator, both as stand-alone algorithms and as
   a "combined mode", or Authenticated Encryption with Associated Data
   (AEAD) algorithm.

   This document does not introduce any new crypto, but is meant to
   serve as a stable reference and an implementation guide.  It is a
   product of the Crypto Forum Research Group (CFRG).

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This document is a product of the Internet Research Task Force
   (IRTF).  The IRTF publishes the results of Internet-related research
   and development activities.  These results might not be suitable for
   deployment.  This RFC represents the consensus of the Crypto Forum
   Research Group of the Internet Research Task Force (IRTF).  Documents
   approved for publication by the IRSG are not a candidate for any
   level of Internet Standard; see Section 2 of RFC 5741.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   http://www.rfc-editor.org/info/rfc7539.

Copyright Notice

   Copyright (c) 2015 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.
   
Table of Contents

   1.  Introduction
     1.1.  Conventions Used in This Document
   2.  The Algorithms
     2.1.  The ChaCha Quarter Round
       2.1.1.  Test Vector for the ChaCha Quarter Round
     2.2.  A Quarter Round on the ChaCha State
       2.2.1.  Test Vector for the Quarter Round on the ChaCha State
     2.3.  The ChaCha20 Block Function
       2.3.1.  The ChaCha20 Block Function in Pseudocode
       2.3.2.  Test Vector for the ChaCha20 Block Function
     2.4.  The ChaCha20 Encryption Algorithm
       2.4.1.  The ChaCha20 Encryption Algorithm in Pseudocode
       2.4.2.  Example and Test Vector for the ChaCha20 Cipher
     2.5.  The Poly1305 Algorithm
       2.5.1.  The Poly1305 Algorithms in Pseudocode
       2.5.2.  Poly1305 Example and Test Vector
     2.6.  Generating the Poly1305 Key Using ChaCha20
       2.6.1.  Poly1305 Key Generation in Pseudocode
       2.6.2.  Poly1305 Key Generation Test Vector
     2.7.  A Pseudorandom Function for Crypto Suites based on
           ChaCha/Poly1305
     2.8.  AEAD Construction
       2.8.1.  Pseudocode for the AEAD Construction
       2.8.2.  Example and Test Vector for AEAD_CHACHA20_POLY1305
   3.  Implementation Advice
   4.  Security Considerations
   5.  IANA Considerations
   6.  References
     6.1.  Normative References
     6.2.  Informative References
   Appendix A.  Additional Test Vectors
     A.1.  The ChaCha20 Block Functions
     A.2.  ChaCha20 Encryption
     A.3.  Poly1305 Message Authentication Code
     A.4.  Poly1305 Key Generation Using ChaCha20
     A.5.  ChaCha20-Poly1305 AEAD Decryption
   Appendix B.  Performance Measurements of ChaCha20
   Acknowledgements
   Authors' Addresses

1.  Introduction

   The Advanced Encryption Standard (AES -- [FIPS-197]) has become the
   gold standard in encryption.  Its efficient design, widespread
   implementation, and hardware support allow for high performance in
   many areas.  On most modern platforms, AES is anywhere from four to
   ten times as fast as the previous most-used cipher, Triple Data
   Encryption Standard (3DES -- [SP800-67]), which makes it not only the
   best choice, but the only practical choice.

   There are several problems with this.  If future advances in
   cryptanalysis reveal a weakness in AES, users will be in an
   unenviable position.  With the only other widely supported cipher
   being the much slower 3DES, it is not feasible to reconfigure
   deployments to use 3DES.  [Standby-Cipher] describes this issue and
   the need for a standby cipher in greater detail.  Another problem is
   that while AES is very fast on dedicated hardware, its performance on
   platforms that lack such hardware is considerably lower.  Yet another
   problem is that many AES implementations are vulnerable to cache-
   collision timing attacks ([Cache-Collisions]).

   This document provides a definition and implementation guide for
   three algorithms:

   1.  The ChaCha20 cipher.  This is a high-speed cipher first described
       in [ChaCha].  It is considerably faster than AES in software-only
       implementations, making it around three times as fast on
       platforms that lack specialized AES hardware.  See Appendix B for
       some hard numbers.  ChaCha20 is also not sensitive to timing
       attacks (see the security considerations in Section 4).  This
       algorithm is described in Section 2.4

   2.  The Poly1305 authenticator.  This is a high-speed message
       authentication code.  Implementation is also straightforward and
       easy to get right.  The algorithm is described in Section 2.5.

   3.  The CHACHA20-POLY1305 Authenticated Encryption with Associated
       Data (AEAD) construction, described in Section 2.8.

   This document does not introduce these new algorithms for the first
   time.  They have been defined in scientific papers by
   D. J. Bernstein, which are referenced by this document.  The purpose
   of this document is to serve as a stable reference for IETF documents
   making use of these algorithms.

   These algorithms have undergone rigorous analysis.  Several papers
   discuss the security of Salsa and ChaCha ([LatinDances],
   [LatinDances2], [Zhenqing2012]).

   This document represents the consensus of the Crypto Forum Research
   Group (CFRG).

1.1.  Conventions Used in This Document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].

   The description of the ChaCha algorithm will at various time refer to
   the ChaCha state as a "vector" or as a "matrix".  This follows the
   use of these terms in Professor Bernstein's paper.  The matrix
   notation is more visually convenient and gives a better notion as to
   why some rounds are called "column rounds" while others are called
   "diagonal rounds".  Here's a diagram of how the matrices relate to
   vectors (using the C language convention of zero being the index
   origin).

      0   1   2   3
      4   5   6   7
      8   9  10  11
     12  13  14  15

   The elements in this vector or matrix are 32-bit unsigned integers.

   The algorithm name is "ChaCha".  "ChaCha20" is a specific instance
   where 20 "rounds" (or 80 quarter rounds -- see Section 2.1) are used.
   Other variations are defined, with 8 or 12 rounds, but in this
   document we only describe the 20-round ChaCha, so the names "ChaCha"
   and "ChaCha20" will be used interchangeably.

2.  The Algorithms

   The subsections below describe the algorithms used and the AEAD
   construction.

2.1.  The ChaCha Quarter Round

   The basic operation of the ChaCha algorithm is the quarter round.  It
   operates on four 32-bit unsigned integers, denoted a, b, c, and d.
   The operation is as follows (in C-like notation):

   1.  a += b; d ^= a; d <<<= 16;
   2.  c += d; b ^= c; b <<<= 12;
   3.  a += b; d ^= a; d <<<= 8;
   4.  c += d; b ^= c; b <<<= 7;

   Where "+" denotes integer addition modulo 2^32, "^" denotes a bitwise
   Exclusive OR (XOR), and "<<< n" denotes an n-bit left rotation
   (towards the high bits).

   For example, let's see the add, XOR, and roll operations from the
   fourth line with sample numbers:

   o  a = 0x11111111
   o  b = 0x01020304
   o  c = 0x77777777
   o  d = 0x01234567
   o  c = c + d = 0x77777777 + 0x01234567 = 0x789abcde
   o  b = b ^ c = 0x01020304 ^ 0x789abcde = 0x7998bfda
   o  b = b <<< 7 = 0x7998bfda <<< 7 = 0xcc5fed3c

2.1.1.  Test Vector for the ChaCha Quarter Round

   For a test vector, we will use the same numbers as in the example,
   adding something random for c.

   o  a = 0x11111111
   o  b = 0x01020304
   o  c = 0x9b8d6f43
   o  d = 0x01234567

   After running a Quarter Round on these four numbers, we get these:

   o  a = 0xea2a92f4
   o  b = 0xcb1cf8ce
   o  c = 0x4581472e
   o  d = 0x5881c4bb

2.2.  A Quarter Round on the ChaCha State

   The ChaCha state does not have four integer numbers: it has 16.  So
   the quarter-round operation works on only four of them -- hence the
   name.  Each quarter round operates on four predetermined numbers in
   the ChaCha state.  We will denote by QUARTERROUND(x,y,z,w) a quarter-
   round operation on the numbers at indices x, y, z, and w of the
   ChaCha state when viewed as a vector.  For example, if we apply
   QUARTERROUND(1,5,9,13) to a state, this means running the quarter-
   round operation on the elements marked with an asterisk, while
   leaving the others alone:

      0  *a   2   3
      4  *b   6   7
      8  *c  10  11
     12  *d  14  15

   Note that this run of quarter round is part of what is called a
   "column round".

2.2.1.  Test Vector for the Quarter Round on the ChaCha State

   For a test vector, we will use a ChaCha state that was generated
   randomly:

   Sample ChaCha State

       879531e0  c5ecf37d  516461b1  c9a62f8a
       44c20ef3  3390af7f  d9fc690b  2a5f714c
       53372767  b00a5631  974c541a  359e9963
       5c971061  3d631689  2098d9d6  91dbd320

   We will apply the QUARTERROUND(2,7,8,13) operation to this state.
   For obvious reasons, this one is part of what is called a "diagonal
   round":

   After applying QUARTERROUND(2,7,8,13)

       879531e0  c5ecf37d *bdb886dc  c9a62f8a
       44c20ef3  3390af7f  d9fc690b *cfacafd2
      *e46bea80  b00a5631  974c541a  359e9963
       5c971061 *ccc07c79  2098d9d6  91dbd320

   Note that only the numbers in positions 2, 7, 8, and 13 changed.

2.3.  The ChaCha20 Block Function

   The ChaCha block function transforms a ChaCha state by running
   multiple quarter rounds.

   The inputs to ChaCha20 are:

   o  A 256-bit key, treated as a concatenation of eight 32-bit little-
      endian integers.

   o  A 96-bit nonce, treated as a concatenation of three 32-bit little-
      endian integers.

   o  A 32-bit block count parameter, treated as a 32-bit little-endian
      integer.

   The output is 64 random-looking bytes.

   The ChaCha algorithm described here uses a 256-bit key.  The original
   algorithm also specified 128-bit keys and 8- and 12-round variants,
   but these are out of scope for this document.  In this section, we
   describe the ChaCha block function.

   Note also that the original ChaCha had a 64-bit nonce and 64-bit
   block count.  We have modified this here to be more consistent with
   recommendations in Section 3.2 of [RFC5116].  This limits the use of
   a single (key,nonce) combination to 2^32 blocks, or 256 GB, but that
   is enough for most uses.  In cases where a single key is used by
   multiple senders, it is important to make sure that they don't use
   the same nonces.  This can be assured by partitioning the nonce space
   so that the first 32 bits are unique per sender, while the other 64
   bits come from a counter.

   The ChaCha20 state is initialized as follows:

   o  The first four words (0-3) are constants: 0x61707865, 0x3320646e,
      0x79622d32, 0x6b206574.

   o  The next eight words (4-11) are taken from the 256-bit key by
      reading the bytes in little-endian order, in 4-byte chunks.

   o  Word 12 is a block counter.  Since each block is 64-byte, a 32-bit
      word is enough for 256 gigabytes of data.

   o  Words 13-15 are a nonce, which should not be repeated for the same
      key.  The 13th word is the first 32 bits of the input nonce taken
      as a little-endian integer, while the 15th word is the last 32
      bits.

       cccccccc  cccccccc  cccccccc  cccccccc
       kkkkkkkk  kkkkkkkk  kkkkkkkk  kkkkkkkk
       kkkkkkkk  kkkkkkkk  kkkkkkkk  kkkkkkkk
       bbbbbbbb  nnnnnnnn  nnnnnnnn  nnnnnnnn

   c=constant k=key b=blockcount n=nonce

   ChaCha20 runs 20 rounds, alternating between "column rounds" and
   "diagonal rounds".  Each round consists of four quarter-rounds, and
   they are run as follows.  Quarter rounds 1-4 are part of a "column"
   round, while 5-8 are part of a "diagonal" round:

   1.  QUARTERROUND ( 0, 4, 8,12)
   2.  QUARTERROUND ( 1, 5, 9,13)
   3.  QUARTERROUND ( 2, 6,10,14)
   4.  QUARTERROUND ( 3, 7,11,15)
   5.  QUARTERROUND ( 0, 5,10,15)
   6.  QUARTERROUND ( 1, 6,11,12)
   7.  QUARTERROUND ( 2, 7, 8,13)
   8.  QUARTERROUND ( 3, 4, 9,14)

   At the end of 20 rounds (or 10 iterations of the above list), we add
   the original input words to the output words, and serialize the
   result by sequencing the words one-by-one in little-endian order.

   Note: "addition" in the above paragraph is done modulo 2^32.  In some
   machine languages, this is called carryless addition on a 32-bit
   word.

2.3.1.  The ChaCha20 Block Function in Pseudocode

   Note: This section and a few others contain pseudocode for the
   algorithm explained in a previous section.  Every effort was made for
   the pseudocode to accurately reflect the algorithm as described in
   the preceding section.  If a conflict is still present, the textual
   explanation and the test vectors are normative.

      inner_block (state):
         Qround(state, 0, 4, 8,12)
         Qround(state, 1, 5, 9,13)
         Qround(state, 2, 6,10,14)
         Qround(state, 3, 7,11,15)
         Qround(state, 0, 5,10,15)
         Qround(state, 1, 6,11,12)
         Qround(state, 2, 7, 8,13)
         Qround(state, 3, 4, 9,14)
         end

      chacha20_block(key, counter, nonce):
         state = constants | key | counter | nonce
         working_state = state
         for i=1 upto 10
            inner_block(working_state)
            end
         state += working_state
         return serialize(state)
         end

2.3.2.  Test Vector for the ChaCha20 Block Function

   For a test vector, we will use the following inputs to the ChaCha20
   block function:

   o  Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13:
      14:15:16:17:18:19:1a:1b:1c:1d:1e:1f.  The key is a sequence of
      octets with no particular structure before we copy it into the
      ChaCha state.

   o  Nonce = (00:00:00:09:00:00:00:4a:00:00:00:00)

   o  Block Count = 1.

   After setting up the ChaCha state, it looks like this:

   ChaCha state with the key setup.

       61707865  3320646e  79622d32  6b206574
       03020100  07060504  0b0a0908  0f0e0d0c
       13121110  17161514  1b1a1918  1f1e1d1c
       00000001  09000000  4a000000  00000000

   After running 20 rounds (10 column rounds interleaved with 10
   "diagonal rounds"), the ChaCha state looks like this:

   ChaCha state after 20 rounds

       837778ab  e238d763  a67ae21e  5950bb2f
       c4f2d0c7  fc62bb2f  8fa018fc  3f5ec7b7
       335271c2  f29489f3  eabda8fc  82e46ebd
       d19c12b4  b04e16de  9e83d0cb  4e3c50a2

   Finally, we add the original state to the result (simple vector or
   matrix addition), giving this:

   ChaCha state at the end of the ChaCha20 operation

       e4e7f110  15593bd1  1fdd0f50  c47120a3
       c7f4d1c7  0368c033  9aaa2204  4e6cd4c3
       466482d2  09aa9f07  05d7c214  a2028bd9
       d19c12b5  b94e16de  e883d0cb  4e3c50a2

   After we serialize the state, we get this:

  Serialized Block:
  000  10 f1 e7 e4 d1 3b 59 15 50 0f dd 1f a3 20 71 c4  .....;Y.P.... q.
  016  c7 d1 f4 c7 33 c0 68 03 04 22 aa 9a c3 d4 6c 4e  ....3.h.."....lN
  032  d2 82 64 46 07 9f aa 09 14 c2 d7 05 d9 8b 02 a2  ..dF............
  048  b5 12 9c d1 de 16 4e b9 cb d0 83 e8 a2 50 3c 4e  ......N......P<N

2.4.  The ChaCha20 Encryption Algorithm

   ChaCha20 is a stream cipher designed by D. J. Bernstein.  It is a
   refinement of the Salsa20 algorithm, and it uses a 256-bit key.

   ChaCha20 successively calls the ChaCha20 block function, with the
   same key and nonce, and with successively increasing block counter
   parameters.  ChaCha20 then serializes the resulting state by writing
   the numbers in little-endian order, creating a keystream block.
   Concatenating the keystream blocks from the successive blocks forms a
   keystream.  The ChaCha20 function then performs an XOR of this
   keystream with the plaintext.  Alternatively, each keystream block
   can be XORed with a plaintext block before proceeding to create the
   next block, saving some memory.  There is no requirement for the
   plaintext to be an integral multiple of 512 bits.  If there is extra
   keystream from the last block, it is discarded.  Specific protocols
   MAY require that the plaintext and ciphertext have certain length.
   Such protocols need to specify how the plaintext is padded and how
   much padding it receives.

   The inputs to ChaCha20 are:

   o  A 256-bit key

   o  A 32-bit initial counter.  This can be set to any number, but will
      usually be zero or one.  It makes sense to use one if we use the
      zero block for something else, such as generating a one-time
      authenticator key as part of an AEAD algorithm.

   o  A 96-bit nonce.  In some protocols, this is known as the
      Initialization Vector.

   o  An arbitrary-length plaintext

   The output is an encrypted message, or "ciphertext", of the same
   length.

   Decryption is done in the same way.  The ChaCha20 block function is
   used to expand the key into a keystream, which is XORed with the
   ciphertext giving back the plaintext.

2.4.1.  The ChaCha20 Encryption Algorithm in Pseudocode

     chacha20_encrypt(key, counter, nonce, plaintext):
        for j = 0 upto floor(len(plaintext)/64)-1
           key_stream = chacha20_block(key, counter+j, nonce)
           block = plaintext[(j*64)..(j*64+63)]
           encrypted_message +=  block ^ key_stream
           end
        if ((len(plaintext) % 64) != 0)
           j = floor(len(plaintext)/64)
           key_stream = chacha20_block(key, counter+j, nonce)
           block = plaintext[(j*64)..len(plaintext)-1]
           encrypted_message += (block^key_stream)[0..len(plaintext)%64]
           end
        return encrypted_message
        end

2.4.2.  Example and Test Vector for the ChaCha20 Cipher

   For a test vector, we will use the following inputs to the ChaCha20
   block function:

   o  Key = 00:01:02:03:04:05:06:07:08:09:0a:0b:0c:0d:0e:0f:10:11:12:13:
      14:15:16:17:18:19:1a:1b:1c:1d:1e:1f.

   o  Nonce = (00:00:00:00:00:00:00:4a:00:00:00:00).

   o  Initial Counter = 1.

   We use the following for the plaintext.  It was chosen to be long
   enough to require more than one block, but not so long that it would
   make this example cumbersome (so, less than 3 blocks):

  Plaintext Sunscreen:
  000  4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c  Ladies and Gentl
  016  65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73  emen of the clas
  032  73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63  s of '99: If I c
  048  6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f  ould offer you o
  064  6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20  nly one tip for
  080  74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73  the future, suns
  096  63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69  creen would be i
  112  74 2e                                            t.

   The following figure shows four ChaCha state matrices:

   1.  First block as it is set up.

   2.  Second block as it is set up.  Note that these blocks are only
       two bits apart -- only the counter in position 12 is different.

   3.  Third block is the first block after the ChaCha20 block
       operation.

   4.  Final block is the second block after the ChaCha20 block
       operation was applied.

   After that, we show the keystream.

   First block setup:
       61707865  3320646e  79622d32  6b206574
       03020100  07060504  0b0a0908  0f0e0d0c
       13121110  17161514  1b1a1918  1f1e1d1c
       00000001  00000000  4a000000  00000000

   Second block setup:
       61707865  3320646e  79622d32  6b206574
       03020100  07060504  0b0a0908  0f0e0d0c
       13121110  17161514  1b1a1918  1f1e1d1c
       00000002  00000000  4a000000  00000000

   First block after block operation:
       f3514f22  e1d91b40  6f27de2f  ed1d63b8
       821f138c  e2062c3d  ecca4f7e  78cff39e
       a30a3b8a  920a6072  cd7479b5  34932bed
       40ba4c79  cd343ec6  4c2c21ea  b7417df0

   Second block after block operation:
       9f74a669  410f633f  28feca22  7ec44dec
       6d34d426  738cb970  3ac5e9f3  45590cc4
       da6e8b39  892c831a  cdea67c1  2b7e1d90
       037463f3  a11a2073  e8bcfb88  edc49139

   Keystream:
   22:4f:51:f3:40:1b:d9:e1:2f:de:27:6f:b8:63:1d:ed:8c:13:1f:82:3d:2c:06
   e2:7e:4f:ca:ec:9e:f3:cf:78:8a:3b:0a:a3:72:60:0a:92:b5:79:74:cd:ed:2b
   93:34:79:4c:ba:40:c6:3e:34:cd:ea:21:2c:4c:f0:7d:41:b7:69:a6:74:9f:3f
   63:0f:41:22:ca:fe:28:ec:4d:c4:7e:26:d4:34:6d:70:b9:8c:73:f3:e9:c5:3a
   c4:0c:59:45:39:8b:6e:da:1a:83:2c:89:c1:67:ea:cd:90:1d:7e:2b:f3:63

   Finally, we XOR the keystream with the plaintext, yielding the
   ciphertext:

  Ciphertext Sunscreen:
  000  6e 2e 35 9a 25 68 f9 80 41 ba 07 28 dd 0d 69 81  n.5.%h..A..(..i.
  016  e9 7e 7a ec 1d 43 60 c2 0a 27 af cc fd 9f ae 0b  .~z..C`..'......
  032  f9 1b 65 c5 52 47 33 ab 8f 59 3d ab cd 62 b3 57  ..e.RG3..Y=..b.W
  048  16 39 d6 24 e6 51 52 ab 8f 53 0c 35 9f 08 61 d8  .9.$.QR..S.5..a.
  064  07 ca 0d bf 50 0d 6a 61 56 a3 8e 08 8a 22 b6 5e  ....P.jaV....".^
  080  52 bc 51 4d 16 cc f8 06 81 8c e9 1a b7 79 37 36  R.QM.........y76
  096  5a f9 0b bf 74 a3 5b e6 b4 0b 8e ed f2 78 5e 42  Z...t.[......x^B
  112  87 4d                                            .M

2.5.  The Poly1305 Algorithm

   Poly1305 is a one-time authenticator designed by D. J. Bernstein.
   Poly1305 takes a 32-byte one-time key and a message and produces a
   16-byte tag.  This tag is used to authenticate the message.

   The original article ([Poly1305]) is titled "The Poly1305-AES
   message-authentication code", and the MAC function there requires a
   128-bit AES key, a 128-bit "additional key", and a 128-bit (non-
   secret) nonce.  AES is used there for encrypting the nonce, so as to
   get a unique (and secret) 128-bit string, but as the paper states,
   "There is nothing special about AES here.  One can replace AES with
   an arbitrary keyed function from an arbitrary set of nonces to
   16-byte strings."

   Regardless of how the key is generated, the key is partitioned into
   two parts, called "r" and "s".  The pair (r,s) should be unique, and
   MUST be unpredictable for each invocation (that is why it was
   originally obtained by encrypting a nonce), while "r" MAY be
   constant, but needs to be modified as follows before being used: ("r"
   is treated as a 16-octet little-endian number):

   o  r[3], r[7], r[11], and r[15] are required to have their top four
      bits clear (be smaller than 16)

   o  r[4], r[8], and r[12] are required to have their bottom two bits
      clear (be divisible by 4)

   The following sample code clamps "r" to be appropriate:

   /*
   Adapted from poly1305aes_test_clamp.c version 20050207
   D. J. Bernstein
   Public domain.
   */

   #include "poly1305aes_test.h"

   void poly1305aes_test_clamp(unsigned char r[16])
   {
     r[3] &= 15;
     r[7] &= 15;
     r[11] &= 15;
     r[15] &= 15;
     r[4] &= 252;
     r[8] &= 252;
     r[12] &= 252;
   }

   The "s" should be unpredictable, but it is perfectly acceptable to
   generate both "r" and "s" uniquely each time.  Because each of them
   is 128 bits, pseudorandomly generating them (see Section 2.6) is also
   acceptable.

   The inputs to Poly1305 are:

   o  A 256-bit one-time key

   o  An arbitrary length message

   The output is a 128-bit tag.

   First, the "r" value should be clamped.

   Next, set the constant prime "P" be 2^130-5:
   3fffffffffffffffffffffffffffffffb.  Also set a variable "accumulator"
   to zero.

   Next, divide the message into 16-byte blocks.  The last one might be
   shorter:

   o  Read the block as a little-endian number.

   o  Add one bit beyond the number of octets.  For a 16-byte block,
      this is equivalent to adding 2^128 to the number.  For the shorter
      block, it can be 2^120, 2^112, or any power of two that is evenly
      divisible by 8, all the way down to 2^8.

   o  If the block is not 17 bytes long (the last block), pad it with
      zeros.  This is meaningless if you are treating the blocks as
      numbers.

   o  Add this number to the accumulator.

   o  Multiply by "r".

   o  Set the accumulator to the result modulo p.  To summarize: Acc =
      ((Acc+block)*r) % p.

   Finally, the value of the secret key "s" is added to the accumulator,
   and the 128 least significant bits are serialized in little-endian
   order to form the tag.

2.5.1.  The Poly1305 Algorithms in Pseudocode

      clamp(r): r &= 0x0ffffffc0ffffffc0ffffffc0fffffff
      poly1305_mac(msg, key):
         r = (le_bytes_to_num(key[0..15])
         clamp(r)
         s = le_num(key[16..31])
         accumulator = 0
         p = (1<<130)-5
         for i=1 upto ceil(msg length in bytes / 16)
            n = le_bytes_to_num(msg[((i-1)*16)..(i*16)] | [0x01])
            a += n
            a = (r * a) % p
            end
         a += s
         return num_to_16_le_bytes(a)
         end

2.5.2.  Poly1305 Example and Test Vector

   For our example, we will dispense with generating the one-time key
   using AES, and assume that we got the following keying material:

   o  Key Material: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8:01:0
      3:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:f5:1b

   o  s as an octet string:
      01:03:80:8a:fb:0d:b2:fd:4a:bf:f6:af:41:49:f5:1b

   o  s as a 128-bit number: 1bf54941aff6bf4afdb20dfb8a800301

   o  r before clamping: 85:d6:be:78:57:55:6d:33:7f:44:52:fe:42:d5:06:a8

   o  Clamped r as a number: 806d5400e52447c036d555408bed685

   For our message, we'll use a short text:

  Message to be Authenticated:
  000  43 72 79 70 74 6f 67 72 61 70 68 69 63 20 46 6f  Cryptographic Fo
  016  72 75 6d 20 52 65 73 65 61 72 63 68 20 47 72 6f  rum Research Gro
  032  75 70                                            up

   Since Poly1305 works in 16-byte chunks, the 34-byte message divides
   into three blocks.  In the following calculation, "Acc" denotes the
   accumulator and "Block" the current block:

   Block #1

   Acc = 00
   Block = 6f4620636968706172676f7470797243
   Block with 0x01 byte = 016f4620636968706172676f7470797243
   Acc + block = 016f4620636968706172676f7470797243
   (Acc+Block) * r =
        b83fe991ca66800489155dcd69e8426ba2779453994ac90ed284034da565ecf
   Acc = ((Acc+Block)*r) % P = 2c88c77849d64ae9147ddeb88e69c83fc

   Block #2

   Acc = 2c88c77849d64ae9147ddeb88e69c83fc
   Block = 6f7247206863726165736552206d7572
   Block with 0x01 byte = 016f7247206863726165736552206d7572
   Acc + block = 437febea505c820f2ad5150db0709f96e
   (Acc+Block) * r =
        21dcc992d0c659ba4036f65bb7f88562ae59b32c2b3b8f7efc8b00f78e548a26
   Acc = ((Acc+Block)*r) % P = 2d8adaf23b0337fa7cccfb4ea344b30de

   Last Block

   Acc = 2d8adaf23b0337fa7cccfb4ea344b30de
   Block = 7075
   Block with 0x01 byte = 017075
   Acc + block = 2d8adaf23b0337fa7cccfb4ea344ca153
   (Acc + Block) * r =
        16d8e08a0f3fe1de4fe4a15486aca7a270a29f1e6c849221e4a6798b8e45321f
   ((Acc + Block) * r) % P = 28d31b7caff946c77c8844335369d03a7

   Adding s, we get this number, and serialize if to get the tag:

   Acc + s = 2a927010caf8b2bc2c6365130c11d06a8

   Tag: a8:06:1d:c1:30:51:36:c6:c2:2b:8b:af:0c:01:27:a9

2.6.  Generating the Poly1305 Key Using ChaCha20

   As said in Section 2.5, it is acceptable to generate the one-time
   Poly1305 pseudorandomly.  This section defines such a method.

   To generate such a key pair (r,s), we will use the ChaCha20 block
   function described in Section 2.3.  This assumes that we have a
   256-bit session key for the Message Authentication Code (MAC)
   function, such as SK_ai and SK_ar in Internet Key Exchange Protocol
   version 2 (IKEv2) ([RFC7296]), the integrity key in the Encapsulating
   Security Payload (ESP) and Authentication Header (AH), or the
   client_write_MAC_key and server_write_MAC_key in TLS.  Any document
   that specifies the use of Poly1305 as a MAC algorithm for some
   protocol must specify that 256 bits are allocated for the integrity
   key.  Note that in the AEAD construction defined in Section 2.8, the
   same key is used for encryption and key generation, so the use of
   SK_a* or *_write_MAC_key is only for stand-alone Poly1305.

   The method is to call the block function with the following
   parameters:

   o  The 256-bit session integrity key is used as the ChaCha20 key.

   o  The block counter is set to zero.

   o  The protocol will specify a 96-bit or 64-bit nonce.  This MUST be
      unique per invocation with the same key, so it MUST NOT be
      randomly generated.  A counter is a good way to implement this,
      but other methods, such as a Linear Feedback Shift Register (LFSR)
      are also acceptable.  ChaCha20 as specified here requires a 96-bit
      nonce.  So if the provided nonce is only 64-bit, then the first 32
      bits of the nonce will be set to a constant number.  This will
      usually be zero, but for protocols with multiple senders it may be
      different for each sender, but should be the same for all
      invocations of the function with the same key by a particular
      sender.

   After running the block function, we have a 512-bit state.  We take
   the first 256 bits or the serialized state, and use those as the one-
   time Poly1305 key: the first 128 bits are clamped and form "r", while
   the next 128 bits become "s".  The other 256 bits are discarded.

   Note that while many protocols have provisions for a nonce for
   encryption algorithms (often called Initialization Vectors, or IVs),
   they usually don't have such a provision for the MAC function.  In
   that case, the per-invocation nonce will have to come from somewhere
   else, such as a message counter.

2.6.1.  Poly1305 Key Generation in Pseudocode

      poly1305_key_gen(key,nonce):
         counter = 0
         block = chacha20_block(key,counter,nonce)
         return block[0..31]
         end

2.6.2.  Poly1305 Key Generation Test Vector

   For this example, we'll set:

  Key:
  000  80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f  ................
  016  90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f  ................

   Nonce:
   000  00 00 00 00 00 01 02 03 04 05 06 07              ............

   The ChaCha state setup with key, nonce, and block counter zero:
         61707865  3320646e  79622d32  6b206574
         83828180  87868584  8b8a8988  8f8e8d8c
         93929190  97969594  9b9a9998  9f9e9d9c
         00000000  00000000  03020100  07060504

   The ChaCha state after 20 rounds:
         8ba0d58a  cc815f90  27405081  7194b24a
         37b633a8  a50dfde3  e2b8db08  46a6d1fd
         7da03782  9183a233  148ad271  b46773d1
         3cc1875a  8607def1  ca5c3086  7085eb87

  Output bytes:
  000  8a d5 a0 8b 90 5f 81 cc 81 50 40 27 4a b2 94 71  ....._...P@'J..q
  016  a8 33 b6 37 e3 fd 0d a5 08 db b8 e2 fd d1 a6 46  .3.7...........F

   And that output is also the 32-byte one-time key used for Poly1305.

2.7.  A Pseudorandom Function for Crypto Suites based on ChaCha/Poly1305

   Some protocols, such as IKEv2 ([RFC7296]), require a Pseudorandom
   Function (PRF), mostly for key derivation.  In the IKEv2 definition,
   a PRF is a function that accepts a variable-length key and a
   variable-length input, and returns a fixed-length output.  Most
   commonly, Hashed MAC (HMAC) constructions are used for this purpose,
   and often the same function is used for both message authentication
   and PRF.

   Poly1305 is not a suitable choice for a PRF.  Poly1305 prohibits
   using the same key twice, whereas the PRF in IKEv2 is used multiple
   times with the same key.  Additionally, unlike HMAC, Poly1305 is
   biased, so using it for key derivation would reduce the security of
   the symmetric encryption.

   Chacha20 could be used as a key-derivation function, by generating an
   arbitrarily long keystream.  However, that is not what protocols such
   as IKEv2 require.

   For this reason, this document does not specify a PRF and recommends
   that crypto suites use some other PRF such as PRF_HMAC_SHA2_256 (see
   Section 2.1.2 of [RFC4868]).

2.8.  AEAD Construction

   AEAD_CHACHA20_POLY1305 is an authenticated encryption with additional
   data algorithm.  The inputs to AEAD_CHACHA20_POLY1305 are:

   o  A 256-bit key

   o  A 96-bit nonce -- different for each invocation with the same key

   o  An arbitrary length plaintext

   o  Arbitrary length additional authenticated data (AAD)

   Some protocols may have unique per-invocation inputs that are not 96
   bits in length.  For example, IPsec may specify a 64-bit nonce.  In
   such a case, it is up to the protocol document to define how to
   transform the protocol nonce into a 96-bit nonce, for example, by
   concatenating a constant value.

   The ChaCha20 and Poly1305 primitives are combined into an AEAD that
   takes a 256-bit key and 96-bit nonce as follows:

   o  First, a Poly1305 one-time key is generated from the 256-bit key
      and nonce using the procedure described in Section 2.6.

   o  Next, the ChaCha20 encryption function is called to encrypt the
      plaintext, using the same key and nonce, and with the initial
      counter set to 1.

   o  Finally, the Poly1305 function is called with the Poly1305 key
      calculated above, and a message constructed as a concatenation of
      the following:

      *  The AAD

      *  padding1 -- the padding is up to 15 zero bytes, and it brings
         the total length so far to an integral multiple of 16.  If the
         length of the AAD was already an integral multiple of 16 bytes,
         this field is zero-length.

      *  The ciphertext

      *  padding2 -- the padding is up to 15 zero bytes, and it brings
         the total length so far to an integral multiple of 16.  If the
         length of the ciphertext was already an integral multiple of 16
         bytes, this field is zero-length.

      *  The length of the additional data in octets (as a 64-bit
         little-endian integer).

      *  The length of the ciphertext in octets (as a 64-bit little-
         endian integer).

   The output from the AEAD is twofold:

   o  A ciphertext of the same length as the plaintext.

   o  A 128-bit tag, which is the output of the Poly1305 function.

   Decryption is similar with the following differences:

   o  The roles of ciphertext and plaintext are reversed, so the
      ChaCha20 encryption function is applied to the ciphertext,
      producing the plaintext.

   o  The Poly1305 function is still run on the AAD and the ciphertext,
      not the plaintext.

   o  The calculated tag is bitwise compared to the received tag.  The
      message is authenticated if and only if the tags match.

   A few notes about this design:

   1.  The amount of encrypted data possible in a single invocation is
       2^32-1 blocks of 64 bytes each, because of the size of the block
       counter field in the ChaCha20 block function.  This gives a total
       of 247,877,906,880 bytes, or nearly 256 GB.  This should be
       enough for traffic protocols such as IPsec and TLS, but may be
       too small for file and/or disk encryption.  For such uses, we can
       return to the original design, reduce the nonce to 64 bits, and
       use the integer at position 13 as the top 32 bits of a 64-bit
       block counter, increasing the total message size to over a
       million petabytes (1,180,591,620,717,411,303,360 bytes to be
       exact).

   2.  Despite the previous item, the ciphertext length field in the
       construction of the buffer on which Poly1305 runs limits the
       ciphertext (and hence, the plaintext) size to 2^64 bytes, or
       sixteen thousand petabytes (18,446,744,073,709,551,616 bytes to
       be exact).

   The AEAD construction in this section is a novel composition of
   ChaCha20 and Poly1305.  A security analysis of this composition is
   given in [Procter].

   Here is a list of the parameters for this construction as defined in
   Section 4 of RFC 5116:

   o  K_LEN (key length) is 32 octets.

   o  P_MAX (maximum size of the plaintext) is 247,877,906,880 bytes, or
      nearly 256 GB.

   o  A_MAX (maximum size of the associated data) is set to 2^64-1
      octets by the length field for associated data.

   o  N_MIN = N_MAX = 12 octets.

   o  C_MAX = P_MAX + tag length = 247,877,906,896 octets.

   Distinct AAD inputs (as described in Section 3.3 of RFC 5116) shall
   be concatenated into a single input to AEAD_CHACHA20_POLY1305.  It is
   up to the application to create a structure in the AAD input if it is
   needed.

2.8.1.  Pseudocode for the AEAD Construction

      pad16(x):
         if (len(x) % 16)==0
            then return NULL
            else return copies(0, 16-(len(x)%16))
         end

      chacha20_aead_encrypt(aad, key, iv, constant, plaintext):
         nonce = constant | iv
         otk = poly1305_key_gen(key, nonce)
         ciphertext = chacha20_encrypt(key, 1, nonce, plaintext)
         mac_data = aad | pad16(aad)
         mac_data |= ciphertext | pad16(ciphertext)
         mac_data |= num_to_4_le_bytes(aad.length)
         mac_data |= num_to_4_le_bytes(ciphertext.length)
         tag = poly1305_mac(mac_data, otk)
         return (ciphertext, tag)

2.8.2.  Example and Test Vector for AEAD_CHACHA20_POLY1305

   For a test vector, we will use the following inputs to the
   AEAD_CHACHA20_POLY1305 function:

  Plaintext:
  000  4c 61 64 69 65 73 20 61 6e 64 20 47 65 6e 74 6c  Ladies and Gentl
  016  65 6d 65 6e 20 6f 66 20 74 68 65 20 63 6c 61 73  emen of the clas
  032  73 20 6f 66 20 27 39 39 3a 20 49 66 20 49 20 63  s of '99: If I c
  048  6f 75 6c 64 20 6f 66 66 65 72 20 79 6f 75 20 6f  ould offer you o
  064  6e 6c 79 20 6f 6e 65 20 74 69 70 20 66 6f 72 20  nly one tip for
  080  74 68 65 20 66 75 74 75 72 65 2c 20 73 75 6e 73  the future, suns
  096  63 72 65 65 6e 20 77 6f 75 6c 64 20 62 65 20 69  creen would be i
  112  74 2e                                            t.

   AAD:
   000  50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7              PQRS........

  Key:
  000  80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f  ................
  016  90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f  ................

   IV:
   000  40 41 42 43 44 45 46 47                          @ABCDEFG

   32-bit fixed-common part:
   000  07 00 00 00                                      ....

   Setup for generating Poly1305 one-time key (sender id=7):
       61707865  3320646e  79622d32  6b206574
       83828180  87868584  8b8a8988  8f8e8d8c
       93929190  97969594  9b9a9998  9f9e9d9c
       00000000  00000007  43424140  47464544

   After generating Poly1305 one-time key:
       252bac7b  af47b42d  557ab609  8455e9a4
       73d6e10a  ebd97510  7875932a  ff53d53e
       decc7ea2  b44ddbad  e49c17d1  d8430bc9
       8c94b7bc  8b7d4b4b  3927f67d  1669a432

  Poly1305 Key:
  000  7b ac 2b 25 2d b4 47 af 09 b6 7a 55 a4 e9 55 84  {.+%-.G...zU..U.
  016  0a e1 d6 73 10 75 d9 eb 2a 93 75 78 3e d5 53 ff  ...s.u..*.ux>.S.

  Poly1305 r =  455e9a4057ab6080f47b42c052bac7b
  Poly1305 s = ff53d53e7875932aebd9751073d6e10a

   keystream bytes:
   9f:7b:e9:5d:01:fd:40:ba:15:e2:8f:fb:36:81:0a:ae:
   c1:c0:88:3f:09:01:6e:de:dd:8a:d0:87:55:82:03:a5:
   4e:9e:cb:38:ac:8e:5e:2b:b8:da:b2:0f:fa:db:52:e8:
   75:04:b2:6e:be:69:6d:4f:60:a4:85:cf:11:b8:1b:59:
   fc:b1:c4:5f:42:19:ee:ac:ec:6a:de:c3:4e:66:69:78:
   8e:db:41:c4:9c:a3:01:e1:27:e0:ac:ab:3b:44:b9:cf:
   5c:86:bb:95:e0:6b:0d:f2:90:1a:b6:45:e4:ab:e6:22:
   15:38

  Ciphertext:
  000  d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2  ...4d.`.{...S.~.
  016  a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6  ...Q)n......6.b.
  032  3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b  =..^..g....i..r.
  048  1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36  .q.....)....~.;6
  064  92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58  ....-w......(..X
  080  fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc  ..$...u.U...H1..
  096  3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b  ?....Kz..v.e...K
  112  61 16                                            a.

  AEAD Construction for Poly1305:
  000  50 51 52 53 c0 c1 c2 c3 c4 c5 c6 c7 00 00 00 00  PQRS............
  016  d3 1a 8d 34 64 8e 60 db 7b 86 af bc 53 ef 7e c2  ...4d.`.{...S.~.
  032  a4 ad ed 51 29 6e 08 fe a9 e2 b5 a7 36 ee 62 d6  ...Q)n......6.b.
  048  3d be a4 5e 8c a9 67 12 82 fa fb 69 da 92 72 8b  =..^..g....i..r.
  064  1a 71 de 0a 9e 06 0b 29 05 d6 a5 b6 7e cd 3b 36  .q.....)....~.;6
  080  92 dd bd 7f 2d 77 8b 8c 98 03 ae e3 28 09 1b 58  ....-w......(..X
  096  fa b3 24 e4 fa d6 75 94 55 85 80 8b 48 31 d7 bc  ..$...u.U...H1..
  112  3f f4 de f0 8e 4b 7a 9d e5 76 d2 65 86 ce c6 4b  ?....Kz..v.e...K
  128  61 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00  a...............
  144  0c 00 00 00 00 00 00 00 72 00 00 00 00 00 00 00  ........r.......

   Note the four zero bytes in line 000 and the 14 zero bytes in line
   128

   Tag:
   1a:e1:0b:59:4f:09:e2:6a:7e:90:2e:cb:d0:60:06:91

3.  Implementation Advice

   Each block of ChaCha20 involves 16 move operations and one increment
   operation for loading the state, 80 each of XOR, addition and Roll
   operations for the rounds, 16 more add operations and 16 XOR
   operations for protecting the plaintext.  Section 2.3 describes the
   ChaCha block function as "adding the original input words".  This
   implies that before starting the rounds on the ChaCha state, we copy
   it aside, only to add it in later.  This is correct, but we can save
   a few operations if we instead copy the state and do the work on the
   copy.  This way, for the next block you don't need to recreate the
   state, but only to increment the block counter.  This saves
   approximately 5.5% of the cycles.

   It is not recommended to use a generic big number library such as the
   one in OpenSSL for the arithmetic operations in Poly1305.  Such
   libraries use dynamic allocation to be able to handle an integer of
   any size, but that flexibility comes at the expense of performance as
   well as side-channel security.  More efficient implementations that
   run in constant time are available, one of them in D. J. Bernstein's
   own library, NaCl ([NaCl]).  A constant-time but not optimal approach
   would be to naively implement the arithmetic operations for 288-bit
   integers, because even a naive implementation will not exceed 2^288
   in the multiplication of (acc+block) and r.  An efficient constant-
   time implementation can be found in the public domain library
   poly1305-donna ([Poly1305_Donna]).

4.  Security Considerations

   The ChaCha20 cipher is designed to provide 256-bit security.

   The Poly1305 authenticator is designed to ensure that forged messages
   are rejected with a probability of 1-(n/(2^102)) for a 16n-byte
   message, even after sending 2^64 legitimate messages, so it is
   SUF-CMA (strong unforgeability against chosen-message attacks) in the
   terminology of [AE].

   Proving the security of either of these is beyond the scope of this
   document.  Such proofs are available in the referenced academic
   papers ([ChaCha], [Poly1305], [LatinDances], [LatinDances2], and
   [Zhenqing2012]).

   The most important security consideration in implementing this
   document is the uniqueness of the nonce used in ChaCha20.  Counters
   and LFSRs are both acceptable ways of generating unique nonces, as is
   encrypting a counter using a 64-bit cipher such as DES.  Note that it
   is not acceptable to use a truncation of a counter encrypted with a
   128-bit or 256-bit cipher, because such a truncation may repeat after
   a short time.

   Consequences of repeating a nonce: If a nonce is repeated, then both
   the one-time Poly1305 key and the keystream are identical between the
   messages.  This reveals the XOR of the plaintexts, because the XOR of
   the plaintexts is equal to the XOR of the ciphertexts.

   The Poly1305 key MUST be unpredictable to an attacker.  Randomly
   generating the key would fulfill this requirement, except that
   Poly1305 is often used in communications protocols, so the receiver
   should know the key.  Pseudorandom number generation such as by
   encrypting a counter is acceptable.  Using ChaCha with a secret key
   and a nonce is also acceptable.

   The algorithms presented here were designed to be easy to implement
   in constant time to avoid side-channel vulnerabilities.  The
   operations used in ChaCha20 are all additions, XORs, and fixed
   rotations.  All of these can and should be implemented in constant
   time.  Access to offsets into the ChaCha state and the number of
   operations do not depend on any property of the key, eliminating the
   chance of information about the key leaking through the timing of
   cache misses.

   For Poly1305, the operations are addition, multiplication. and
   modulus, all on numbers with greater than 128 bits.  This can be done
   in constant time, but a naive implementation (such as using some
   generic big number library) will not be constant time.  For example,
   if the multiplication is performed as a separate operation from the
   modulus, the result will sometimes be under 2^256 and sometimes be
   above 2^256.  Implementers should be careful about timing side-
   channels for Poly1305 by using the appropriate implementation of
   these operations.

   Validating the authenticity of a message involves a bitwise
   comparison of the calculated tag with the received tag.  In most use
   cases, nonces and AAD contents are not "used up" until a valid
   message is received.  This allows an attacker to send multiple
   identical messages with different tags until one passes the tag
   comparison.  This is hard if the attacker has to try all 2^128
   possible tags one by one.  However, if the timing of the tag
   comparison operation reveals how long a prefix of the calculated and
   received tags is identical, the number of messages can be reduced
   significantly.  For this reason, with online protocols,
   implementation MUST use a constant-time comparison function rather
   than relying on optimized but insecure library functions such as the
   C language's memcmp().

5.  IANA Considerations

   IANA has assigned an entry in the "Authenticated Encryption with
   Associated Data (AEAD) Parameters" registry with 29 as the Numeric
   ID, "AEAD_CHACHA20_POLY1305" as the name, and this document as
   reference.

6.  References

6.1.  Normative References

   [ChaCha]   Bernstein, D., "ChaCha, a variant of Salsa20", January
              2008, <http://cr.yp.to/chacha/chacha-20080128.pdf>.

   [Poly1305] Bernstein, D., "The Poly1305-AES message-authentication
              code", March 2005,
              <http://cr.yp.to/mac/poly1305-20050329.pdf>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <http://www.rfc-editor.org/info/rfc2119>.

6.2.  Informative References

   [AE]       Bellare, M. and C. Namprempre, "Authenticated Encryption:
              Relations among notions and analysis of the generic
              composition paradigm", September 2008,
              <http://dl.acm.org/citation.cfm?id=1410269>.

   [Cache-Collisions]
              Bonneau, J. and I. Mironov, "Cache-Collision Timing
              Attacks Against AES", 2006,
              <http://research.microsoft.com/pubs/64024/aes-timing.pdf>.

   [FIPS-197] National Institute of Standards and Technology, "Advanced
              Encryption Standard (AES)", FIPS PUB 197, November 2001,
              <http://csrc.nist.gov/publications/fips/fips197/
              fips-197.pdf>.

   [LatinDances]
              Aumasson, J., Fischer, S., Khazaei, S., Meier, W., and C.
              Rechberger, "New Features of Latin Dances: Analysis of
              Salsa, ChaCha, and Rumba", December 2007,
              <http://cr.yp.to/rumba20/newfeatures-20071218.pdf>.

   [LatinDances2]
              Ishiguro, T., Kiyomoto, S., and Y. Miyake, "Modified
              version of 'Latin Dances Revisited: New Analytic Results
              of Salsa20 and ChaCha'", February 2012,
              <https://eprint.iacr.org/2012/065.pdf>.

   [NaCl]     Bernstein, D., Lange, T., and P. Schwabe, "NaCl:
              Networking and Cryptography library", July 2012,
              <http://nacl.cr.yp.to>.

   [Poly1305_Donna]
              Floodyberry, A., "poly1305-donna", February 2014,
              <https://github.com/floodyberry/poly1305-donna>.

   [Procter]  Procter, G., "A Security Analysis of the Composition of
              ChaCha20 and Poly1305", August 2014,
              <http://eprint.iacr.org/2014/613.pdf>.

   [RFC4868]  Kelly, S. and S. Frankel, "Using HMAC-SHA-256, HMAC-SHA-
              384, and HMAC-SHA-512 with IPsec", RFC 4868,
              DOI 10.17487/RFC4868, May 2007,
              <http://www.rfc-editor.org/info/rfc4868>.

   [RFC5116]  McGrew, D., "An Interface and Algorithms for Authenticated
              Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008,
              <http://www.rfc-editor.org/info/rfc5116>.

   [RFC7296]  Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T.
              Kivinen, "Internet Key Exchange Protocol Version 2
              (IKEv2)", STD 79, RFC 7296, DOI 10.17487/RFC7296, October
              2014, <http://www.rfc-editor.org/info/rfc7296>.

   [SP800-67] National Institute of Standards and Technology,
              "Recommendation for the Triple Data Encryption Algorithm
              (TDEA) Block Cipher", NIST 800-67, January 2012,
              <http://csrc.nist.gov/publications/nistpubs/800-67-Rev1/
              SP-800-67-Rev1.pdf>.

   [Standby-Cipher]
              McGrew, D., Grieco, A., and Y. Sheffer, "Selection of
              Future Cryptographic Standards", Work in Progress,
              draft-mcgrew-standby-cipher-00, January 2013.

   [Zhenqing2012]
              Zhenqing, S., Bin, Z., Dengguo, F., and W. Wenling,
              "Improved Key Recovery Attacks on Reduced-Round Salsa20
              and ChaCha*", 2012.

Appendix A.  Additional Test Vectors

   The subsections of this appendix contain more test vectors for the
   algorithms in the sub-sections of Section 2.

A.1.  The ChaCha20 Block Functions

  Test Vector #1:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Block Counter = 0

    ChaCha state at the end
        ade0b876  903df1a0  e56a5d40  28bd8653
        b819d2bd  1aed8da0  ccef36a8  c70d778b
        7c5941da  8d485751  3fe02477  374ad8b8
        f4b8436a  1ca11815  69b687c3  8665eeb2

  Keystream:
  000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
  016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..
  032  da 41 59 7c 51 57 48 8d 77 24 e0 3f b8 d8 4a 37  .AY|QWH.w$.?..J7
  048  6a 43 b8 f4 15 18 a1 1c c3 87 b6 69 b2 ee 65 86  jC.........i..e.

  Test Vector #2:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Block Counter = 1

    ChaCha state at the end
        bee7079f  7a385155  7c97ba98  0d082d73
        a0290fcb  6965e348  3e53c612  ed7aee32
        7621b729  434ee69c  b03371d5  d539d874
        281fed31  45fb0a51  1f0ae1ac  6f4d794b

  Keystream:
  000  9f 07 e7 be 55 51 38 7a 98 ba 97 7c 73 2d 08 0d  ....UQ8z...|s-..
  016  cb 0f 29 a0 48 e3 65 69 12 c6 53 3e 32 ee 7a ed  ..).H.ei..S>2.z.
  032  29 b7 21 76 9c e6 4e 43 d5 71 33 b0 74 d8 39 d5  ).!v..NC.q3.t.9.
  048  31 ed 1f 28 51 0a fb 45 ac e1 0a 1f 4b 79 4d 6f  1..(Q..E....KyMo

  Test Vector #3:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Block Counter = 1

    ChaCha state at the end
        2452eb3a  9249f8ec  8d829d9b  ddd4ceb1
        e8252083  60818b01  f38422b8  5aaa49c9
        bb00ca8e  da3ba7b4  c4b592d1  fdf2732f
        4436274e  2561b3c8  ebdd4aa6  a0136c00

  Keystream:
  000  3a eb 52 24 ec f8 49 92 9b 9d 82 8d b1 ce d4 dd  :.R$..I.........
  016  83 20 25 e8 01 8b 81 60 b8 22 84 f3 c9 49 aa 5a  . %....`."...I.Z
  032  8e ca 00 bb b4 a7 3b da d1 92 b5 c4 2f 73 f2 fd  ......;...../s..
  048  4e 27 36 44 c8 b3 61 25 a6 4a dd eb 00 6c 13 a0  N'6D..a%.J...l..

  Test Vector #4:
  ==============

  Key:
  000  00 ff 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Block Counter = 2

    ChaCha state at the end
        fb4dd572  4bc42ef1  df922636  327f1394
        a78dea8f  5e269039  a1bebbc1  caf09aae
        a25ab213  48a6b46c  1b9d9bcb  092c5be6
        546ca624  1bec45d5  87f47473  96f0992e

  Keystream:
  000  72 d5 4d fb f1 2e c4 4b 36 26 92 df 94 13 7f 32  r.M....K6&.....2
  016  8f ea 8d a7 39 90 26 5e c1 bb be a1 ae 9a f0 ca  ....9.&^........
  032  13 b2 5a a2 6c b4 a6 48 cb 9b 9d 1b e6 5b 2c 09  ..Z.l..H.....[,.
  048  24 a6 6c 54 d5 45 ec 1b 73 74 f4 87 2e 99 f0 96  $.lT.E..st......

  Test Vector #5:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

  Block Counter = 0

    ChaCha state at the end
        374dc6c2  3736d58c  b904e24a  cd3f93ef
        88228b1a  96a4dfb3  5b76ab72  c727ee54
        0e0e978a  f3145c95  1b748ea8  f786c297
        99c28f5f  628314e8  398a19fa  6ded1b53

  Keystream:
  000  c2 c6 4d 37 8c d5 36 37 4a e2 04 b9 ef 93 3f cd  ..M7..67J.....?.
  016  1a 8b 22 88 b3 df a4 96 72 ab 76 5b 54 ee 27 c7  ..".....r.v[T.'.
  032  8a 97 0e 0e 95 5c 14 f3 a8 8e 74 1b 97 c2 86 f7  .....\....t.....
  048  5f 8f c2 99 e8 14 83 62 fa 19 8a 39 53 1b ed 6d  _......b...9S..m

A.2.  ChaCha20 Encryption

  Test Vector #1:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Initial Block Counter = 0

  Plaintext:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  032  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  048  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Ciphertext:
  000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
  016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..
  032  da 41 59 7c 51 57 48 8d 77 24 e0 3f b8 d8 4a 37  .AY|QWH.w$.?..J7
  048  6a 43 b8 f4 15 18 a1 1c c3 87 b6 69 b2 ee 65 86  jC.........i..e.

  Test Vector #2:
  ==============

  Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

  Initial Block Counter = 1

  Plaintext:
  000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
  016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
  032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
  048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
  064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
  080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
  096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
  112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
  128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
  144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
  160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
  176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
  192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
  208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
  224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
  240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
  256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
  272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
  288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
  304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
  320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
  336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
  352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
  368  73 73 65 64 20 74 6f                             ssed to

  Ciphertext:
  000  a3 fb f0 7d f3 fa 2f de 4f 37 6c a2 3e 82 73 70  ...}../.O7l.>.sp
  016  41 60 5d 9f 4f 4f 57 bd 8c ff 2c 1d 4b 79 55 ec  A`].OOW...,.KyU.
  032  2a 97 94 8b d3 72 29 15 c8 f3 d3 37 f7 d3 70 05  *....r)....7..p.
  048  0e 9e 96 d6 47 b7 c3 9f 56 e0 31 ca 5e b6 25 0d  ....G...V.1.^.%.
  064  40 42 e0 27 85 ec ec fa 4b 4b b5 e8 ea d0 44 0e  @B.'....KK....D.
  080  20 b6 e8 db 09 d8 81 a7 c6 13 2f 42 0e 52 79 50   ........./B.RyP
  096  42 bd fa 77 73 d8 a9 05 14 47 b3 29 1c e1 41 1c  B..ws....G.)..A.
  112  68 04 65 55 2a a6 c4 05 b7 76 4d 5e 87 be a8 5a  h.eU*....vM^...Z
  128  d0 0f 84 49 ed 8f 72 d0 d6 62 ab 05 26 91 ca 66  ...I..r..b..&..f
  144  42 4b c8 6d 2d f8 0e a4 1f 43 ab f9 37 d3 25 9d  BK.m-....C..7.%.
  160  c4 b2 d0 df b4 8a 6c 91 39 dd d7 f7 69 66 e9 28  ......l.9...if.(
  176  e6 35 55 3b a7 6c 5c 87 9d 7b 35 d4 9e b2 e6 2b  .5U;.l\..{5....+
  192  08 71 cd ac 63 89 39 e2 5e 8a 1e 0e f9 d5 28 0f  .q..c.9.^.....(.
  208  a8 ca 32 8b 35 1c 3c 76 59 89 cb cf 3d aa 8b 6c  ..2.5.<vY...=..l
  224  cc 3a af 9f 39 79 c9 2b 37 20 fc 88 dc 95 ed 84  .:..9y.+7 ......
  240  a1 be 05 9c 64 99 b9 fd a2 36 e7 e8 18 b0 4b 0b  ....d....6....K.
  256  c3 9c 1e 87 6b 19 3b fe 55 69 75 3f 88 12 8c c0  ....k.;.Uiu?....
  272  8a aa 9b 63 d1 a1 6f 80 ef 25 54 d7 18 9c 41 1f  ...c..o..%T...A.
  288  58 69 ca 52 c5 b8 3f a3 6f f2 16 b9 c1 d3 00 62  Xi.R..?.o......b
  304  be bc fd 2d c5 bc e0 91 19 34 fd a7 9a 86 f6 e6  ...-.....4......
  320  98 ce d7 59 c3 ff 9b 64 77 33 8f 3d a4 f9 cd 85  ...Y...dw3.=....
  336  14 ea 99 82 cc af b3 41 b2 38 4d d9 02 f3 d1 ab  .......A.8M.....
  352  7a c6 1d d2 9c 6f 21 ba 5b 86 2f 37 30 e3 7c fd  z....o!.[./70.|.
  368  c4 fd 80 6c 22 f2 21                             ...l".!

  Test Vector #3:
  ==============

  Key:
  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

  Nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

  Initial Block Counter = 42

  Plaintext:
  000  27 54 77 61 73 20 62 72 69 6c 6c 69 67 2c 20 61  'Twas brillig, a
  016  6e 64 20 74 68 65 20 73 6c 69 74 68 79 20 74 6f  nd the slithy to
  032  76 65 73 0a 44 69 64 20 67 79 72 65 20 61 6e 64  ves.Did gyre and
  048  20 67 69 6d 62 6c 65 20 69 6e 20 74 68 65 20 77   gimble in the w
  064  61 62 65 3a 0a 41 6c 6c 20 6d 69 6d 73 79 20 77  abe:.All mimsy w
  080  65 72 65 20 74 68 65 20 62 6f 72 6f 67 6f 76 65  ere the borogove
  096  73 2c 0a 41 6e 64 20 74 68 65 20 6d 6f 6d 65 20  s,.And the mome
  112  72 61 74 68 73 20 6f 75 74 67 72 61 62 65 2e     raths outgrabe.

  Ciphertext:
  000  62 e6 34 7f 95 ed 87 a4 5f fa e7 42 6f 27 a1 df  b.4....._..Bo'..
  016  5f b6 91 10 04 4c 0d 73 11 8e ff a9 5b 01 e5 cf  _....L.s....[...
  032  16 6d 3d f2 d7 21 ca f9 b2 1e 5f b1 4c 61 68 71  .m=..!...._.Lahq
  048  fd 84 c5 4f 9d 65 b2 83 19 6c 7f e4 f6 05 53 eb  ...O.e...l....S.
  064  f3 9c 64 02 c4 22 34 e3 2a 35 6b 3e 76 43 12 a6  ..d.."4.*5k>vC..
  080  1a 55 32 05 57 16 ea d6 96 25 68 f8 7d 3f 3f 77  .U2.W....%h.}??w
  096  04 c6 a8 d1 bc d1 bf 4d 50 d6 15 4b 6d a7 31 b1  .......MP..Km.1.
  112  87 b5 8d fd 72 8a fa 36 75 7a 79 7a c1 88 d1     ....r..6uzyz...

A.3.  Poly1305 Message Authentication Code

   Notice how, in test vector #2, r is equal to zero.  The part of the
   Poly1305 algorithm where the accumulator is multiplied by r means
   that with r equal zero, the tag will be equal to s regardless of the
   content of the text.  Fortunately, all the proposed methods of
   generating r are such that getting this particular weak key is very
   unlikely.

  Test Vector #1:
  ==============

  One-time Poly1305 Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Text to MAC:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  032  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  048  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Tag:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Test Vector #2:
  ==============

  One-time Poly1305 Key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>

  Text to MAC:
  000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
  016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
  032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
  048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
  064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
  080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
  096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
  112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
  128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
  144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
  160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
  176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
  192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
  208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
  224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
  240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
  256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
  272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
  288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
  304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
  320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
  336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
  352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
  368  73 73 65 64 20 74 6f                             ssed to

  Tag:
  000  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>

  Test Vector #3:
  ==============

  One-time Poly1305 Key:
  000  36 e5 f6 b5 c5 e0 60 70 f0 ef ca 96 22 7a 86 3e  6.....`p...."z.>
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  Text to MAC:
  000  41 6e 79 20 73 75 62 6d 69 73 73 69 6f 6e 20 74  Any submission t
  016  6f 20 74 68 65 20 49 45 54 46 20 69 6e 74 65 6e  o the IETF inten
  032  64 65 64 20 62 79 20 74 68 65 20 43 6f 6e 74 72  ded by the Contr
  048  69 62 75 74 6f 72 20 66 6f 72 20 70 75 62 6c 69  ibutor for publi
  064  63 61 74 69 6f 6e 20 61 73 20 61 6c 6c 20 6f 72  cation as all or
  080  20 70 61 72 74 20 6f 66 20 61 6e 20 49 45 54 46   part of an IETF
  096  20 49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 20   Internet-Draft
  112  6f 72 20 52 46 43 20 61 6e 64 20 61 6e 79 20 73  or RFC and any s
  128  74 61 74 65 6d 65 6e 74 20 6d 61 64 65 20 77 69  tatement made wi
  144  74 68 69 6e 20 74 68 65 20 63 6f 6e 74 65 78 74  thin the context
  160  20 6f 66 20 61 6e 20 49 45 54 46 20 61 63 74 69   of an IETF acti
  176  76 69 74 79 20 69 73 20 63 6f 6e 73 69 64 65 72  vity is consider
  192  65 64 20 61 6e 20 22 49 45 54 46 20 43 6f 6e 74  ed an "IETF Cont
  208  72 69 62 75 74 69 6f 6e 22 2e 20 53 75 63 68 20  ribution". Such
  224  73 74 61 74 65 6d 65 6e 74 73 20 69 6e 63 6c 75  statements inclu
  240  64 65 20 6f 72 61 6c 20 73 74 61 74 65 6d 65 6e  de oral statemen
  256  74 73 20 69 6e 20 49 45 54 46 20 73 65 73 73 69  ts in IETF sessi
  272  6f 6e 73 2c 20 61 73 20 77 65 6c 6c 20 61 73 20  ons, as well as
  288  77 72 69 74 74 65 6e 20 61 6e 64 20 65 6c 65 63  written and elec
  304  74 72 6f 6e 69 63 20 63 6f 6d 6d 75 6e 69 63 61  tronic communica
  320  74 69 6f 6e 73 20 6d 61 64 65 20 61 74 20 61 6e  tions made at an
  336  79 20 74 69 6d 65 20 6f 72 20 70 6c 61 63 65 2c  y time or place,
  352  20 77 68 69 63 68 20 61 72 65 20 61 64 64 72 65   which are addre
  368  73 73 65 64 20 74 6f                             ssed to

  Tag:
  000  f3 47 7e 7c d9 54 17 af 89 a6 b8 79 4c 31 0c f0  .G~|.T.....yL1..

  Test Vector #4:
  ==============

  One-time Poly1305 Key:
  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

  Text to MAC:
  000  27 54 77 61 73 20 62 72 69 6c 6c 69 67 2c 20 61  'Twas brillig, a
  016  6e 64 20 74 68 65 20 73 6c 69 74 68 79 20 74 6f  nd the slithy to
  032  76 65 73 0a 44 69 64 20 67 79 72 65 20 61 6e 64  ves.Did gyre and
  048  20 67 69 6d 62 6c 65 20 69 6e 20 74 68 65 20 77   gimble in the w
  064  61 62 65 3a 0a 41 6c 6c 20 6d 69 6d 73 79 20 77  abe:.All mimsy w
  080  65 72 65 20 74 68 65 20 62 6f 72 6f 67 6f 76 65  ere the borogove
  096  73 2c 0a 41 6e 64 20 74 68 65 20 6d 6f 6d 65 20  s,.And the mome
  112  72 61 74 68 73 20 6f 75 74 67 72 61 62 65 2e     raths outgrabe.

  Tag:
  000  45 41 66 9a 7e aa ee 61 e7 08 dc 7c bc c5 eb 62  EAf.~..a...|...b

   Test Vector #5: If one uses 130-bit partial reduction, does the code
   handle the case where partially reduced final result is not fully
   reduced?

   R:
   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   tag:
   03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   Test Vector #6: What happens if addition of s overflows modulo 2^128?

   R:
   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   S:
   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   data:
   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   tag:
   03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   Test Vector #7: What happens if data limb is all ones and there is
   carry from lower limb?

   R:
   01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   F0 FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   tag:
   05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   Test Vector #8: What happens if final result from polynomial part is
   exactly 2^130-5?

   R:
   01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   FB FE FE FE FE FE FE FE FE FE FE FE FE FE FE FE
   01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
   tag:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

   Test Vector #9: What happens if final result from polynomial part is
   exactly 2^130-6?

   R:
   02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   FD FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF
   tag:
   FA FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF

   Test Vector #10: What happens if 5*H+L-type reduction produces
   131-bit intermediate result?

   R:
   01 00 00 00 00 00 00 00 04 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   E3 35 94 D7 50 5E 43 B9 00 00 00 00 00 00 00 00
   33 94 D7 50 5E 43 79 CD 01 00 00 00 00 00 00 00
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   tag:
   14 00 00 00 00 00 00 00 55 00 00 00 00 00 00 00

   Test Vector #11: What happens if 5*H+L-type reduction produces
   131-bit final result?

   R:
   01 00 00 00 00 00 00 00 04 00 00 00 00 00 00 00
   S:
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   data:
   E3 35 94 D7 50 5E 43 B9 00 00 00 00 00 00 00 00
   33 94 D7 50 5E 43 79 CD 01 00 00 00 00 00 00 00
   00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
   tag:
   13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

A.4.  Poly1305 Key Generation Using ChaCha20

  Test Vector #1:
  ==============

  The key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................

  The nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 00              ............

  Poly1305 one-time key:
  000  76 b8 e0 ad a0 f1 3d 90 40 5d 6a e5 53 86 bd 28  v.....=.@]j.S..(
  016  bd d2 19 b8 a0 8d ed 1a a8 36 ef cc 8b 77 0d c7  .........6...w..

  Test Vector #2:
  ==============

  The key:
  000  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  ................
  016  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01  ................

  The nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

  Poly1305 one-time key:
  000  ec fa 25 4f 84 5f 64 74 73 d3 cb 14 0d a9 e8 76  ..%O._dts......v
  016  06 cb 33 06 6c 44 7b 87 bc 26 66 dd e3 fb b7 39  ..3.lD{..&f....9

  Test Vector #3:
  ==============

  The key:
  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

  The nonce:
  000  00 00 00 00 00 00 00 00 00 00 00 02              ............

  Poly1305 one-time key:
  000  96 5e 3b c6 f9 ec 7e d9 56 08 08 f4 d2 29 f9 4b  .^;...~.V....).K
  016  13 7f f2 75 ca 9b 3f cb dd 59 de aa d2 33 10 ae  ...u..?..Y...3..

A.5.  ChaCha20-Poly1305 AEAD Decryption

   Below we see decrypting a message.  We receive a ciphertext, a nonce,
   and a tag.  We know the key.  We will check the tag and then
   (assuming that it validates) decrypt the ciphertext.  In this
   particular protocol, we'll assume that there is no padding of the
   plaintext.

  The key:
  000  1c 92 40 a5 eb 55 d3 8a f3 33 88 86 04 f6 b5 f0  ..@..U...3......
  016  47 39 17 c1 40 2b 80 09 9d ca 5c bc 20 70 75 c0  G9..@+....\. pu.

  Ciphertext:
  000  64 a0 86 15 75 86 1a f4 60 f0 62 c7 9b e6 43 bd  d...u...`.b...C.
  016  5e 80 5c fd 34 5c f3 89 f1 08 67 0a c7 6c 8c b2  ^.\.4\....g..l..
  032  4c 6c fc 18 75 5d 43 ee a0 9e e9 4e 38 2d 26 b0  Ll..u]C....N8-&.
  048  bd b7 b7 3c 32 1b 01 00 d4 f0 3b 7f 35 58 94 cf  ...<2.....;.5X..
  064  33 2f 83 0e 71 0b 97 ce 98 c8 a8 4a bd 0b 94 81  3/..q......J....
  080  14 ad 17 6e 00 8d 33 bd 60 f9 82 b1 ff 37 c8 55  ...n..3.`....7.U
  096  97 97 a0 6e f4 f0 ef 61 c1 86 32 4e 2b 35 06 38  ...n...a..2N+5.8
  112  36 06 90 7b 6a 7c 02 b0 f9 f6 15 7b 53 c8 67 e4  6..{j|.....{S.g.
  128  b9 16 6c 76 7b 80 4d 46 a5 9b 52 16 cd e7 a4 e9  ..lv{.MF..R.....
  144  90 40 c5 a4 04 33 22 5e e2 82 a1 b0 a0 6c 52 3e  .@...3"^.....lR>
  160  af 45 34 d7 f8 3f a1 15 5b 00 47 71 8c bc 54 6a  .E4..?..[.Gq..Tj
  176  0d 07 2b 04 b3 56 4e ea 1b 42 22 73 f5 48 27 1a  ..+..VN..B"s.H'.
  192  0b b2 31 60 53 fa 76 99 19 55 eb d6 31 59 43 4e  ..1`S.v..U..1YCN
  208  ce bb 4e 46 6d ae 5a 10 73 a6 72 76 27 09 7a 10  ..NFm.Z.s.rv'.z.
  224  49 e6 17 d9 1d 36 10 94 fa 68 f0 ff 77 98 71 30  I....6...h..w.q0
  240  30 5b ea ba 2e da 04 df 99 7b 71 4d 6c 6f 2c 29  0[.......{qMlo,)
  256  a6 ad 5c b4 02 2b 02 70 9b                       ..\..+.p.

  The nonce:
  000  00 00 00 00 01 02 03 04 05 06 07 08              ............

  The AAD:
  000  f3 33 88 86 00 00 00 00 00 00 4e 91              .3........N.

  Received Tag:
  000  ee ad 9d 67 89 0c bb 22 39 23 36 fe a1 85 1f 38  ...g..."9#6....8

   First, we calculate the one-time Poly1305 key

  @@@  ChaCha state with key setup
        61707865  3320646e  79622d32  6b206574
        a540921c  8ad355eb  868833f3  f0b5f604
        c1173947  09802b40  bc5cca9d  c0757020
        00000000  00000000  04030201  08070605

  @@@  ChaCha state after 20 rounds
        a94af0bd  89dee45c  b64bb195  afec8fa1
        508f4726  63f554c0  1ea2c0db  aa721526
        11b1e514  a0bacc0f  828a6015  d7825481
        e8a4a850  d9dcbbd6  4c2de33a  f8ccd912

  @@@ out bytes:
  bd:f0:4a:a9:5c:e4:de:89:95:b1:4b:b6:a1:8f:ec:af:
  26:47:8f:50:c0:54:f5:63:db:c0:a2:1e:26:15:72:aa

  Poly1305 one-time key:
  000  bd f0 4a a9 5c e4 de 89 95 b1 4b b6 a1 8f ec af  ..J.\.....K.....
  016  26 47 8f 50 c0 54 f5 63 db c0 a2 1e 26 15 72 aa  &G.P.T.c....&.r.

   Next, we construct the AEAD buffer

  Poly1305 Input:
  000  f3 33 88 86 00 00 00 00 00 00 4e 91 00 00 00 00  .3........N.....
  016  64 a0 86 15 75 86 1a f4 60 f0 62 c7 9b e6 43 bd  d...u...`.b...C.
  032  5e 80 5c fd 34 5c f3 89 f1 08 67 0a c7 6c 8c b2  ^.\.4\....g..l..
  048  4c 6c fc 18 75 5d 43 ee a0 9e e9 4e 38 2d 26 b0  Ll..u]C....N8-&.
  064  bd b7 b7 3c 32 1b 01 00 d4 f0 3b 7f 35 58 94 cf  ...<2.....;.5X..
  080  33 2f 83 0e 71 0b 97 ce 98 c8 a8 4a bd 0b 94 81  3/..q......J....
  096  14 ad 17 6e 00 8d 33 bd 60 f9 82 b1 ff 37 c8 55  ...n..3.`....7.U
  112  97 97 a0 6e f4 f0 ef 61 c1 86 32 4e 2b 35 06 38  ...n...a..2N+5.8
  128  36 06 90 7b 6a 7c 02 b0 f9 f6 15 7b 53 c8 67 e4  6..{j|.....{S.g.
  144  b9 16 6c 76 7b 80 4d 46 a5 9b 52 16 cd e7 a4 e9  ..lv{.MF..R.....
  160  90 40 c5 a4 04 33 22 5e e2 82 a1 b0 a0 6c 52 3e  .@...3"^.....lR>
  176  af 45 34 d7 f8 3f a1 15 5b 00 47 71 8c bc 54 6a  .E4..?..[.Gq..Tj
  192  0d 07 2b 04 b3 56 4e ea 1b 42 22 73 f5 48 27 1a  ..+..VN..B"s.H'.
  208  0b b2 31 60 53 fa 76 99 19 55 eb d6 31 59 43 4e  ..1`S.v..U..1YCN
  224  ce bb 4e 46 6d ae 5a 10 73 a6 72 76 27 09 7a 10  ..NFm.Z.s.rv'.z.
  240  49 e6 17 d9 1d 36 10 94 fa 68 f0 ff 77 98 71 30  I....6...h..w.q0
  256  30 5b ea ba 2e da 04 df 99 7b 71 4d 6c 6f 2c 29  0[.......{qMlo,)
  272  a6 ad 5c b4 02 2b 02 70 9b 00 00 00 00 00 00 00  ..\..+.p........
  288  0c 00 00 00 00 00 00 00 09 01 00 00 00 00 00 00  ................

   We calculate the Poly1305 tag and find that it matches

  Calculated Tag:
  000  ee ad 9d 67 89 0c bb 22 39 23 36 fe a1 85 1f 38  ...g..."9#6....8

   Finally, we decrypt the ciphertext

  Plaintext::
  000  49 6e 74 65 72 6e 65 74 2d 44 72 61 66 74 73 20  Internet-Drafts
  016  61 72 65 20 64 72 61 66 74 20 64 6f 63 75 6d 65  are draft docume
  032  6e 74 73 20 76 61 6c 69 64 20 66 6f 72 20 61 20  nts valid for a
  048  6d 61 78 69 6d 75 6d 20 6f 66 20 73 69 78 20 6d  maximum of six m
  064  6f 6e 74 68 73 20 61 6e 64 20 6d 61 79 20 62 65  onths and may be
  080  20 75 70 64 61 74 65 64 2c 20 72 65 70 6c 61 63   updated, replac
  096  65 64 2c 20 6f 72 20 6f 62 73 6f 6c 65 74 65 64  ed, or obsoleted
  112  20 62 79 20 6f 74 68 65 72 20 64 6f 63 75 6d 65   by other docume
  128  6e 74 73 20 61 74 20 61 6e 79 20 74 69 6d 65 2e  nts at any time.
  144  20 49 74 20 69 73 20 69 6e 61 70 70 72 6f 70 72   It is inappropr
  160  69 61 74 65 20 74 6f 20 75 73 65 20 49 6e 74 65  iate to use Inte
  176  72 6e 65 74 2d 44 72 61 66 74 73 20 61 73 20 72  rnet-Drafts as r
  192  65 66 65 72 65 6e 63 65 20 6d 61 74 65 72 69 61  eference materia
  208  6c 20 6f 72 20 74 6f 20 63 69 74 65 20 74 68 65  l or to cite the
  224  6d 20 6f 74 68 65 72 20 74 68 61 6e 20 61 73 20  m other than as
  240  2f e2 80 9c 77 6f 72 6b 20 69 6e 20 70 72 6f 67  /...work in prog
  256  72 65 73 73 2e 2f e2 80 9d                       ress./...

Appendix B.  Performance Measurements of ChaCha20

   The following measurements were made by Adam Langley for a blog post
   published on February 27th, 2014.  The original blog post was
   available at the time of this writing at
   <https://www.imperialviolet.org/2014/02/27/tlssymmetriccrypto.html>.

     +----------------------------+-------------+-------------------+
     | Chip                       | AES-128-GCM | ChaCha20-Poly1305 |
     +----------------------------+-------------+-------------------+
     | OMAP 4460                  |  24.1 MB/s  |     75.3 MB/s     |
     | Snapdragon S4 Pro          |  41.5 MB/s  |     130.9 MB/s    |
     | Sandy Bridge Xeon (AES-NI) |   900 MB/s  |      500 MB/s     |
     +----------------------------+-------------+-------------------+

                         Table 1: Speed Comparison

Acknowledgements

   ChaCha20 and Poly1305 were invented by Daniel J. Bernstein.  The AEAD
   construction and the method of creating the one-time Poly1305 key
   were invented by Adam Langley.

   Thanks to Robert Ransom, Watson Ladd, Stefan Buhler, Dan Harkins, and
   Kenny Paterson for their helpful comments and explanations.  Thanks
   to Niels Moller for suggesting the more efficient AEAD construction
   in this document.  Special thanks to Ilari Liusvaara for providing
   extra test vectors, helpful comments, and for being the first to
   attempt an implementation from this document.  Thanks to Sean
   Parkinson for suggesting improvements to the examples and the
   pseudocode.  Thanks to David Ireland for pointing out a bug in the
   pseudocode, and to Stephen Farrell and Alyssa Rowan for pointing out
   missing advise in the security considerations.

   Special thanks goes to Gordon Procter for performing a security
   analysis of the composition and publishing [Procter].

Authors' Addresses

   Yoav Nir
   Check Point Software Technologies, Ltd.
   5 Hasolelim St.
   Tel Aviv  6789735
   Israel

   EMail: ynir.ietf@gmail.com


   Adam Langley
   Google, Inc.

   EMail: agl@google.com

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<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""><div><blockquote type=3D"cite" class=3D""><div =
class=3D""><meta http-equiv=3D"Content-Type" content=3D"text/html =
charset=3Dutf-8" class=3D""><div style=3D"word-wrap: break-word; =
-webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" =
class=3D""><div class=3D""></div><div class=3D""><br class=3D""></div><div=
 class=3D""><div class=3D""><blockquote type=3D"cite" class=3D""><div =
class=3D"">On 16 Nov 2016, at 10:06, Sean Turner &lt;<a =
href=3D"mailto:sean@sn3rd.com" class=3D"">sean@sn3rd.com</a>&gt; =
wrote:</div><br class=3D"Apple-interchange-newline"><div class=3D""><div =
class=3D"">+1 - if you got the cycles.<br class=3D""><br class=3D"">spt<br=
 class=3D""><br class=3D""><blockquote type=3D"cite" class=3D"">On Nov =
14, 2016, at 15:55, Eric Rescorla &lt;<a href=3D"mailto:ekr@rtfm.com" =
class=3D"">ekr@rtfm.com</a>&gt; wrote:<br class=3D""><br class=3D"">This =
seems like a good plan.<br class=3D""><br class=3D"">-Ekr<br =
class=3D""><br class=3D""><br class=3D"">On Mon, Nov 14, 2016 at 3:32 =
PM, Yoav Nir &lt;<a href=3D"mailto:ynir.ietf@gmail.com" =
class=3D"">ynir.ietf@gmail.com</a>&gt; wrote:<br class=3D"">Hi<br =
class=3D""><br class=3D"">RFC 7539 (=E2=80=9CChaCha20 and Poly1305 for =
IETF Protocols=E2=80=9D)[1] is now implemented in many places and =
referenced by 3 RFCs and 8 Internet Drafts ([2])<br class=3D""><br =
class=3D"">However, the quality of the document is not where we=E2=80=99d =
like it to be. There have been 7 errata filed against it. Most of it is =
editorial or insignificant, but still no errata is better than some =
errata.<br class=3D""><br class=3D"">So what do the participants and =
chairs think about spinning up a quick[4] rfc7539bis that has the same =
text, except that the errata will be merged in?<br class=3D""><br =
class=3D"">I think such a document should be fairly easy and quick.<br =
class=3D""><br class=3D"">Yoav<br class=3D""><br class=3D"">P.S: and =
yes, of course I=E2=80=99m volunteering to write it.<br class=3D""><br =
class=3D"">[1] <a href=3D"https://tools.ietf.org/html/rfc7539" =
class=3D"">https://tools.ietf.org/html/rfc7539</a><br class=3D"">[2] <a =
href=3D"https://datatracker.ietf.org/doc/rfc7539/referencedby/" =
class=3D"">https://datatracker.ietf.org/doc/rfc7539/referencedby/</a><br =
class=3D"">[3] <a =
href=3D"https://www.rfc-editor.org/errata_search.php?rfc=3D7539" =
class=3D"">https://www.rfc-editor.org/errata_search.php?rfc=3D7539</a><br =
class=3D"">[4] My spell check actually corrected =E2=80=9Cquick=E2=80=9D =
to =E2=80=9Cquic=E2=80=9D. The contents of my mails are veering far away =
from regular English.<br class=3D""><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""><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""></blockquote><br class=3D""></div></div></blockquote></div><br =
class=3D""></div></div></div></blockquote></div><br =
class=3D""></div></body></html>=

--Apple-Mail=_1E7E1AB1-22FD-4F92-9C14-085497C6341E--

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From nobody Sat Jan 14 11:08:09 2017
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From: Leonard den Ottolander <leonard-lists@den.ottolander.nl>
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Subject: [Cfrg] A little room for AES-192 in TLS?
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L.S.,

Seeing how AES-192 seems to hold up well against related key attacks (at
least the (theoretical) one described in
http://eprint.iacr.org/2009/317) I am rather surprised no AES-192
ciphers have been defined for TLS
(http://www.iana.org/assignments/tls-parameters/tls-parameters.xhtml#tls-parameters-4). I feel the cipher is being treated rather stepmotherly.

I do understand that the number of slots for ciphers in the above list
is somewhat limited and additions should be considered carefully.

However, seeing that there are over 60 TLS_DH_* ciphers in that list and
well over 60 CAMMELIAs - to be clear, I am not arguing against the
latter algorithm - the argument not to include AES-192 ciphers in that
list seems somewhat arbitrary.

Also there still seems to be plenty of space available (slots 0x01-55,*
and 0x56,0x01-0xC0,0x00) until this "definition by permutation" approach
can be replaced by a cheaper "definition by slot" where the slots are
chained, i.e. using identifiers for key exchanges, asymmetrical ciphers,
symmetrical ciphers and block modes separately.

Even though I have an interest in mathematics and number theory I do not
claim to have anything more than a rudimentary understanding of the
mathematics involved so please correct me where my insights are wrong.

On superficial reading of http://eprint.iacr.org/2009/317 I grasp that
the higher resistance of AES-192 vs. AES-256 is caused by the fact that
"the key schedule of AES-192 has better diffusion".

What is causing this better diffusion? Is it the fact that the key size
of AES-192 is not, and the block size is a power of 2? I seem to
remember reading somewhere about DES that the odd key size vs the block
size was considered a strength.

Have the same analyses been done for AES-128? How is AES-128 holding up
against these attacks?

Seeing that we live in "a world of 2^50 keys" and the fact that AES-192
seems to be more robust against related key attacks than AES-256 is I
would like to suggest the inclusion of a few AES-192 ciphers in TLS,
lets say all equivalents of AES-256, possibly reduced by the ciphers
that use hashes weaker than SHA256. Not sure if "DH" and "DH_anon" are
different approaches, but those could be excluded as well, resulting in
something like this list:

TLS_RSA_WITH_AES_192_CBC_SHA256
TLS_DHE_DSS_WITH_AES_192_CBC_SHA256
TLS_DHE_RSA_WITH_AES_192_CBC_SHA256
TLS_RSA_WITH_AES_192_GCM_SHA384
TLS_DHE_RSA_WITH_AES_192_GCM_SHA384
TLS_DHE_DSS_WITH_AES_192_GCM_SHA384
TLS_PSK_WITH_AES_192_GCM_SHA384
TLS_DHE_PSK_WITH_AES_192_GCM_SHA384
TLS_RSA_PSK_WITH_AES_192_GCM_SHA384
TLS_PSK_WITH_AES_192_CBC_SHA384
TLS_DHE_PSK_WITH_AES_192_CBC_SHA384
TLS_RSA_PSK_WITH_AES_192_CBC_SHA384
TLS_ECDHE_ECDSA_WITH_AES_192_CBC_SHA384
TLS_ECDH_ECDSA_WITH_AES_192_CBC_SHA384
TLS_ECDHE_RSA_WITH_AES_192_CBC_SHA384
TLS_ECDH_RSA_WITH_AES_192_CBC_SHA384
TLS_ECDHE_ECDSA_WITH_AES_192_GCM_SHA384
TLS_ECDH_ECDSA_WITH_AES_192_GCM_SHA384
TLS_ECDHE_RSA_WITH_AES_192_GCM_SHA384
TLS_ECDH_RSA_WITH_AES_192_GCM_SHA384
TLS_ECDHE_PSK_WITH_AES_192_CBC_SHA384
TLS_RSA_WITH_AES_192_CCM
TLS_DHE_RSA_WITH_AES_192_CCM
TLS_RSA_WITH_AES_192_CCM_8
TLS_DHE_RSA_WITH_AES_192_CCM_8
TLS_PSK_WITH_AES_192_CCM
TLS_DHE_PSK_WITH_AES_192_CCM
TLS_PSK_WITH_AES_192_CCM_8
TLS_PSK_DHE_WITH_AES_192_CCM_8
TLS_ECDHE_ECDSA_WITH_AES_192_CCM
TLS_ECDHE_ECDSA_WITH_AES_192_CCM_8

Thank you for considering this request.

Regards,
Leonard den Ottolander.

-- 
mount -t life -o ro /dev/dna /genetic/research



From nobody Sat Jan 14 11:50:31 2017
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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   Date: Sat, 14 Jan 2017 20:08:01 +0100
   From: Leonard den Ottolander <leonard-lists@den.ottolander.nl>

   Seeing how AES-192 seems to hold up well against related key attacks (at
   least the (theoretical) one described in
   http://eprint.iacr.org/2009/317) I am rather surprised no AES-192
   ciphers have been defined for TLS
   (http://www.iana.org/assignments/tls-parameters/tls-parameters.xhtml#tls=
-parameters-4). I feel the cipher is being treated rather stepmotherly.

I would be surprised if TLS relied in any way on resistance to
related-key attacks.  The only advantage for TLS's sake would be in
situations requiring greater performance than AES-256 can attain,
where a security level below 2^96 against future quantum cryptanalysis
or multi-target attacks are acceptable.

That said, proposals for TLS are probably better heard at the IETF
working group for TLS.

   Also there still seems to be plenty of space available (slots 0x01-55,*
   and 0x56,0x01-0xC0,0x00) until this "definition by permutation" approach
   can be replaced by a cheaper "definition by slot" where the slots are
   chained, i.e. using identifiers for key exchanges, asymmetrical ciphers,
   symmetrical ciphers and block modes separately.

It turns out that handing inexpert users a dizzying array of
cryptographic acronym soups and seasonings to combine securely does
not tend to yield very good results.  The enormous enumeration of
precombined cipher suites is bad enough; asking users to make sensible
choices to combine their parts is worse.


From nobody Sun Jan 15 08:57:19 2017
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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Hello Taylor,

On Sat, 2017-01-14 at 19:50 +0000, Taylor R Campbell wrote: 
> Date: Sat, 14 Jan 2017 20:08:01 +0100
>    From: Leonard den Ottolander <leonard-lists@den.ottolander.nl>
> 
>    Seeing how AES-192 seems to hold up well against related key attacks (at
>    least the (theoretical) one described in
>    http://eprint.iacr.org/2009/317) I am rather surprised no AES-192
>    ciphers have been defined for TLS
>    (http://www.iana.org/assignments/tls-parameters/tls-parameters.xhtml#tls-parameters-4).
>    I feel the cipher is being treated rather stepmotherly.
> 
> I would be surprised if TLS relied in any way on resistance to
> related-key attacks.

I would say any encryption scheme worth its salt relies on resistance
against any kind of attack. With its constant key regeneration TLS seems
amongst the first use cases where related key attacks could be a
concern. More so than in f.e. disk encryption.

> The only advantage for TLS's sake would be in
> situations requiring greater performance than AES-256 can attain,
> where a security level below 2^96 against future quantum cryptanalysis
> or multi-target attacks are acceptable.

Well, assuming Shor and/or Grover half the effective strength of
symmetric ciphers and these related key attacks were to be practical the
effectiveness of AES-256 would fall below 2^50 against ~ 2^89 for
AES-192. Your consideration would disqualify AES-256 in that scenario as
well.

Although both attacks might improve the fact that the research states
"the key schedule of AES-192 has better diffusion" seems to imply it is
fundamentally more resistant against related key attacks. If this is
true and related key attacks are a concern AES-192 might be favourable
over AES-256. Not for its greater performance but because it is actually
more resistant against related key attacks than AES-256.

> That said, proposals for TLS are probably better heard at the IETF
> working group for TLS.

> Also there still seems to be plenty of space available (slots 0x01-55,*
>    and 0x56,0x01-0xC0,0x00) until this "definition by permutation" approach
>    can be replaced by a cheaper "definition by slot" where the slots are
>    chained, i.e. using identifiers for key exchanges, asymmetrical ciphers,
>    symmetrical ciphers and block modes separately.
> 
> It turns out that handing inexpert users a dizzying array of
> cryptographic acronym soups and seasonings to combine securely does
> not tend to yield very good results.  The enormous enumeration of
> precombined cipher suites is bad enough; asking users to make sensible
> choices to combine their parts is worse.

Cipher choices are mostly made by system administrators and software
implementers, not so much by inexpert users. Has your browser or SSH
client ever asked you which cipher you would want to use for your
connection?

Also, the amount of choices is not significantly increased (seeing that
most possible iterations are already listed), only the way they are
represented. So I am not sure the splitting into slots makes the array
as a whole more dizzying. Whether the slots are separate or concatenated
does not fundamentally change the choices the sysadmin has to make.

But we are drifting slightly of topic here. My reason for sending an
email is to establish whether or not AES-192 is indeed inherently more
secure against related key attacks than AES-256, and thus more resilient
against f.e. manipulation of the generated keys. And perhaps some
insights whether this is related to the "skewed" cipher vs. block size.

Regards,
Leonard.

P.S. Please reply to list only.

-- 
mount -t life -o ro /dev/dna /genetic/research








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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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   Date: Sun, 15 Jan 2017 17:57:07 +0100
   From: Leonard den Ottolander <leonard-lists@den.ottolander.nl>

   I would say any encryption scheme worth its salt relies on resistance
   against any kind of attack. With its constant key regeneration TLS seems
   amongst the first use cases where related key attacks could be a
   concern. More so than in f.e. disk encryption.

Only very unusual protocols ever use related keys.  In sensible
protocols, every key is drawn independently uniformly at random.


From nobody Mon Jan 16 06:43:44 2017
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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On Sun, 2017-01-15 at 20:59 +0000, Taylor R Campbell wrote: 
> Only very unusual protocols ever use related keys.  In sensible
> protocols, every key is drawn independently uniformly at random.

Protocols that are designed to use related keys? I hope not!

Compare http://eprint.iacr.org/2009/317 4.1 Related-key attack model:

"Compared to other cryptanalytic attacks in which the attacker can manipu-
late only the plaintexts and/or the ciphertexts the choice of the relation between
secret keys gives additional degree of freedom to the attacker. The downside of
this freedom is that such attacks might be harder to mount in practice. Still,
designers usually try to build "ideal" primitives which can be automatically used
without further analysis in the widest possible set of applications, protocols, or
modes of operation. Thus resistance to such attacks is an important design goal
for block ciphers, and in fact it was one of the stated design goals of the Rijndael
algorithm, which was selected as the Advanced Encryption Standard."

So the question remains if indeed AES-192 is inherently more resistant
to this kind of attack (more of an "ideal primitive" in this respect)
than AES-256 or do I read too much in the remark "the key schedule of
AES-192 has better diffusion" in 6 Attack on AES-192?

Regards,
Leonard.

-- 
mount -t life -o ro /dev/dna /genetic/research




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

Generally, I think the sense of the WG is to try to minimize the number of
ciphers/suits.

Speaking personally, what would make me be in favor of adding AES-192 would
be
some statement from CFRG that they thought that it was significantly
stronger than
AES-256. Absent that, I think it would be better to leave it out of TLS.

-Ekr


On Mon, Jan 16, 2017 at 7:59 AM, John Mattsson <john.mattsson@ericsson.com>
wrote:

> Note that there are trivial generic related-key attacks on AES-192 with #K
> = D = T = M = 2^96
>
> http://dx.doi.org/10.1080/0161-118791861749
>
> Regards,
> John
>
>
> On 2017-01-16, 15:43, "Cfrg on behalf of Leonard den Ottolander"
> <cfrg-bounces@irtf.org on behalf of leonard-lists@den.ottolander.nl>
> wrote:
>
> >On Sun, 2017-01-15 at 20:59 +0000, Taylor R Campbell wrote:
> >> Only very unusual protocols ever use related keys.  In sensible
> >> protocols, every key is drawn independently uniformly at random.
> >
> >Protocols that are designed to use related keys? I hope not!
> >
> >Compare http://eprint.iacr.org/2009/317 4.1 Related-key attack model:
> >
> >"Compared to other cryptanalytic attacks in which the attacker can manipu-
> >late only the plaintexts and/or the ciphertexts the choice of the
> >relation between
> >secret keys gives additional degree of freedom to the attacker. The
> >downside of
> >this freedom is that such attacks might be harder to mount in practice.
> >Still,
> >designers usually try to build "ideal" primitives which can be
> >automatically used
> >without further analysis in the widest possible set of applications,
> >protocols, or
> >modes of operation. Thus resistance to such attacks is an important
> >design goal
> >for block ciphers, and in fact it was one of the stated design goals of
> >the Rijndael
> >algorithm, which was selected as the Advanced Encryption Standard."
> >
> >So the question remains if indeed AES-192 is inherently more resistant
> >to this kind of attack (more of an "ideal primitive" in this respect)
> >than AES-256 or do I read too much in the remark "the key schedule of
> >AES-192 has better diffusion" in 6 Attack on AES-192?
> >
> >Regards,
> >Leonard.
> >
> >--
> >mount -t life -o ro /dev/dna /genetic/research
> >
> >
> >
> >_______________________________________________
> >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
>

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<div dir=3D"ltr">Generally, I think the sense of the WG is to try to minimi=
ze the number of ciphers/suits.<div><br></div><div>Speaking personally, wha=
t would make me be in favor of adding AES-192 would be</div><div>some state=
ment from CFRG that they thought that it was significantly stronger than</d=
iv><div>AES-256. Absent that, I think it would be better to leave it out of=
 TLS.</div><div><br></div><div>-Ekr</div><div><br></div></div><div class=3D=
"gmail_extra"><br><div class=3D"gmail_quote">On Mon, Jan 16, 2017 at 7:59 A=
M, John Mattsson <span dir=3D"ltr">&lt;<a href=3D"mailto:john.mattsson@eric=
sson.com" target=3D"_blank">john.mattsson@ericsson.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">Note that there are trivial generic rel=
ated-key attacks on AES-192 with #K<br>
=3D D =3D T =3D M =3D 2^96<br>
<br>
<a href=3D"http://dx.doi.org/10.1080/0161-118791861749" rel=3D"noreferrer" =
target=3D"_blank">http://dx.doi.org/10.1080/<wbr>0161-118791861749</a><br>
<br>
Regards,<br>
John<br>
<br>
<br>
On 2017-01-16, 15:43, &quot;Cfrg on behalf of Leonard den Ottolander&quot;<=
br>
<div class=3D"HOEnZb"><div class=3D"h5">&lt;<a href=3D"mailto:cfrg-bounces@=
irtf.org">cfrg-bounces@irtf.org</a> on behalf of <a href=3D"mailto:leonard-=
lists@den.ottolander.nl">leonard-lists@den.ottolander.<wbr>nl</a>&gt; wrote=
:<br>
<br>
&gt;On Sun, 2017-01-15 at 20:59 +0000, Taylor R Campbell wrote:<br>
&gt;&gt; Only very unusual protocols ever use related keys.=C2=A0 In sensib=
le<br>
&gt;&gt; protocols, every key is drawn independently uniformly at random.<b=
r>
&gt;<br>
&gt;Protocols that are designed to use related keys? I hope not!<br>
&gt;<br>
&gt;Compare <a href=3D"http://eprint.iacr.org/2009/317" rel=3D"noreferrer" =
target=3D"_blank">http://eprint.iacr.org/2009/<wbr>317</a> 4.1 Related-key =
attack model:<br>
&gt;<br>
&gt;&quot;Compared to other cryptanalytic attacks in which the attacker can=
 manipu-<br>
&gt;late only the plaintexts and/or the ciphertexts the choice of the<br>
&gt;relation between<br>
&gt;secret keys gives additional degree of freedom to the attacker. The<br>
&gt;downside of<br>
&gt;this freedom is that such attacks might be harder to mount in practice.=
<br>
&gt;Still,<br>
&gt;designers usually try to build &quot;ideal&quot; primitives which can b=
e<br>
&gt;automatically used<br>
&gt;without further analysis in the widest possible set of applications,<br=
>
&gt;protocols, or<br>
&gt;modes of operation. Thus resistance to such attacks is an important<br>
&gt;design goal<br>
&gt;for block ciphers, and in fact it was one of the stated design goals of=
<br>
&gt;the Rijndael<br>
&gt;algorithm, which was selected as the Advanced Encryption Standard.&quot=
;<br>
&gt;<br>
&gt;So the question remains if indeed AES-192 is inherently more resistant<=
br>
&gt;to this kind of attack (more of an &quot;ideal primitive&quot; in this =
respect)<br>
&gt;than AES-256 or do I read too much in the remark &quot;the key schedule=
 of<br>
&gt;AES-192 has better diffusion&quot; in 6 Attack on AES-192?<br>
&gt;<br>
&gt;Regards,<br>
&gt;Leonard.<br>
&gt;<br>
&gt;--<br>
&gt;mount -t life -o ro /dev/dna /genetic/research<br>
&gt;<br>
&gt;<br>
&gt;<br>
&gt;_____________________________<wbr>__________________<br>
&gt;Cfrg mailing list<br>
&gt;<a href=3D"mailto:Cfrg@irtf.org">Cfrg@irtf.org</a><br>
&gt;<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg" rel=3D"noreferre=
r" target=3D"_blank">https://www.irtf.org/mailman/<wbr>listinfo/cfrg</a><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></div>

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From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: Eric Rescorla <ekr@rtfm.com>, John Mattsson <john.mattsson@ericsson.com>
Thread-Topic: [Cfrg] A little room for AES-192 in TLS?
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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Date: Mon, 16 Jan 2017 21:09:01 +0300
From: "Stanislav V. Smyshlyaev" <smyshsv@gmail.com>
In-Reply-To: <D4A2B50D.7E040%kenny.paterson@rhul.ac.uk>
References: <20170115205926.853FB60A6D@jupiter.mumble.net> <1484577818.5104.1.camel@quad> <D4A2A7CE.57FDF%john.mattsson@ericsson.com> <CABcZeBPGxT=9iiChy4PxD_zMHWcHU=AhCLoe7wEHHtryw2rfwg@mail.gmail.com> <D4A2B50D.7E040%kenny.paterson@rhul.ac.uk>
To: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>, Eric Rescorla <ekr@rtfm.com>, John Mattsson <john.mattsson@ericsson.com>
Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/53fIlVhs85zYIko_j1GR5BftduE>
Cc: cfrg@irtf.org, Leonard den Ottolander <leonard-lists@den.ottolander.nl>
Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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From: Tony Arcieri <bascule@gmail.com>
Date: Mon, 16 Jan 2017 10:09:33 -0800
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To: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
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Cc: "cfrg@irtf.org" <cfrg@irtf.org>, Leonard den Ottolander <leonard-lists@den.ottolander.nl>
Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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On Mon, Jan 16, 2017 at 9:37 AM, Paterson, Kenny <Kenny.Paterson@rhul.ac.uk>
wrote:

> Anyone else from CFRG have an opinion on this?


I would rate the chances of a related key attack against TLS as
"vanishingly small". The use of key derivation functions ensures keys will
not be related.

In practice, AES-192 is generally not used: AES-128 and AES-256 are used
almost exclusively. I think the general trend is to switch to AES-256 in
new systems.

Adding AES-192 ciphersuites sounds like an awful lot of additional
complexity both for specifiers and implementers for something I suspect no
one will ever use. Personally I would rather see that energy go into e.g.
post-quantum ciphersuites.

-- 
Tony Arcieri

--001a1143225021458405463a17b0
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<div dir=3D"ltr"><div class=3D"gmail_extra"><div class=3D"gmail_quote">On M=
on, Jan 16, 2017 at 9:37 AM, 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 class=3D"gmail_quote" style=3D"=
margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Anyone else =
from CFRG have an opinion on this?</blockquote><div><br></div><div>I would =
rate the chances of a related key attack against TLS as &quot;vanishingly s=
mall&quot;. The use of key derivation functions ensures keys will not be re=
lated.</div><div><br></div><div>In practice, AES-192 is generally not used:=
 AES-128 and AES-256 are used almost exclusively. I think the general trend=
 is to switch to AES-256 in new systems.</div><div><br></div><div>Adding AE=
S-192 ciphersuites sounds like an awful lot of additional complexity both f=
or specifiers and implementers for something I suspect no one will ever use=
. Personally I would rather see that energy go into e.g. post-quantum ciphe=
rsuites.</div><div><br></div></div>-- <br><div class=3D"gmail_signature" da=
ta-smartmail=3D"gmail_signature">Tony Arcieri<br></div>
</div></div>

--001a1143225021458405463a17b0--


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From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: Sean Turner <sean@sn3rd.com>, IRTF CFRG <cfrg@irtf.org>
Thread-Topic: [Cfrg] Help with the use of contexts
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Subject: Re: [Cfrg] Help with the use of contexts
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On Wed, Jan 4, 2017 at 1:55 PM, Sean Turner <sean@sn3rd.com> wrote:

> The TLS WG is nearing the end of our journey moving EC-based algorithms
> for TLS 1.2 (and earlier) from Informational to Standards track [0].  Whi=
le
> we were doing that we also added in 25519 and x448 as well as EdDSA.
>
> I=E2=80=99d like to get some input from the CFRG on the use of contexts; =
the
> "context label" is a way to provide domain separation between signatures
> made in different contexts, avoiding cross-protocol attacks.  s10.3 of
> draft-irtf-cfrg-eddsa includes the following:
>
> Contexts SHOULD NOT be used opportunistically, as that kind of use
> is very error-prone.  If contexts are used, one SHOULD require all
> signature schemes available for use in that purpose support
> contexts.
>
> This is great advice for new protocols because it=E2=80=99s easy to make =
all the
> schemes the same, but for existing protocols like TLS where there=E2=80=
=99s zero
> chance of obsoleting the existing signature schemes and defining new
> signature schemes with contexts it makes you wonder what
> =E2=80=9Copportunistically=E2=80=9D means. I.e., would setting a context =
parameter for
> Ed448 and no other already defined signature scheme be considered
> opportunistic?
>

Domain separation for signed values is important and TLS already defines
context strings for signature operations:
https://tools.ietf.org/html/draft-ietf-tls-tls13-18#section-4.4.2

The way that this is constructed (due to me) is generic for any signature
scheme. (Basically just have the context string be NUL-terminated at the
beginning of the signed message.)

So for TLS I believe that the issue is already taken care of. It would also
probably just add pain for implementers if the context string were to be
duplicated as an input to the signature scheme where signature schemes
support it.


Cheers

AGL

--=20
Adam Langley agl@imperialviolet.org https://www.imperialviolet.org

--94eb2c061a1cc562ab05463a96b4
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<div dir=3D"ltr"><div class=3D"gmail_extra"><div class=3D"gmail_quote">On W=
ed, Jan 4, 2017 at 1:55 PM, Sean Turner <span dir=3D"ltr">&lt;<a href=3D"ma=
ilto:sean@sn3rd.com" target=3D"_blank">sean@sn3rd.com</a>&gt;</span> wrote:=
<br><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">The TLS WG is nearing=
 the end of our journey moving EC-based algorithms for TLS 1.2 (and earlier=
) from Informational to Standards track [0].=C2=A0 While we were doing that=
 we also added in 25519 and x448 as well as EdDSA.<br>
<br>
I=E2=80=99d like to get some input from the CFRG on the use of contexts; th=
e &quot;context label&quot; is a way to provide domain separation between s=
ignatures made in different contexts, avoiding cross-protocol attacks.=C2=
=A0 s10.3 of draft-irtf-cfrg-eddsa includes the following:<br>
<br>
Contexts SHOULD NOT be used opportunistically, as that kind of use<br>
is very error-prone.=C2=A0 If contexts are used, one SHOULD require all<br>
signature schemes available for use in that purpose support<br>
contexts.<br>
<br>
This is great advice for new protocols because it=E2=80=99s easy to make al=
l the schemes the same, but for existing protocols like TLS where there=E2=
=80=99s zero chance of obsoleting the existing signature schemes and defini=
ng new signature schemes with contexts it makes you wonder what =E2=80=9Cop=
portunistically=E2=80=9D means. I.e., would setting a context parameter for=
 Ed448 and no other already defined signature scheme be considered opportun=
istic?<br></blockquote><div><br></div><div>Domain separation for signed val=
ues is important and TLS already defines context strings for signature oper=
ations:=C2=A0<a href=3D"https://tools.ietf.org/html/draft-ietf-tls-tls13-18=
#section-4.4.2">https://tools.ietf.org/html/draft-ietf-tls-tls13-18#section=
-4.4.2</a></div><div><br></div><div>The way that this is constructed (due t=
o me) is generic for any signature scheme. (Basically just have the context=
 string be NUL-terminated at the beginning of the signed message.)</div><di=
v><br></div><div>So for TLS I believe that the issue is already taken care =
of. It would also probably just add pain for implementers if the context st=
ring were to be duplicated as an input to the signature scheme where signat=
ure schemes support it.</div><div><br></div><div><br></div><div>Cheers</div=
><div><br></div><div>AGL</div><div>=C2=A0</div></div>-- <br><div class=3D"g=
mail_signature">Adam Langley <a href=3D"mailto:agl@imperialviolet.org" targ=
et=3D"_blank">agl@imperialviolet.org</a> <a href=3D"https://www.imperialvio=
let.org" target=3D"_blank">https://www.imperialviolet.org</a></div>
</div></div>

--94eb2c061a1cc562ab05463a96b4--


From nobody Mon Jan 16 11:07:39 2017
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From: Leonard den Ottolander <leonard-lists@den.ottolander.nl>
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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Hello Tony,

On Mon, 2017-01-16 at 10:09 -0800, Tony Arcieri wrote:
> I would rate the chances of a related key attack against TLS as
> "vanishingly small". The use of key derivation functions ensures keys will
> not be related.

How about a scenario where an adversary is able to compromise the
software in such a way that related keys are being generated
occasionally and possibly even used for encryption of known plain text
(protocol headers come to mind)? This scenario is assuming the adversary
is not fully in control of the source code but is capable to inject
subtle bugs "under the radar". Would AES-192 hold up better in such a
scenario than AES-256?

And how can one extrapolate the attacks and analyses mentioned in
http://eprint.iacr.org/2009/317 to use them as an indication of possible
cryptanalytic advances?

> In practice, AES-192 is generally not used: AES-128 and AES-256 are used
> almost exclusively. I think the general trend is to switch to AES-256 in
> new systems.

This is a circular argument. AES-192 is not generally used because it is
not in the specifications. Using that as an argument not to put it in
the specs is well, circular.

Bruce Schneier wrote about this in 2009:
https://www.schneier.com/blog/archives/2009/07/another_new_aes.html &
https://www.schneier.com/academic/paperfiles/paper-rijndael.pdf

In the blog he states "The attack exploits the fact that the key
schedule for 256-bit version is pretty lousy -- something we pointed out
in our 2000 paper -- but doesn't extend to AES with a 128-bit key."

He even goes so far as to state "And for new applications I suggest that
people don't use AES-256."

> Adding AES-192 ciphersuites sounds like an awful lot of additional
> complexity both for specifiers and implementers for something I suspect no
> one will ever use.

A software like f.e. OpenSSL has an AES implementation that does support
AES-192. I'm not sure if the GCM code needs modifications for it to work
with AES-192, but for the rest all that is required is to add the
references to the new ciphers in the source code. I don't see how one
can qualify the addition of a few references to a list as "complex".

> Personally I would rather see that energy go into e.g.
> post-quantum ciphersuites.

I thought symmetric ciphers are considered somewhat quantum resistant so
I'm not sure the PQ argument is very valid here. Also, if AES-192 is
inherently more secure than AES-256 that would probably also be the case
in a PQ world.

By the way, I'm all for the implementation and specification of post
quantum symmetric ciphers. I could imagine something along the lines of
triple AES (GCM3 with mask 1 and 2 concatenated and XORed in the middle
with either mask 1 or 2 again.) Or perhaps an extension of Rijndael to
use a block of 256 bits and a key of 480 :) .

So the question remains if AES-192 has certain characteristics that
warrant inclusion. The fact that "the key schedule for 256-bit version
is pretty lousy" and the mentioned attacks have complexity of < 2^100
for AES-256, but > 2^179 for AES-192 might speak for it.

Regards,
Leonard.

-- 
mount -t life -o ro /dev/dna /genetic/research



From nobody Mon Jan 16 11:14:32 2017
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Date: Mon, 16 Jan 2017 21:14:16 +0200
From: Ilari Liusvaara <ilariliusvaara@welho.com>
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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On Mon, Jan 16, 2017 at 08:07:31PM +0100, Leonard den Ottolander wrote:
> Hello Tony,
> 
> On Mon, 2017-01-16 at 10:09 -0800, Tony Arcieri wrote:
> > I would rate the chances of a related key attack against TLS as
> > "vanishingly small". The use of key derivation functions ensures keys will
> > not be related.
> 
> How about a scenario where an adversary is able to compromise the
> software in such a way that related keys are being generated
> occasionally and possibly even used for encryption of known plain text
> (protocol headers come to mind)? This scenario is assuming the adversary
> is not fully in control of the source code but is capable to inject
> subtle bugs "under the radar". Would AES-192 hold up better in such a
> scenario than AES-256?

The key derivations are interop-critical, so compromises like that would
be found real quick (since essentially nothing would work anymore).
 

And there is at least one place in TLS 1.2 that can be undetectably
compromised by a server in a way that lets adversary passively decrypt
most connections.


-Ilari


From nobody Mon Jan 16 11:18:36 2017
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From: "Salz, Rich" <rsalz@akamai.com>
To: Leonard den Ottolander <leonard-lists@den.ottolander.nl>, "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] A little room for AES-192 in TLS?
Thread-Index: AQHSb3JE35QdAtT7x0CRQruWUbnzSqE7gsUAgAAVHoCAAAfRAIAAE5+AgAAI+oCAABAygP//rfNw
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References: <20170115205926.853FB60A6D@jupiter.mumble.net> <1484577818.5104.1.camel@quad> <D4A2A7CE.57FDF%john.mattsson@ericsson.com> <CABcZeBPGxT=9iiChy4PxD_zMHWcHU=AhCLoe7wEHHtryw2rfwg@mail.gmail.com> <D4A2B50D.7E040%kenny.paterson@rhul.ac.uk> <CAHOTMVJrHBn4AR7PCJ14xKYCVjdxF7SiswiOABX_g6A5gsQGDg@mail.gmail.com> <1484593651.5104.49.camel@quad>
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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> How about a scenario where an adversary is able to compromise the
> software in such a way that related keys are being generated occasionally
> and possibly even used for encryption of known plain text (protocol heade=
rs
> come to mind)?

To the best of my knowledge, partial compromise of software is not somethin=
g that has been in the IETF threat model.  "All or nothing" if you will.

> And how can one extrapolate the attacks and analyses mentioned in
> http://eprint.iacr.org/2009/317 to use them as an indication of possible
> cryptanalytic advances?

One simple idea, which I have suggested in the TLS mailing list, is that yo=
u search to see if anyone has done anything in this area in the past eight =
years.
=20
> > used almost exclusively. I think the general trend is to switch to
> > AES-256 in new systems.
>=20
> This is a circular argument.

Not quite.  It is an argument saying that we are using AES256 in spite of w=
hat one paper says.

> I don't see how one can qualify the addition
> of a few references to a list as "complex".

Have you done much software deployment, especially at Internet scale?  This=
 is about far more than just adding IANA entries.  Did you see my post in t=
he  TLS group that talked to this?
=20
> So the question remains if AES-192 has certain characteristics that warra=
nt
> inclusion. The fact that "the key schedule for 256-bit version is pretty =
lousy"
> and the mentioned attacks have complexity of < 2^100 for AES-256, but >
> 2^179 for AES-192 might speak for it.

Has anyone but Bruce shared that viewpoint?

It's been nine years.  Surely *something* must have happened that you can f=
ind?


From nobody Mon Jan 16 12:06:06 2017
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From: John Mattsson <john.mattsson@ericsson.com>
To: Leonard den Ottolander <leonard-lists@den.ottolander.nl>, "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] A little room for AES-192 in TLS?
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From nobody Mon Jan 16 12:10:01 2017
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Subject: Re: [Cfrg] Help with the use of contexts
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Adam Langley writes:
> The way that this is constructed (due to me) is generic for any
> signature scheme. (Basically just have the context string be
> NUL-terminated at the beginning of the signed message.)

In other words, there's still a simple sign-a-message layer that uses
the standard signature API, that works with all signature systems, and
that minimizes costs for implementors and auditors. On top of this
there's a universal

   def sign_a_context_and_data(c,d):
     if '\0' in c: raise Exception('NUL not allowed in contexts')
     return sign(c + '\0' + d)

layer used by the protocol (and by any other protocols that want it).
Everyone can see how this works from a spec perspective and from a
software-engineering perspective.

For comparison, trying to modify the interface and specification of
every sign() function creates a transition nightmare, with nobody able
to answer basic questions about how this approach is actually supposed
to work. What's the advantage supposed to be?

I would really like to see this unnecessary complexity eliminated from
CFRG's signature specifications. Please see

   https://www.ietf.org/mail-archive/web/cfrg/current/msg08167.html

for further comments.

---Dan


From nobody Mon Jan 16 13:50:56 2017
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References: <20170115205926.853FB60A6D@jupiter.mumble.net> <1484577818.5104.1.camel@quad> <D4A2A7CE.57FDF%john.mattsson@ericsson.com> <CABcZeBPGxT=9iiChy4PxD_zMHWcHU=AhCLoe7wEHHtryw2rfwg@mail.gmail.com> <D4A2B50D.7E040%kenny.paterson@rhul.ac.uk> <CAHOTMVJrHBn4AR7PCJ14xKYCVjdxF7SiswiOABX_g6A5gsQGDg@mail.gmail.com> <1484593651.5104.49.camel@quad>
From: Tony Arcieri <bascule@gmail.com>
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--94eb2c1243ee6f9d7905463d2df0
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On Mon, Jan 16, 2017 at 11:07 AM, Leonard den Ottolander <
leonard-lists@den.ottolander.nl> wrote:

> How about a scenario where an adversary is able to compromise the
> software in such a way that related keys are being generated
> occasionally and possibly even used for encryption of known plain text
> (protocol headers come to mind)? This scenario is assuming the adversary
> is not fully in control of the source code but is capable to inject
> subtle bugs "under the radar". Would AES-192 hold up better in such a
> scenario than AES-256?
>

Even in the event an attacker was able to pull off some sort of fault
attack and create related keys, as others have already noted the other side
will notice these keys are wrong and snap shut before the attacker can pull
off the rest of the attack. The next time you connect it will rekey. I
personally cannot think of any way to make TLS behave in such a way related
key attacks are even possible, even giving an attacker such a powerful tool
as precision fault attacks (and with such a powerful tool, they could
likely change the client's preferred ciphersuites as well).

This is a circular argument. AES-192 is not generally used because it is
> not in the specifications.


This argument holds not just for TLS, but pretty much any protocols that
use AES. In practice, nobody uses AES-192, because there is little reason
to choose it over either of the other options.


> Bruce Schneier wrote about this in 2009:
> https://www.schneier.com/blog/archives/2009/07/another_new_aes.html &
> https://www.schneier.com/academic/paperfiles/paper-rijndael.pdf
>
> In the blog he states "The attack exploits the fact that the key
> schedule for 256-bit version is pretty lousy -- something we pointed out
> in our 2000 paper -- but doesn't extend to AES with a 128-bit key."
>

Sounds like you just made an argument for AES-128.

-- 
Tony Arcieri

--94eb2c1243ee6f9d7905463d2df0
Content-Type: text/html; charset=UTF-8
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<div dir=3D"ltr"><div class=3D"gmail_extra"><div class=3D"gmail_quote">On M=
on, Jan 16, 2017 at 11:07 AM, Leonard den Ottolander <span dir=3D"ltr">&lt;=
<a href=3D"mailto:leonard-lists@den.ottolander.nl" target=3D"_blank">leonar=
d-lists@den.ottolander.nl</a>&gt;</span> wrote:<br><blockquote class=3D"gma=
il_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-lef=
t:1ex">How about a scenario where an adversary is able to compromise the<br=
>
software in such a way that related keys are being generated<br>
occasionally and possibly even used for encryption of known plain text<br>
(protocol headers come to mind)? This scenario is assuming the adversary<br=
>
is not fully in control of the source code but is capable to inject<br>
subtle bugs &quot;under the radar&quot;. Would AES-192 hold up better in su=
ch a<br>
scenario than AES-256?<br></blockquote><div><br></div><div>Even in the even=
t an attacker was able to pull off some sort of fault attack and create rel=
ated keys, as others have already noted the other side will notice these ke=
ys are wrong and snap shut before the attacker can pull off the rest of the=
 attack. The next time you connect it will rekey. I personally cannot think=
 of any way to make TLS behave in such a way related key attacks are even p=
ossible, even giving an attacker such a powerful tool as precision fault at=
tacks (and with such a powerful tool, they could likely change the client&#=
39;s preferred ciphersuites as well).</div><div><br></div><blockquote class=
=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padd=
ing-left:1ex">This is a circular argument. AES-192 is not generally used be=
cause it is<br>
not in the specifications.</blockquote><div><br></div><div>This argument ho=
lds not just for TLS, but pretty much any protocols that use AES. In practi=
ce, nobody uses AES-192, because there is little reason to choose it over e=
ither of the other options.</div><div>=C2=A0</div><blockquote class=3D"gmai=
l_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left=
:1ex"><span class=3D"">Bruce Schneier wrote about this in 2009:<br>
<a href=3D"https://www.schneier.com/blog/archives/2009/07/another_new_aes.h=
tml" rel=3D"noreferrer" target=3D"_blank">https://www.schneier.com/blog/<wb=
r>archives/2009/07/another_new_<wbr>aes.html</a> &amp;<br>
<a href=3D"https://www.schneier.com/academic/paperfiles/paper-rijndael.pdf"=
 rel=3D"noreferrer" target=3D"_blank">https://www.schneier.com/<wbr>academi=
c/paperfiles/paper-<wbr>rijndael.pdf</a><br>
<br>
In the blog he states &quot;The attack exploits the fact that the key<br>
schedule for 256-bit version is pretty lousy -- something we pointed out<br=
>
in our 2000 paper -- but doesn&#39;t extend to AES with a 128-bit key.&quot=
;<br></span></blockquote><div><br></div><div>Sounds like you just made an a=
rgument for AES-128.</div><div><br></div></div>-- <br><div class=3D"gmail_s=
ignature" data-smartmail=3D"gmail_signature">Tony Arcieri<br></div>
</div></div>

--94eb2c1243ee6f9d7905463d2df0--


From nobody Mon Jan 16 23:58:12 2017
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Subject: [Cfrg] I-D Action: draft-irtf-cfrg-augpake-07.txt
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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-07.txt
	Pages           : 20
	Date            : 2017-01-16

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 password is chosen from a
   small set of dictionary whose space is within the off-line dictionary
   attacks.  The AugPAKE protocol described here is secure against
   passive attacks, active attacks and off-line 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 off-line 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's also a htmlized version available at:
https://tools.ietf.org/html/draft-irtf-cfrg-augpake-07

A diff from the previous version is available at:
https://www.ietf.org/rfcdiff?url2=draft-irtf-cfrg-augpake-07


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/


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From: Yaron Sheffer <yaronf.ietf@gmail.com>
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Subject: Re: [Cfrg] Help with the use of contexts
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> Domain separation for signed values is important and TLS already defines
> context strings for signature operations:
> https://tools.ietf.org/html/draft-ietf-tls-tls13-18#section-4.4.2
>
> The way that this is constructed (due to me) is generic for any signature
> scheme. (Basically just have the context string be NUL-terminated at the
> beginning of the signed message.)
>
> So for TLS I believe that the issue is already taken care of. It would also
> probably just add pain for implementers if the context string were to be
> duplicated as an input to the signature scheme where signature schemes
> support it.
>
>
> Cheers
>
> AGL

Hi Adam,

Wide industry adoption of TLS 1.2 took around 10 years. So IMO saying 
"this is solved in TLS 1.3" is not a good enough answer, if in the 
meantime we will continue to see cross-protocol and cross-TLS-version 
attacks.

Please note that the original post refers to "TLS 1.2 (and earlier)."

Thanks,
	Yaron


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Subject: Re: [Cfrg] Help with the use of contexts
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This is a cryptographically signed message in MIME format.

--------------ms040503020209030907020508
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On 16/01/17 20:09, D. J. Bernstein wrote:
> I would really like to see this unnecessary complexity eliminated from
> CFRG's signature specifications.

I'm relatively neutral on the use or non-use of contexts,
but lean more towards Dan's position that the API changes
involved mean that practically, it's better to not demand
contexts.

However, I really do wish that CFRG specs would not offer
both choices - that will simply lead to repeating this
discussion each time an IETF protocol wants to use the CFRG
spec. And of course, different decisions will be made over
time, leading to slightly more mess than would otherwise
exist. That's not a showstopper thing, but life will be
better if the choice is not offered.

So, I'd support eliminating contexts from CFRG specs and
saying something like "if you want that, and it's not a
bad idea for avoiding cross-protocol attacks, then do it
at a layer above the crypto API."

Cheers,
S.

PS: random idea - I wonder if analysis of wireshark
dissector source code, or some application calling
such code, might be a fine way to spot potential
cross-protocol attacks - anyone know if that's been
tried?


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From: Leonard den Ottolander <leonard-lists@den.ottolander.nl>
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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On Mon, 2017-01-16 at 19:18 +0000, Salz, Rich wrote:
> > And how can one extrapolate the attacks and analyses mentioned in
> > http://eprint.iacr.org/2009/317 to use them as an indication of possible
> > cryptanalytic advances?
> 
> One simple idea, which I have suggested in the TLS mailing list, is
> that you search to see if anyone has done anything in this area in the
> past eight years.

Are you suggesting that because this research is 8 years old its
findings are not valid? So far noone has really answered the question if
the aforementioned analysis indicates that AES-192 might be more
resistant to cryptanalysis than AES-256.

So although I don't think the fact that the research I reference is 8
years old invalidates it in any way I dug around a bit.

http://eprint.iacr.org/2010/248 improves the attack on AES-192 from
2^176 to 2^169. The original attack against AES-256 in
http://eprint.iacr.org/2009/317 had complexity of 2^119 which they
improved to 2^99.5 soon after original publication.

And there is

https://books.google.nl/books?id=weETxBt-VAMC&pg=PA316&lpg=PA316&dq=aes+256+key+schedule+strength&source=bl&ots=GTfhsVdh7E&sig=y0ZE9_3OBCRbbpLHvq0PAAZqRmg&hl=en&sa=X&redir_esc=y#v=onepage&q=aes%20256%20key%20schedule%20strength&f=false

Advances in Cryptology - EUROCRYPT 2010: 29th Annual International
Conference...

This is only a partial paper, but I'll cite from the conclusions of Key
Recovery Attacks of Practical Complexity, 8 Conclusions (page 316):

"The main problem seems to be the key schedule of AES-256, which is "not
of industrial strength": It does not mix the initial key sufficiently,
it is too linear, and as a result it has unusually long key
differentials of probability 1. In addition the similarity between the
key schedule and the data encryption in AES makes it possible to
repeatedly cancel data differences with corresponding key differences
over many rounds. Ironically, the new attacks work best against AES-256
(which was supposed to be the strongest member of the AES family), and
do not currently seem to work against AES-128."

"The most disturbing aspect of the new attacks is that AES-256 can no
longer be considered as a safe black box construction, which can be
dropped into any security application with little thought about how it
is used."

> > > used almost exclusively. I think the general trend is to switch to
> > > AES-256 in new systems.
> > 
> > This is a circular argument.
> 
> Not quite.  It is an argument saying that we are using AES256 in spite of what one paper says.

I was responding to the first part of that paragraph: "In practice,
AES-192 is generally not used: AES-128 and AES-256 are used
almost exclusively." To that I say, AES-192 is not being used because
it's not in the specs. Then refusing to add it to the specs is what I
call a circular argument. And you cannot argue nobody wants to use it as
it is not available for use. If I wanted to I could not use AES-192
except in private use scenario's as noone is offering such ciphers, i.e.
there is noone to "talk AES-192 to". If such ciphers were available and
nobody would use them then you could draw the conclusion that "nobody
wants to use it".

> > I don't see how one can qualify the addition
> > of a few references to a list as "complex".
> 
> Have you done much software deployment, especially at Internet scale?
> This is about far more than just adding IANA entries.  Did you see my
> post in the  TLS group that talked to this?

I'm just not entirely convinced by your arguments. Have you seen any
breakage in middleboxes when the ARIA ciphers were added in 2011? I
acknowledge adding ciphers is not a zero effort, but to describe it as
complex is inaccurate.

As for software implementation, I already argued that if the cipher is
available in the software adding references so it can be used is
trivial. And implementers can always ignore the new ciphers in the list.
It's not like openssl broke because it ignores the ARIA ciphers
altogether.
 
> > So the question remains if AES-192 has certain characteristics that warrant
> > inclusion. The fact that "the key schedule for 256-bit version is pretty lousy"
> > and the mentioned attacks have complexity of < 2^100 for AES-256, but >
> > 2^179 for AES-192 might speak for it.
> 
> Has anyone but Bruce shared that viewpoint?

Well clearly the authors of Related-key Cryptanalysis of the Full
AES-192 and AES-256, Alex Biryukov and Dmitry Khovratovich agree with
him on the relatively poor quality of the key schedule of AES-256 even
though their wording is not quite as strong as his. Plus the authors of
the EuroCrypt article quoted above (the two previous authors and Orr
Dunkelman, Nathan Keller and Adi Shamir).

And there's references to that study in http://eprint.iacr.org/2011/710
and http://eprint.iacr.org/2016/025 so I guess you could count those
authors too.

Regards,
Leonard.

-- 
mount -t life -o ro /dev/dna /genetic/research



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From: "Salz, Rich" <rsalz@akamai.com>
To: Leonard den Ottolander <leonard-lists@den.ottolander.nl>, "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] A little room for AES-192 in TLS?
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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> Are you suggesting that because this research is 8 years old its findings=
 are
> not valid?

Yes, kinda.  If the sky really was falling eight years ago, then where are =
the other papers?

> "The most disturbing aspect of the new attacks is that AES-256 can no lon=
ger
> be considered as a safe black box construction, which can be dropped into
> any security application with little thought about how it is used."

Well, luckily, that is not the case with TLS.  The particular attack about =
keys, as has been explained, isn't relevant to AES-in-TLS.  Your compromise=
, while not only outside the typical IETF scope, has been shown to fail as =
the other side will abort the connection.

> work best against AES-256 (which was supposed to be the strongest member
> of the AES family), and do not currently seem to work against AES-128."

Luckily we use AES128.

> And you cannot argue nobody wants to use it as it is not available for us=
e. If I
> wanted to I could not use AES-192 except in private use scenario's as noo=
ne
> is offering such ciphers, i.e.

Yes.

> I
> acknowledge adding ciphers is not a zero effort, but to describe it as co=
mplex
> is inaccurate.

We disagree.

You can write up an individual RFC that defines AES192 ciphers for use in T=
LS, and ask IANA to register them, and then "let the market decide."  I sug=
gest you focus on a couple, and not try for full parity by defining a coupl=
e of dozen, as the registrar is likely to reject it.

Or you can keep posting here (and as previously pointed out, more appropria=
tely the TLS list) and see if you can convince anyone.
=20
=20


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From: Watson Ladd <watsonbladd@gmail.com>
Date: Tue, 17 Jan 2017 07:06:45 -0800
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Subject: Re: [Cfrg] Help with the use of contexts
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On Jan 17, 2017 3:48 AM, "Stephen Farrell" <stephen.farrell@cs.tcd.ie>
wrote:



On 16/01/17 20:09, D. J. Bernstein wrote:
> I would really like to see this unnecessary complexity eliminated from
> CFRG's signature specifications.

I'm relatively neutral on the use or non-use of contexts,
but lean more towards Dan's position that the API changes
involved mean that practically, it's better to not demand
contexts.

However, I really do wish that CFRG specs would not offer
both choices - that will simply lead to repeating this
discussion each time an IETF protocol wants to use the CFRG
spec. And of course, different decisions will be made over
time, leading to slightly more mess than would otherwise
exist. That's not a showstopper thing, but life will be
better if the choice is not offered.

So, I'd support eliminating contexts from CFRG specs and
saying something like "if you want that, and it's not a
bad idea for avoiding cross-protocol attacks, then do it
at a layer above the crypto API."

Cheers,
S.

PS: random idea - I wonder if analysis of wireshark
dissector source code, or some application calling
such code, might be a fine way to spot potential
cross-protocol attacks - anyone know if that's been
tried?


What we want is to determine if the intersection of two badly specified
possibly context sensitive languages is empty. This is tricky. If protocols
stuck to regular languages it would be decideable.



_______________________________________________
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<div dir=3D"auto"><div><br><div class=3D"gmail_extra"><br><div class=3D"gma=
il_quote">On Jan 17, 2017 3:48 AM, &quot;Stephen Farrell&quot; &lt;<a href=
=3D"mailto:stephen.farrell@cs.tcd.ie">stephen.farrell@cs.tcd.ie</a>&gt; wro=
te:<br type=3D"attribution"><blockquote class=3D"quote" style=3D"margin:0 0=
 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class=3D"quoted-t=
ext"><br>
<br>
On 16/01/17 20:09, D. J. Bernstein wrote:<br>
&gt; I would really like to see this unnecessary complexity eliminated from=
<br>
&gt; CFRG&#39;s signature specifications.<br>
<br>
</div>I&#39;m relatively neutral on the use or non-use of contexts,<br>
but lean more towards Dan&#39;s position that the API changes<br>
involved mean that practically, it&#39;s better to not demand<br>
contexts.<br>
<br>
However, I really do wish that CFRG specs would not offer<br>
both choices - that will simply lead to repeating this<br>
discussion each time an IETF protocol wants to use the CFRG<br>
spec. And of course, different decisions will be made over<br>
time, leading to slightly more mess than would otherwise<br>
exist. That&#39;s not a showstopper thing, but life will be<br>
better if the choice is not offered.<br>
<br>
So, I&#39;d support eliminating contexts from CFRG specs and<br>
saying something like &quot;if you want that, and it&#39;s not a<br>
bad idea for avoiding cross-protocol attacks, then do it<br>
at a layer above the crypto API.&quot;<br>
<br>
Cheers,<br>
S.<br>
<br>
PS: random idea - I wonder if analysis of wireshark<br>
dissector source code, or some application calling<br>
such code, might be a fine way to spot potential<br>
cross-protocol attacks - anyone know if that&#39;s been<br>
tried?<br></blockquote></div></div></div><div dir=3D"auto"><br></div><div d=
ir=3D"auto"><div class=3D"gmail_extra"><div class=3D"gmail_quote"><blockquo=
te class=3D"quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;pa=
dding-left:1ex"></blockquote></div></div></div><div dir=3D"auto">What we wa=
nt is to determine if the intersection of two badly specified possibly cont=
ext sensitive languages is empty. This is tricky. If protocols stuck to reg=
ular languages it would be decideable.</div><div dir=3D"auto"><br></div><di=
v dir=3D"auto"><div class=3D"gmail_extra"><div class=3D"gmail_quote"><block=
quote class=3D"quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid=
;padding-left:1ex">
<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>
<br></blockquote></div><br></div></div></div>

--94eb2c1a03d61722ab05464ba64d--


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From: Yoav Nir <ynir.ietf@gmail.com>
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References: <20170115205926.853FB60A6D@jupiter.mumble.net> <1484577818.5104.1.camel@quad> <D4A2A7CE.57FDF%john.mattsson@ericsson.com> <CABcZeBPGxT=9iiChy4PxD_zMHWcHU=AhCLoe7wEHHtryw2rfwg@mail.gmail.com> <D4A2B50D.7E040%kenny.paterson@rhul.ac.uk> <CAHOTMVJrHBn4AR7PCJ14xKYCVjdxF7SiswiOABX_g6A5gsQGDg@mail.gmail.com> <1484593651.5104.49.camel@quad> <1df3ba4212e44f9d8e3e6fabf8610cc0@usma1ex-dag1mb1.msg.corp.akamai.com> <1484662079.5135.49.camel@quad> <9d54608c721c465788a38e5cc8e8cac6@usma1ex-dag1mb1.msg.corp.akamai.com>
To: Rich Salz <rsalz@akamai.com>
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Cc: "cfrg@irtf.org" <cfrg@irtf.org>, Leonard den Ottolander <leonard-lists@den.ottolander.nl>
Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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On 17 Jan 2017, at 16:48, Salz, Rich <rsalz@akamai.com> wrote:

>> acknowledge adding ciphers is not a zero effort, but to describe it =
as complex
>> is inaccurate.
>=20
> We disagree.
>=20
> You can write up an individual RFC that defines AES192 ciphers for use =
in TLS, and ask IANA to register them, and then "let the market decide." =
 I suggest you focus on a couple, and not try for full parity by =
defining a couple of dozen, as the registrar is likely to reject it.
>=20
> Or you can keep posting here (and as previously pointed out, more =
appropriately the TLS list) and see if you can convince anyone.

An individual RFC (or even an RFC from the TLS WG) is no substitute for =
convincing people.  There are over 8000 RFCs. None of us implement all =
of them.

So an AES-192 RFC won=E2=80=99t cause universal support for these =
ciphersuites any more that RFC 6209 caused universal support for ARIA.

He can even donate code to OpenSSL (AES-192 already exists, but you need =
the ciphersuites) but he still need to convince people (you?) to (i) =
accept it and (ii) make it part of the default or =E2=80=9Cstrong=E2=80=9D=
 or whatever the recommended configuration is called these days.

And he=E2=80=99ll need to convince browser maintainers to add it to the =
browsers. And then there=E2=80=99s the other dozens of implementations.

If you want a technology implemented and deployed, you still need to =
convince a lot of people. RFCs are (relatively) easy.

Yoav


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To: Stephen Farrell <stephen.farrell@cs.tcd.ie>
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Subject: Re: [Cfrg] Help with the use of contexts
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> On 17 Jan 2017, at 13:48, Stephen Farrell <stephen.farrell@cs.tcd.ie> =
wrote:
>=20
>=20
>=20
> On 16/01/17 20:09, D. J. Bernstein wrote:
>> I would really like to see this unnecessary complexity eliminated =
from
>> CFRG's signature specifications.
>=20
> I'm relatively neutral on the use or non-use of contexts,
> but lean more towards Dan's position that the API changes
> involved mean that practically, it's better to not demand
> contexts.

Me too.

> However, I really do wish that CFRG specs would not offer
> both choices - that will simply lead to repeating this
> discussion each time an IETF protocol wants to use the CFRG
> spec. And of course, different decisions will be made over
> time,

Not over time. In the next few months the IESG is going to get documents =
about EdDSA signatures from TLS, IPsecME and curdle for signatures in =
TLS, IKE, and PKIX respectively.  If the decision is not the same in all =
of them, I think (hope) that the IESG would ask why.

> leading to slightly more mess than would otherwise
> exist. That's not a showstopper thing, but life will be
> better if the choice is not offered.
>=20
> So, I'd support eliminating contexts from CFRG specs and
> saying something like "if you want that, and it's not a
> bad idea for avoiding cross-protocol attacks, then do it
> at a layer above the crypto API."
>=20
> Cheers,
> S.
>=20
> PS: random idea - I wonder if analysis of wireshark
> dissector source code, or some application calling
> such code, might be a fine way to spot potential
> cross-protocol attacks - anyone know if that's been
> tried?
>=20
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg


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From: William Whyte <wwhyte@securityinnovation.com>
Date: Tue, 17 Jan 2017 11:03:32 -0500
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To: "Salz, Rich" <rsalz@akamai.com>
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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It seems like we need a better 256-bit algorithm than AES-256: the related
key attacks might not be a concern in TLS, but if use of AES-256 in TLS
causes its widespread use in other contexts, it will sooner or later be
used in a context where the related key attacks matter. I would support
deprecating AES-256 throughout IETF in favor of a better alternative.

It doesn't seem like AES-192 is the right choice for that alternative.
Among other things, it's not 256-bit :-).

What *should* CFRG be recommending as a 256-bit symmetric algorithm?

Cheers,

William

On Tue, Jan 17, 2017 at 9:48 AM, Salz, Rich <rsalz@akamai.com> wrote:

> > Are you suggesting that because this research is 8 years old its
> findings are
> > not valid?
>
> Yes, kinda.  If the sky really was falling eight years ago, then where are
> the other papers?
>
> > "The most disturbing aspect of the new attacks is that AES-256 can no
> longer
> > be considered as a safe black box construction, which can be dropped into
> > any security application with little thought about how it is used."
>
> Well, luckily, that is not the case with TLS.  The particular attack about
> keys, as has been explained, isn't relevant to AES-in-TLS.  Your
> compromise, while not only outside the typical IETF scope, has been shown
> to fail as the other side will abort the connection.
>
> > work best against AES-256 (which was supposed to be the strongest member
> > of the AES family), and do not currently seem to work against AES-128."
>
> Luckily we use AES128.
>
> > And you cannot argue nobody wants to use it as it is not available for
> use. If I
> > wanted to I could not use AES-192 except in private use scenario's as
> noone
> > is offering such ciphers, i.e.
>
> Yes.
>
> > I
> > acknowledge adding ciphers is not a zero effort, but to describe it as
> complex
> > is inaccurate.
>
> We disagree.
>
> You can write up an individual RFC that defines AES192 ciphers for use in
> TLS, and ask IANA to register them, and then "let the market decide."  I
> suggest you focus on a couple, and not try for full parity by defining a
> couple of dozen, as the registrar is likely to reject it.
>
> Or you can keep posting here (and as previously pointed out, more
> appropriately the TLS list) and see if you can convince anyone.
>
>
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>

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<div dir=3D"ltr">It seems like we need a better 256-bit algorithm than AES-=
256: the related key attacks might not be a concern in TLS, but if use of A=
ES-256 in TLS causes its widespread use in other contexts, it will sooner o=
r later be used in a context where the related key attacks matter. I would =
support deprecating AES-256 throughout IETF in favor of a better alternativ=
e.<div><br></div><div>It doesn&#39;t seem like AES-192 is the right choice =
for that alternative. Among other things, it&#39;s not 256-bit :-).</div><d=
iv><br></div><div>What *should* CFRG be recommending as a 256-bit symmetric=
 algorithm?</div><div><br></div><div>Cheers,</div><div><br></div><div>Willi=
am</div></div><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">On =
Tue, Jan 17, 2017 at 9:48 AM, Salz, Rich <span dir=3D"ltr">&lt;<a href=3D"m=
ailto:rsalz@akamai.com" target=3D"_blank">rsalz@akamai.com</a>&gt;</span> w=
rote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;borde=
r-left:1px #ccc solid;padding-left:1ex"><span class=3D"">&gt; Are you sugge=
sting that because this research is 8 years old its findings are<br>
&gt; not valid?<br>
<br>
</span>Yes, kinda.=C2=A0 If the sky really was falling eight years ago, the=
n where are the other papers?<br>
<span class=3D""><br>
&gt; &quot;The most disturbing aspect of the new attacks is that AES-256 ca=
n no longer<br>
&gt; be considered as a safe black box construction, which can be dropped i=
nto<br>
&gt; any security application with little thought about how it is used.&quo=
t;<br>
<br>
</span>Well, luckily, that is not the case with TLS.=C2=A0 The particular a=
ttack about keys, as has been explained, isn&#39;t relevant to AES-in-TLS.=
=C2=A0 Your compromise, while not only outside the typical IETF scope, has =
been shown to fail as the other side will abort the connection.<br>
<span class=3D""><br>
&gt; work best against AES-256 (which was supposed to be the strongest memb=
er<br>
&gt; of the AES family), and do not currently seem to work against AES-128.=
&quot;<br>
<br>
</span>Luckily we use AES128.<br>
<span class=3D""><br>
&gt; And you cannot argue nobody wants to use it as it is not available for=
 use. If I<br>
&gt; wanted to I could not use AES-192 except in private use scenario&#39;s=
 as noone<br>
&gt; is offering such ciphers, i.e.<br>
<br>
</span>Yes.<br>
<span class=3D""><br>
&gt; I<br>
&gt; acknowledge adding ciphers is not a zero effort, but to describe it as=
 complex<br>
&gt; is inaccurate.<br>
<br>
</span>We disagree.<br>
<br>
You can write up an individual RFC that defines AES192 ciphers for use in T=
LS, and ask IANA to register them, and then &quot;let the market decide.&qu=
ot;=C2=A0 I suggest you focus on a couple, and not try for full parity by d=
efining a couple of dozen, as the registrar is likely to reject it.<br>
<br>
Or you can keep posting here (and as previously pointed out, more appropria=
tely the TLS list) and see if you can convince anyone.<br>
<div class=3D"HOEnZb"><div class=3D"h5"><br>
<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></div>

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From: Tony Arcieri <bascule@gmail.com>
Date: Tue, 17 Jan 2017 08:07:40 -0800
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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On Tue, Jan 17, 2017 at 8:03 AM, William Whyte <
wwhyte@securityinnovation.com> wrote:

> What *should* CFRG be recommending as a 256-bit symmetric algorithm?
>

ChaCha20 uses a 256-bit key:

https://tools.ietf.org/html/rfc7539

-- 
Tony Arcieri

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<div dir=3D"ltr"><div class=3D"gmail_extra"><div class=3D"gmail_quote">On T=
ue, Jan 17, 2017 at 8:03 AM, William Whyte <span dir=3D"ltr">&lt;<a href=3D=
"mailto:wwhyte@securityinnovation.com" target=3D"_blank">wwhyte@securityinn=
ovation.com</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quote" styl=
e=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);paddin=
g-left:1ex"><div dir=3D"ltr"><div>What *should* CFRG be recommending as a 2=
56-bit symmetric algorithm?</div></div></blockquote><div><br></div><div>Cha=
Cha20 uses a 256-bit key:</div><div><br></div><div><a href=3D"https://tools=
.ietf.org/html/rfc7539">https://tools.ietf.org/html/rfc7539</a>=C2=A0</div>=
</div><div><br></div>-- <br><div class=3D"gmail_signature">Tony Arcieri<br>=
</div>
</div></div>

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Subject: Re: [Cfrg] Help with the use of contexts
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On Tue, Jan 17, 2017 at 3:31 AM, Yaron Sheffer <yaronf.ietf@gmail.com> wrote:
> Wide industry adoption of TLS 1.2 took around 10 years. So IMO saying "this
> is solved in TLS 1.3" is not a good enough answer, if in the meantime we
> will continue to see cross-protocol and cross-TLS-version attacks.

If there are such attacks then they'll continue to be a problem for
TLS 1.2 because only the Ed* schemes have the possibility of a context
string. For ECDSA and RSA, the context still needs to be included in
the signed message somehow. So TLS 1.2 needs a larger change than
wiring up the context inputs of the Ed* schemes if you want to protect
it anyway.


Cheers

AGL

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


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Cc: "cfrg@irtf.org" <cfrg@irtf.org>, Leonard den Ottolander <leonard-lists@den.ottolander.nl>
Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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--001a11469f9e75aa1b05464ca30e
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Please no, just no.

Use 128 bit AES or 256 bits. Please do not create more options. The idea
that there is a need for a cipher between 10 and 14 rounds is just not
sensible. Either you are on the bleeding edge or you take a 40% performance
hit.

I am now of the opinion that all Key Agreement schemes should use a Key
Derivation function, RSA included. So even if your Key Agreement only
delivers 128 bits worth of work factor, you can still use a 256 bit cipher.

If you are doing a master key agreement plus an ephemeral, you should use
the master key agreement to salt the key derivation and so even with 128
bits of work factor on each you will have a total of 256 bits.

Rather than add pointless new cipher suites, I would like to see the key
derivation function fixed so that the ephemeral step cannot weaken the
strength of the agreed key.

--001a11469f9e75aa1b05464ca30e
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<div dir=3D"ltr"><div class=3D"gmail_default" style=3D"font-size:small">Ple=
ase no, just no.</div><div class=3D"gmail_default" style=3D"font-size:small=
"><br></div><div class=3D"gmail_default" style=3D"font-size:small">Use 128 =
bit AES or 256 bits. Please do not create more options. The idea that there=
 is a need for a cipher between 10 and 14 rounds is just not sensible. Eith=
er you are on the bleeding edge or you take a 40% performance hit.</div><di=
v class=3D"gmail_default" style=3D"font-size:small"><br></div><div class=3D=
"gmail_default" style=3D"font-size:small">I am now of the opinion that all =
Key Agreement schemes should use a Key Derivation function, RSA included. S=
o even if your Key Agreement only delivers 128 bits worth of work factor, y=
ou can still use a 256 bit cipher.</div><div class=3D"gmail_default" style=
=3D"font-size:small"><br></div><div class=3D"gmail_default" style=3D"font-s=
ize:small">If you are doing a master key agreement plus an ephemeral, you s=
hould use the master key agreement to salt the key derivation and so even w=
ith 128 bits of work factor on each you will have a total of 256 bits.</div=
><div class=3D"gmail_default" style=3D"font-size:small"><br></div><div clas=
s=3D"gmail_default" style=3D"font-size:small">Rather than add pointless new=
 cipher suites, I would like to see the key derivation function fixed so th=
at the ephemeral step cannot weaken the strength of the agreed key.</div><d=
iv class=3D"gmail_default" style=3D"font-size:small"><br></div><div class=
=3D"gmail_default" style=3D"font-size:small"><br></div></div>

--001a11469f9e75aa1b05464ca30e--


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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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> ChaCha20 uses a 256-bit key:
>=20
> https://tools.ietf.org/html/rfc7539=20

If you model Chacha's internal hash function as a 48-byte-to-64-byte =
PRF, then it is secure against related keys too.

Chacha works by supplying 48 byte (Key || Nonce || Counter) to Chacha's =
internal hash function repeatedly, each time with a counter increment. =
If Chacha's internal hash function is a PRF, then clearly *any* change =
in the key produces independent output.=


From nobody Tue Jan 17 09:24:32 2017
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From: Dan Brown <danibrown@blackberry.com>
To: "D. J. Bernstein" <djb@cr.yp.to>, "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] Help with the use of contexts
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Subject: Re: [Cfrg] Help with the use of contexts
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I agree with Dan Bernstein's suggestion and reasoning below against CFRG's =
currently contextualization of signature schemes, though I would also under=
stand if CFRG does not want to reverse its decisions.

Further points:

Protocol designers should be responsible to enforce uniqueness of protocol =
messages (within and between honest protocols), not just for digital signat=
ures but for all forms of authentication.  How much is this to ask? Isn't t=
hat kind of reliability their bread-and-butter?  If there hadn't been non-u=
niqueness, then cross-protocol attacks would have failed, right?

Adding a context to signatures is a complexity that is (1) not guaranteed t=
o help (no formal security definition, no security proof? And no, I do not =
volunteer), (2) potentially collides with non-contextualized signatures (mu=
st signers now also track whether each non-context signature corresponds to=
 some contextual signature?), (3) blames crypto for too much ;)

-----Original Message-----
From: Cfrg [mailto:cfrg-bounces@irtf.org] On Behalf Of D. J. Bernstein
Sent: Monday, January 16, 2017 3:10 PM
To: cfrg@irtf.org
Subject: Re: [Cfrg] Help with the use of contexts

Adam Langley writes:
> The way that this is constructed (due to me) is generic for any=20
> signature scheme. (Basically just have the context string be=20
> NUL-terminated at the beginning of the signed message.)

In other words, there's still a simple sign-a-message layer that uses the s=
tandard signature API, that works with all signature systems, and that mini=
mizes costs for implementors and auditors. On top of this there's a univers=
al

   def sign_a_context_and_data(c,d):
     if '\0' in c: raise Exception('NUL not allowed in contexts')
     return sign(c + '\0' + d)

layer used by the protocol (and by any other protocols that want it).
Everyone can see how this works from a spec perspective and from a software=
-engineering perspective.

For comparison, trying to modify the interface and specification of every s=
ign() function creates a transition nightmare, with nobody able to answer b=
asic questions about how this approach is actually supposed to work. What's=
 the advantage supposed to be?

I would really like to see this unnecessary complexity eliminated from CFRG=
's signature specifications. Please see

   https://www.ietf.org/mail-archive/web/cfrg/current/msg08167.html

for further comments.

---Dan

_______________________________________________
Cfrg mailing list
Cfrg@irtf.org
https://www.irtf.org/mailman/listinfo/cfrg


From nobody Tue Jan 17 10:28:54 2017
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Date: Tue, 17 Jan 2017 19:28:43 +0100
From: Joan Daemen <jda@noekeon.org>
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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Dear all,

the related-key attacks against AES were interesting from an academic 
point of view as they broke the security claim we made for Rijndael.

However, the attacks require very sophisticated manipulations of the 
secret key by the attacker. For example, even a protocol that would 
allow an attacker to add (or XOR) a value of her choice to the key 
before being used in AES would not allow mounting the attack. If you are 
interested, you can read the paper Vincent and I wrote "On the 
related-key attacks against AES" available at e.g. 
http://jda.noekeon.org/

As for including AES-192 in TLS, I don't see any benefits.

Kind regards,

Joan Daemen


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To: Adam Langley <agl@imperialviolet.org>
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From: Yaron Sheffer <yaronf.ietf@gmail.com>
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Date: Tue, 17 Jan 2017 23:41:54 +0200
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Subject: Re: [Cfrg] Help with the use of contexts
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On 17/01/17 18:12, Adam Langley wrote:
> On Tue, Jan 17, 2017 at 3:31 AM, Yaron Sheffer <yaronf.ietf@gmail.com> wrote:
>> Wide industry adoption of TLS 1.2 took around 10 years. So IMO saying "this
>> is solved in TLS 1.3" is not a good enough answer, if in the meantime we
>> will continue to see cross-protocol and cross-TLS-version attacks.
>
> If there are such attacks then they'll continue to be a problem for
> TLS 1.2 because only the Ed* schemes have the possibility of a context
> string. For ECDSA and RSA, the context still needs to be included in
> the signed message somehow. So TLS 1.2 needs a larger change than
> wiring up the context inputs of the Ed* schemes if you want to protect
> it anyway.

Correct, but this would still eliminate cross-version attacks between 
TLS 1.3 and TLS <= 1.2, for Ed*. In other words, there is (incremental) 
value in adding context opportunistically.

Thanks,
	Yaron


From nobody Tue Jan 17 15:23:00 2017
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Date: Wed, 18 Jan 2017 01:22:52 +0200
From: Ilari Liusvaara <ilariliusvaara@welho.com>
To: Yaron Sheffer <yaronf.ietf@gmail.com>
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Subject: Re: [Cfrg] Help with the use of contexts
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On Tue, Jan 17, 2017 at 11:41:54PM +0200, Yaron Sheffer wrote:
> On 17/01/17 18:12, Adam Langley wrote:
> >On Tue, Jan 17, 2017 at 3:31 AM, Yaron Sheffer <yaronf.ietf@gmail.com> wrote:
> >>Wide industry adoption of TLS 1.2 took around 10 years. So IMO saying "this
> >>is solved in TLS 1.3" is not a good enough answer, if in the meantime we
> >>will continue to see cross-protocol and cross-TLS-version attacks.
> >
> >If there are such attacks then they'll continue to be a problem for
> >TLS 1.2 because only the Ed* schemes have the possibility of a context
> >string. For ECDSA and RSA, the context still needs to be included in
> >the signed message somehow. So TLS 1.2 needs a larger change than
> >wiring up the context inputs of the Ed* schemes if you want to protect
> >it anyway.
> 
> Correct, but this would still eliminate cross-version attacks between TLS
> 1.3 and TLS <= 1.2, for Ed*. In other words, there is (incremental) value in
> adding context opportunistically.

TLS 1.3 server/client signatures are designed to resist confusion to
SSL 3.0 - TLS 1.2 signatures[1] anyway..


[1] There's the confusion possibility with RSA key exchange, but one
really can't do much about that (other than banning all present RSA
keys, but that would be infeasible)..


-Ilari


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From: John Mattsson <john.mattsson@ericsson.com>
To: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>, Yoav Nir <ynir.ietf@gmail.com>, IRTF CFRG <cfrg@irtf.org>
Thread-Topic: [Cfrg] Fwd:  Rev RFC 7539?
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From: "Cooley, Dorothy E" <decoole@nsa.gov>
To: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: AES GCM SIV analysis
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Date: Wed, 18 Jan 2017 16:49:11 +0000
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P { MARGIN-BOTTOM: 0px; MARGIN-TOP: 0px }  =20

NSA's Information Assurance organization did some analysis of AES-GCM-SIV, =
as described in "AES-GCM-SIV:  Nonce Misuse-Resistant Authenticated Encrypt=
ion", dated August 29, 2016 [1].  We shared this analysis privately with th=
e three authors of AES-GCM-SIV, who requested that we post it to the CFRG f=
orum. The attachment describes the results of the analysis. We believe the =
authors will be posting an update shortly.








=20

Any comments on this work can be directed to me.  But I will note that I di=
dn't do the actual analysis (I can't claim to be a 'real' cryptographer the=
se days).

=20


Deb Cooley

NSA Information Assurance Standards.

decoole@nsa.gov

=20

=20

[1]  https://tools.ietf.ort/html/draft-irtf-cfrg-gcmsiv-02

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<div style=3D"color: rgb(0, 0, 0); font-family: Tahoma; font-size: 10pt; di=
rection: ltr;">=0A=
<p>NSA's Information Assurance organization did some analysis of AES-GCM-SI=
V, as described in "AES-GCM-SIV:&nbsp; Nonce Misuse-Resistant Authenticated=
 Encryption", dated August 29, 2016 [1].&nbsp; We shared this analysis priv=
ately with the three authors of AES-GCM-SIV, who requested that we post it =
to the CFRG forum. The attachment describes the results of the analysis. We=
 believe the authors will be posting an update shortly.</p>=0A=
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<div>=0A=
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rection: ltr;">=0A=
<div>=0A=
<p>&nbsp;</p>=0A=
<p>Any comments on this work can be directed to me.&nbsp; But I will note t=
hat I didn't do the actual analysis (I can't claim to be a 'real' cryptogra=
pher these days).</p>=0A=
<p>&nbsp;</p>=0A=
<div style=3D"font-family: Tahoma; font-size: 13px;">=0A=
<p>Deb Cooley</p>=0A=
<p>NSA Information Assurance Standards.</p>=0A=
<p><a href=3D"mailto:decoole@nsa.gov" target=3D"_blank">decoole@nsa.gov</a>=
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From nobody Wed Jan 18 09:12:58 2017
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From: Leonard den Ottolander <leonard-lists@den.ottolander.nl>
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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Hello Joan,

On Tue, 2017-01-17 at 19:28 +0100, Joan Daemen wrote:
> the related-key attacks against AES were interesting from an academic 
> point of view as they broke the security claim we made for Rijndael.

https://books.google.nl/books?id=weETxBt-VAMC&pg=PA316&lpg=PA316&dq=aes
+256+key+schedule
+strength&source=bl&ots=GTfhsVdh7E&sig=y0ZE9_3OBCRbbpLHvq0PAAZqRmg&hl=en&sa=X&redir_esc=y#v=onepage&q=aes%20256%20key%20schedule%20strength&f=false

A better link to the above research is
https://eprint.iacr.org/2009/374 .

This research is rather condemning even though the authors do not claim
these attacks are entirely practical yet they do state:

"While neither AES-128 nor AES-256 can be directly broken by these attacks, the fact that their
hybrid  (which  combines  the  smaller  number  of  rounds  from  AES-128  along  with  the  larger  key
size from AES-256) can be broken with such a low complexity raises serious concern about the
remaining safety margin offered by the AES family of cryptosystems."

This criticism is valid for all AES versions. However:

"The key schedules of AES-128 and AES-192 are slightly different, since they have to apply more
mixing operations to the shorter key in order to produce the slightly smaller number of subkeys for the
various rounds. This small difference in the key schedules plays a major role in making AES-256 more
vulnerable to our attacks, in spite of its longer key and supposedly higher security."

AES-256 appears to be more vulnerable than AES-192 (or AES-128) to these attacks.

I pointed out the example (http://eprint.iacr.org/2009/317) because the
remarks it makes about the AES-256 key schedule seemed to indicate
structural weaknesses. Because Richard insisted I dug a bit deeper I
came up with the above which seems to confirm the "hunch" I was having
that the weak key schedule in AES-256 is a problem in itself.

> However, the attacks require very sophisticated manipulations of the 
> secret key by the attacker.

Please don't use arguments that might be valid for one report to
disqualify another. (This is a request made in general, Richard seems to
be doing this in his last post also.) The argument related key attacks
are mostly hypothetical applies to http://eprint.iacr.org/2009/317 but
not so much to https://eprint.iacr.org/2009/374 .

I quote:
"The attacks are particularly well suited to counter modes
of operation (AES-CTR), since the attacker can get all the chosen plaintexts he needs by starting from
just two chosen initial values and running the counter mode in a natural way."

This kind of manipulation seems not to be that far fetched...

> As for including AES-192 in TLS, I don't see any benefits.

AES-192 has been specified as a valid cipher just as much as AES-128 and
AES-256. The exclusion from TLS was entirely arbitrary. The motivation
for its exclusion is unclear. The wording in RFC-3268 is vague at best:

"The AES supports key lengths of 128, 192 and 256 bits. However, this
document only defines ciphersuites for 128- and 256-bit keys. This
is to avoid unnecessary proliferation of ciphersuites."

The fact that AES-256 appears to be not quite as strong as AES-192 might
render the "proliferation of AES-192" much less unnecessary.

Though AES-192 is not a 256 bit cipher it seems still to be
significantly stronger than AES-128 and does not share the weaknesses of
AES-256. This I believe is a strong argument to include it in TLS.

I do not see how the fact that we now have ChaCha20 is an argument not
to include AES-192. AES-192 has been specified just as much as its
siblings so it's exclusion from TLS is nothing but arbitrary. Why should
we only have one algorithm to choose from? (Again, like I wasn't arguing
against Camellia or AES-128 earlier so am I not arguing against ChaCha20
here. But until we are all chachaing, salsaing and elliptic curving I
would like access to decent crypto that is well established, well
scrutinized and readily available.)

Implementations are available in many cases (eg. openssl) and need only
to be "unlocked" by making entries available in the spec. From the
research I put forward AES-256 seems to have major flaws in the key
schedule that AES-192 does not suffer from.

On the one hand people argue against inclusion of AES-192 because it is
not PQ-resitant, on the other hand people argue I should use AES-128. It
all seems, again that word, rather arbitrary. And in general, the PQ
argument does not hold for the current situation: We need decent crypto
not just PQ but now as well.

To sum up:

- AES-192 was excluded from TLS for arbitrary reasons.
- AES-256 has known weaknesses in its key schedule that some researcher
consider severe.
- AES-192 offers better security than AES-128. There is serious doubt
AES-256 can offer the same level of security. This makes AES-192 a valid
alternative.
- Implementations of AES-192 are readily available.

Regards,
Leonard.

-- 
mount -t life -o ro /dev/dna /genetic/research



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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           : AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption
        Authors         : Shay Gueron
                          Adam Langley
                          Yehuda Lindell
	Filename        : draft-irtf-cfrg-gcmsiv-03.txt
	Pages           : 45
	Date            : 2017-01-18

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's also a htmlized version available at:
https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03

A diff from the previous version is available at:
https://www.ietf.org/rfcdiff?url2=draft-irtf-cfrg-gcmsiv-03


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/


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From: Adam Langley <agl@imperialviolet.org>
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Subject: Re: [Cfrg] AES GCM SIV analysis
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On Wed, Jan 18, 2017 at 8:49 AM, Cooley, Dorothy E <decoole@nsa.gov> wrote:
> NSA's Information Assurance organization did some analysis of AES-GCM-SIV,
> as described in "AES-GCM-SIV:  Nonce Misuse-Resistant Authenticated
> Encryption", dated August 29, 2016 [1].  We shared this analysis privately
> with the three authors of AES-GCM-SIV, who requested that we post it to the
> CFRG forum. The attachment describes the results of the analysis. We believe
> the authors will be posting an update shortly.
>
>
>
> Any comments on this work can be directed to me.  But I will note that I
> didn't do the actual analysis (I can't claim to be a 'real' cryptographer
> these days).
>
>
>
> Deb Cooley
>
> NSA Information Assurance Standards.
>
> decoole@nsa.gov

Dear CFRG,

We thank Deb Cooley's team very much for doing this analysis! As she
mentioned, they shared their results with us prior to posting here so
we already had an update ready and we've just posted
https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03.

This update contains three noteworthy changes:

1) We now XOR the nonce into the result of POLYVAL before encrypting
to form the tag. This was in the original paper, it was even specified
for /decryption/ in -02, but it was omitted in the specification for
encryption. This was a mistake. Without it, an attacker can build a
lookup table of encryptions of zero under a variety of per-nonce keys
and then attack them in parallel (as pointed out in the comments from
the IAD), under a single-user-multi-key model.

Draft -03 fixes this omission and reintroduces the nonce.

2) A different KDF. As I mentioned at the previous CFRG meeting (in
Seoul, 2016) , we had this design in mind but didn't feel that it
warranted a new version of the design. However, since we needed a
respin because of (1), we have included it.

Previously, per-nonce key material was generated by repeated
encryption, E(nonce), E(E(nonce)), and so on. This cascade leads to
impractical but needling issues including those noted by IAD. We now
generate keys by using counter mode and discarding half of each
ciphertext block. This solves those issues and also gives improved
indistinguishability bounds.

In order to make room for the counter, the nonce size has been reduced
to 96 bits.

3) A much more minor change is that we now suggest a limit of 2^8 as
the maximum number of plaintexts encrypted with a single nonce. We
previously noted that AES-GCM-SIV with a fixed nonce is similar to
AES-GCM with a random nonce, and that NIST recommends a limit of 2^32
messages in that context.

Note that we do NOT recommend nonce reuse by choice even inside
AES-GCM-SIV. This is for two reasons. First, encrypting the same
message twice will be detected. Second, the security bounds when using
different nonces are better. For example, when encrypting 2^{32}
messages with the same nonce, the probability of a bad event is
2^{-32}. However, as we have shown, when encryption with different
nonces, it is possible to go up to about 2^{50} messages without any
problem.

If nonces repeat mistakenly, for which providing protection is the
main aim of this mode of operation, then very strong bounds are still
obtained for a large number of ciphertexts (much more than 2^32) as
long as a single nonce is not repeated more than say 2^8 times. In
practice, such an event is highly unlikely.



Cheers

AGL


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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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--001a114743749463bd0546621694
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On Wed, Jan 18, 2017 at 12:12 PM, Leonard den Ottolander <
leonard-lists@den.ottolander.nl> wrote:

>
> - AES-192 was excluded from TLS for arbitrary reasons.
> - AES-256 has known weaknesses in its key schedule that some researcher
> consider severe.
> - AES-192 offers better security than AES-128. There is serious doubt
> AES-256 can offer the same level of security. This makes AES-192 a valid
> alternative.
> - Implementations of AES-192 are readily available.
>
>
=E2=80=8BAES 192 was excluded for the perfectly good reason that there is n=
o
compelling argument for inclusion.

I would like to see the number of suites reduced because the strength of a
cryptographic system depends on the strength of the weakest cipher. Thus
adding ciphers to a system invariably weakens it.

The only way to improve security is to eliminate ciphers. AES 128 is
necessary, so is AES 256. =E2=80=8BI have never seen a point to 192.

If the AES key schedule is bjorked, time for a new cipher comp. At one
point there was the possibility of a really fun itinerary, but the
governments that might have sponsored a non-US cipher standard are not
exactly crypto friendly right now.

--001a114743749463bd0546621694
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<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, Ja=
n 18, 2017 at 12:12 PM, Leonard den Ottolander <span dir=3D"ltr">&lt;<a hre=
f=3D"mailto:leonard-lists@den.ottolander.nl" target=3D"_blank">leonard-list=
s@den.ottolander.nl</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quo=
te" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"=
><br>
- AES-192 was excluded from TLS for arbitrary reasons.<br>
- AES-256 has known weaknesses in its key schedule that some researcher<br>
consider severe.<br>
- AES-192 offers better security than AES-128. There is serious doubt<br>
AES-256 can offer the same level of security. This makes AES-192 a valid<br=
>
alternative.<br>
- Implementations of AES-192 are readily available.<br><div class=3D"HOEnZb=
"><div class=3D"h5"><br></div></div></blockquote><div><br></div><div class=
=3D"gmail_default" style=3D"font-size:small">=E2=80=8BAES 192 was excluded =
for the perfectly good reason that there is no compelling argument for incl=
usion.</div><div class=3D"gmail_default" style=3D"font-size:small"><br></di=
v><div class=3D"gmail_default" style=3D"font-size:small">I would like to se=
e the number of suites reduced because the strength of a cryptographic syst=
em depends on the strength of the weakest cipher. Thus adding ciphers to a =
system invariably weakens it.=C2=A0</div><div class=3D"gmail_default" style=
=3D"font-size:small"><br></div><div class=3D"gmail_default" style=3D"font-s=
ize:small">The only way to improve security is to eliminate ciphers. AES 12=
8 is necessary, so is AES 256. =E2=80=8BI have never seen a point to 192.</=
div><div class=3D"gmail_default" style=3D"font-size:small"><br></div><div c=
lass=3D"gmail_default" style=3D"font-size:small">If the AES key schedule is=
 bjorked, time for a new cipher comp. At one point there was the possibilit=
y of a really fun itinerary, but the governments that might have sponsored =
a non-US cipher standard are not exactly crypto friendly right now.</div></=
div><br></div></div>

--001a114743749463bd0546621694--


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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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Hello Phillip,

On Wed, 2017-01-18 at 12:53 -0500, Phillip Hallam-Baker wrote:
> On Wed, Jan 18, 2017 at 12:12 PM, Leonard den Ottolander <
> leonard-lists@den.ottolander.nl> wrote:
> 
> >
> > - AES-192 was excluded from TLS for arbitrary reasons.
> > - AES-256 has known weaknesses in its key schedule that some researcher
> > consider severe.
> > - AES-192 offers better security than AES-128. There is serious doubt
> > AES-256 can offer the same level of security. This makes AES-192 a valid
> > alternative.
> > - Implementations of AES-192 are readily available.
> >
> >
> ​AES 192 was excluded for the perfectly good reason that there is no
> compelling argument for inclusion.
> 
> I would like to see the number of suites reduced because the strength of a
> cryptographic system depends on the strength of the weakest cipher. Thus
> adding ciphers to a system invariably weakens it.

It appears AES-256 is a weaker link than AES-192 so your general
argument about more is less seems invalid in this case. AES-256 shows
weaknesses that are not so prominent in AES-192.

> The only way to improve security is to eliminate ciphers. AES 128 is
> necessary, so is AES 256. ​I have never seen a point to 192.

I'm trying to make exactly that point :-) . AES-192 does not suffer from
the same weaknesses as AES-256 so the former is probably a more robust
cipher choice than the latter.

> If the AES key schedule is bjorked, time for a new cipher comp. At one
> point there was the possibility of a really fun itinerary, but the
> governments that might have sponsored a non-US cipher standard are not
> exactly crypto friendly right now.

The problems with the key schedule are with AES-256 specifically. Not
with AES in general.

I forgot to mention that AES-192 profits from the hardware support (CPU
AES instructions) that exist. This is not (yet) true for new ciphers.

Regards,
Leonard.

-- 
mount -t life -o ro /dev/dna /genetic/research



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From: Phillip Hallam-Baker <phill@hallambaker.com>
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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On Wed, Jan 18, 2017 at 1:11 PM, Leonard den Ottolander <
leonard-lists@den.ottolander.nl> wrote:

> Hello Phillip,
>
> On Wed, 2017-01-18 at 12:53 -0500, Phillip Hallam-Baker wrote:
> > On Wed, Jan 18, 2017 at 12:12 PM, Leonard den Ottolander <
> > leonard-lists@den.ottolander.nl> wrote:
> >
> > >
> > > - AES-192 was excluded from TLS for arbitrary reasons.
> > > - AES-256 has known weaknesses in its key schedule that some research=
er
> > > consider severe.
> > > - AES-192 offers better security than AES-128. There is serious doubt
> > > AES-256 can offer the same level of security. This makes AES-192 a
> valid
> > > alternative.
> > > - Implementations of AES-192 are readily available.
> > >
> > >
> > =E2=80=8BAES 192 was excluded for the perfectly good reason that there =
is no
> > compelling argument for inclusion.
> >
> > I would like to see the number of suites reduced because the strength o=
f
> a
> > cryptographic system depends on the strength of the weakest cipher. Thu=
s
> > adding ciphers to a system invariably weakens it.
>
> It appears AES-256 is a weaker link than AES-192 so your general
> argument about more is less seems invalid in this case. AES-256 shows
> weaknesses that are not so prominent in AES-192.
> =E2=80=8B\
>
=E2=80=8B
Oh really, the work fact of AES 256 is lower than that of AES 192? Please
show me the paper.

If AES 256 falls then AES goes completely. There is no middle ground.


=E2=80=8B
> > The only way to improve security is to eliminate ciphers. AES 128 is
> > necessary, so is AES 256. =E2=80=8BI have never seen a point to 192.
>
> I'm trying to make exactly that point :-) . AES-192 does not suffer from
> the same weaknesses as AES-256 so the former is probably a more robust
> cipher choice than the latter.


=E2=80=8BI see no evidence that the work factor of AES 256 is less than 2^1=
92. =E2=80=8B

--001a114b0d089501f605466268bc
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<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, Ja=
n 18, 2017 at 1:11 PM, Leonard den Ottolander <span dir=3D"ltr">&lt;<a href=
=3D"mailto:leonard-lists@den.ottolander.nl" target=3D"_blank">leonard-lists=
@den.ottolander.nl</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_quot=
e" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">=
Hello Phillip,<br>
<span class=3D""><br>
On Wed, 2017-01-18 at 12:53 -0500, Phillip Hallam-Baker wrote:<br>
&gt; On Wed, Jan 18, 2017 at 12:12 PM, Leonard den Ottolander &lt;<br>
&gt; <a href=3D"mailto:leonard-lists@den.ottolander.nl">leonard-lists@den.o=
ttolander.<wbr>nl</a>&gt; wrote:<br>
&gt;<br>
&gt; &gt;<br>
&gt; &gt; - AES-192 was excluded from TLS for arbitrary reasons.<br>
&gt; &gt; - AES-256 has known weaknesses in its key schedule that some rese=
archer<br>
&gt; &gt; consider severe.<br>
&gt; &gt; - AES-192 offers better security than AES-128. There is serious d=
oubt<br>
&gt; &gt; AES-256 can offer the same level of security. This makes AES-192 =
a valid<br>
&gt; &gt; alternative.<br>
&gt; &gt; - Implementations of AES-192 are readily available.<br>
&gt; &gt;<br>
&gt; &gt;<br>
&gt; =E2=80=8BAES 192 was excluded for the perfectly good reason that there=
 is no<br>
&gt; compelling argument for inclusion.<br>
&gt;<br>
&gt; I would like to see the number of suites reduced because the strength =
of a<br>
&gt; cryptographic system depends on the strength of the weakest cipher. Th=
us<br>
&gt; adding ciphers to a system invariably weakens it.<br>
<br>
</span>It appears AES-256 is a weaker link than AES-192 so your general<br>
argument about more is less seems invalid in this case. AES-256 shows<br>
weaknesses that are not so prominent in AES-192.<div class=3D"gmail_default=
" style=3D"font-size:small;display:inline">=E2=80=8B\</div></blockquote><di=
v class=3D"gmail_default" style=3D"font-size:small">=E2=80=8B</div><div cla=
ss=3D"gmail_default" style=3D"font-size:small">Oh really, the work fact of =
AES 256 is lower than that of AES 192? Please show me the paper.</div><div =
class=3D"gmail_default" style=3D"font-size:small"><br></div><div class=3D"g=
mail_default" style=3D"font-size:small">If AES 256 falls then AES goes comp=
letely. There is no middle ground.=C2=A0</div><div class=3D"gmail_default" =
style=3D"font-size:small"><br></div><div class=3D"gmail_default" style=3D"f=
ont-size:small"><br></div><blockquote class=3D"gmail_quote" style=3D"margin=
:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class=3D"gmai=
l_default" style=3D"font-size:small;display:inline">=E2=80=8B</div><span cl=
ass=3D"">&gt; The only way to improve security is to eliminate ciphers. AES=
 128 is<br>
&gt; necessary, so is AES 256. =E2=80=8BI have never seen a point to 192.<b=
r>
<br>
</span>I&#39;m trying to make exactly that point :-) . AES-192 does not suf=
fer from<br>
the same weaknesses as AES-256 so the former is probably a more robust<br>
cipher choice than the latter.</blockquote><div><br></div><div><div class=
=3D"gmail_default" style=3D"font-size:small">=E2=80=8BI see no evidence tha=
t the work factor of AES 256 is less than 2^192. =E2=80=8B</div></div><div =
class=3D"gmail_default" style=3D"font-size:small"><br></div><div class=3D"g=
mail_default" style=3D"font-size:small"><br></div><div class=3D"gmail_defau=
lt" style=3D"font-size:small"><br></div></div></div></div>

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From: Adam Langley <agl@imperialviolet.org>
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Subject: Re: [Cfrg] AES GCM SIV analysis
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Also, in the interests of keeping things on the working-group mailing
list, I am including the two follow-ups that Shay and Yehuda sent,
previously, in response to this.

(The discussion took place in two back-and-forth iterations. Hence
they sent two replies, which are attached here.)


-----Message one-----
We greatly thank you for your interest in the AES-GCM-SIV
authenticated encryption scheme, and for your work on analyzing it.

We begin with the first attack. It is well known that in the model of
multi-key security, if there are M different users with M different
keys, and the key-space is of size N, then it is possible to find one
of the keys in time M/N. We cast the attacks you describe in this
light. Specifically, since our CFRG essentially changes the keys in
every encryption, we obtain a multi-key setting even for a single
user. Considering, for example, attack number 1: this attack works
since it is possible to obtain encryptions of a single known block
under many keys. Thus, the original multi-key attack of [1] is
applicable.

Having said the above, we find that the tradeoff between the CFRG and
original GCM-SIV paper to be favorable toward the CFRG. This is
because as with all counter modes, the original GCM-SIV and GCM with a
random nonce (counter) has the property that after 2^32 different
encryptions, the probability of a collision on the nonce (counter) is
about 2^-32. Now, if less than 2^32 encryptions are carried out, then
neither the multi-key attacks nor the collision on the counter is a
concern. However, if more than 2^32 encryptions are computed, then the
amount of work required for the multi-key attacks is still extremely
large, whereas the probability of a collision on the nonce becomes a
very real concern.

We do not dismiss the threat of multi-key attacks, and it has been
recently noted that this may be a real problem in TLS sessions. This
has prompted recent work, one example being [2]. Indeed, [2] explain
that in TLS it is preferable to use a random nonce for GCM even though
a fresh key is used in every session (and thus one could always start
with a fixed nonce of 0). This is exactly to prevent/mitigate
multi-key attacks.

We stand behind our proposal to change keys in every message, and were
surprised that changing the nonce does not solve the problem (Ref. [1]
in your document). We then noticed that in the original GCM-SIV paper
appearing in ACM CCS, we XOR the nonce with the result of POLYHASH on
the AAD and message, and then encrypt it (using AES). While our
intention was to mount some nonce-based key derivation on top of
GCM-SIV, we forgot (in one of the versions of the proposal) this XOR
in the CFRG specification. By returning this XOR, we mitigate the risk
of multi-key attacks since different nonces would now not enable an
attacker to obtain many encryptions of the same (known) block under
different keys.

Regarding the other attacks:

Attack 3 requires 2^128 chosen plaintexts. We do not consider this to
be realistic. Furthermore, when the block size is 128 bits then
everything breaks well before that (with repeating inputs to AES).
Attack 2 is just a type of time-space tradeoff and these types of
bounds are always possible on block ciphers. Note also that in order
to reduce the work time by just two bits, the number of queries
required is already 2^96. As stated regarding attack 3, with a 128-bit
block size everything breaks well before this anyway. Once again, we
thank you for your interest in GCM-SIV, and we will make the change to
mitigate the first attack as described. Although we think that users
of GCM-SIV should not be concerned with the other attacks, as
described above, we appreciate the feedback and we will document them
for full transparency.

[1] E. Biham. How to Forge DES-Encrypted Messages in 228 Steps.
Information Processing Letters, 84(3):117-124, 2002.

[2] M. Bellare and B. Tackmann. The Multi-user Security of
Authenticated Encryption: AES-GCM in TLS 1.3. In CRYPTO 2016, Springer
(LNCS 9814), pages 247-276, 2016.

Shay Gueron and Yehuda Lindell

-----Message two-----

We thank you very much for your response, and greatly appreciate your
feedback and analysis.

We would like to point out what we recommend (and plan to post) a
maximal number of usages (q_max) of a single master key, with
AES-GCM-SIV. This would better put things in context. As we promised
to the CFRG community since we posted the specifications, we are
working on a paper that analyzes the scheme and derives this
recommendation. Hopefully, it will be ready in a few weeks. In order
to explain our bound, let us first denote the 2-key specification in
the CCS paper by GCM-SIV (K1, K2, N, AAD, M). The CFRG proposal can
then be viewed as a two step protocol:

1. Key derivation: Compute (Record_Encryption_Key, Record_Hash_Key) =3D
KDF (Master_Key, N)
2. Encryption: Compute (Tag, C) =3D GCM-SIV (Record_Encryption_Key,
Record_Hash_Key, N, AAD, M)

We now consider the recommended restriction regarding the number q_max
of times that the Master_Key can be used (which actually translates to
how many different nonces can be used, but since a different nonce
should be used for every message this is the same as the number of
different messages, but messages can be long). Our calculation is that
q_max ~ 2^47 is an appropriate recommendation in order to preserve the
2^-32 security margins recommended by NIST. This 2^47 limit is based
on a failure of indistinguishability of the generated nonce-based
keys, unlike the deeper failure that AES-GCM would suffer by a nonce
misuse. This number shows that the additional key derivation increases
the number of allowed usages of a (master) key for AES-GCM-SIV,
compared to the CCS version that was limited to ~2^32 usages(and the
security margins). We are working on a way to increase q_max even
further, and this will be announced in the upcoming paper.

>From a practical viewpoint, we comment that if a user sends, say, 1
million messages per second, then a key replacement after 2^47 usages
would be necessary after ~4 years.

Since AES-GCM-SIV is designed for cases where a user needs to encrypt
multiple messages, but nonce uniqueness may be a concern, we suggest
to compare q_max to the number of times that a key can be used with
AES-GCM with a randomly selected 96-bit IV (i.e., 2^32).

With this limit on q_max, we conclude that your mentioned attacks do
not apply. We understand that you agree with this analysis.

The last question that remains is regarding the current KDF that uses
a hierarchy of keys, and this cascade generates some relation between
the derived keys. We are not extremely concerned with 2^128 work to
extract additional keys /after/ one key is compromised (with no
cryptographic method know so far). However, we agree that for 256-bit
keys, this should not be possible. This brings us to the question
about the KDF. In fact, we have been contemplating amongst ourselves
about a better KDF that not only has better indistinguishability
bounds, but is also faster than the current one. Also, some CFRG
member have very recently asked about this. Therefore, we do intend to
replace the KDF, as follows. AES-GCM-SIV will receive a 96-bit nonce.
The KDF will compute AES (Master_Key, IV || IntToString32 (j)) for
j=3D0, =E2=80=A6, 3 (128-bit key) or j=3D0, =E2=80=A6, 5 (256-bit key). Fro=
m each of these
4 (or 6) generated blocks, 64 bits will be discarded, and then pairs
will be combined into 2 (3) 128-bit values. These will be used as the
Record_Hash_Key and the Record_Encryption_Key. The
indistinguishability advantaged of this KDF (assuming AES is a close
approximation to a random permutation), is bounded by 6q/2^96 where q
is the number of times that the KDF was called with a single (master)
key (see [1]). Now, for q different random nonces, the probability of
an r-multi-collision (i.e., at least one value appears at least r
times), and hence also on the pernonce keys, can be bounded by
1/u^{r-1} * Binomial (q, r) (where u=3D2^96 here). Note that if for
different nonces, there is a collision on the derived keys, this will
not be a case of nonce misuse.

We can require a limited number of allowed nonce repetitions. Based on
the above calculation, the probability that selecting the nonce
(uniformly) at random will show r-multi-collisions (for a large r), is
negligible, when staying with the bounds of q_max. Assume now that for
the q_max (randomly) generated nonces, each value appears at most 4
times. Using some bound on the (intentional) number of messages
encrypted by one selected nonce (and the lengths of the messages and
AAD=E2=80=99s), we can apply the security bounds that we have on GCM-SIV.

We plan to post the updated specification next week.

Thank you again, Shay and Yehuda

[1] S. Gilboa, S. Gueron, =E2=80=9CThe Advantage of Truncated Permutations=
=E2=80=9D,
https://arxiv.org/abs/1610.02518 (submitted on 8 Oct 2016).
[2] K. Suzuki, D. Tonien, K. Kurosawa, K. Toyota, =E2=80=9CBirthday Paradox
for Multi-collisions=E2=80=9D, Proceedings of the 9th International Confere=
nce
on Information Security and Cryptology, 29-40 (2006).
http://dl.acm.org/citation.cfm?id=3D2172962


From nobody Wed Jan 18 10:30:06 2017
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From: Russ Housley <housley@vigilsec.com>
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Subject: Re: [Cfrg] Fwd:  Rev RFC 7539?
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Document: draft-nir-cfrg-rfc7539bis-00
Reviewer: Russ Housley
Review Date: 2017-01-19

Summary: Almost Ready

Major Concerns:

The Abstract says that there are additions to the Security
Considerations; however, I do not see a difference between the
Security Considerations in this document and RFC 7539.


Minor Concerns:

In Section 2.3.1, please add a sentence to define the "|" operator
in a manner similar to the definition for "+" in Section 2.1.


Nits:

Abstract: s/any new crypto/any new cryptographic mechanisms/

Section 2.1 uses "rotation" and "roll" to describe the same operation.
Please pick one term.

In Sections 2.1 and 2.3, I do not think that the line numbers aid the
reader. I think that simple indention would be better.

In Sections 2.1 and 2.1.1, I do not think that the bullets aid the
reader.  I think that simple indention would be better.

Section 2.5.1 includes: r = (le_bytes_to_num(key[0..15]).
I think you want to drop the leading parenthesis.

In Author's address, please capitalize "st."


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From: Brian Smith <brian@briansmith.org>
Date: Wed, 18 Jan 2017 10:51:44 -1000
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Subject: Re: [Cfrg] AES GCM SIV analysis
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On Wed, Jan 18, 2017 at 7:34 AM, Adam Langley <agl@imperialviolet.org> wrote:
> 3) A much more minor change is that we now suggest a limit of 2^8 as
> the maximum number of plaintexts encrypted with a single nonce. We
> previously noted that AES-GCM-SIV with a fixed nonce is similar to
> AES-GCM with a random nonce, and that NIST recommends a limit of 2^32
> messages in that context.

The actual text in the draft is "Thus with AES-GCM-SIV we recommend
that, for a specific key, a nonce not be repeated more than 2^8
times."

Is this a meaningful recommendation? How would one go about following
this recommendation in a practical implementation? In particular,
AES-GCM-SIV is mostly interesting in implementations that cannot
reliably and/or consistently save state, and it seems like any attempt
to write code to enforce this relies on saving state in the manner. Is
the idea here that one would, every 2^8 or so messages, force some
kind of "sync state or force rekey" operation that would be too
expensive to do on every message?

Do we really need a 32-bit counter for this mode? Why not have a
16-bit counter? This would allow single messages up to 1MB. Then one
could more safely use a 96-bit random + 16-bit fixed ID nonce or an
80-bit random + 32-bit fixed ID nonce. In general, super large
messages don't work well with AEADs because it's hard to verify the
integrity of a giant message before using the plaintext, so 32-bit
counters seem excessive. I expect protocols would limit the maximum
message length such that a ~16-bit counter would be sufficient.

Cheers,
Brian
-- 
https://briansmith.org/


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From: John Mattsson <john.mattsson@ericsson.com>
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Thread-Topic: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt
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Date: Wed, 18 Jan 2017 13:33:35 -0800
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Cc: Adam Langley <agl@imperialviolet.org>, "Cooley, Dorothy E" <decoole@nsa.gov>, "cfrg@irtf.org" <cfrg@irtf.org>, Yehuda Lindell <Yehuda.Lindell@biu.ac.il>
Subject: Re: [Cfrg] AES GCM SIV analysis
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>>> Is this a meaningful recommendation?
>>> How would one go about following this recommendation in a practical
implementation?

This is a very valid question, that is answered in the specification. But
perhaps it is worth clarifying on the mailing list. It is rather easy to
adhere to the recommendation. Simply choose the 96-bit nonce uniformly at
random. After, say, 2^{50} encryptions, what the probability that a nonce
repeated, even 5 times, can be bounded from above (see the "multibirthday"
reference in the spec) by 2^(-134).
(To this, you need to add occurrences where the keys also collide. All this
analysis will be posted soon, together with the matching bounds).


>>> Do we really need a 32-bit counter for this mode?
>>> Why not have a 16-bit counter?
Also a very valid question.
The answer is that you don't really need a 32-bit counter.
It is possible for a usage to specify a shorter restriction on the allowed
message length. This will improve the security bounds, which are also a
function of k, where 2^k is the largest number of blocks in a message. You
can choose any k <= 32.

Thanks, Shay



2017-01-18 12:51 GMT-08:00 Brian Smith <brian@briansmith.org>:

> On Wed, Jan 18, 2017 at 7:34 AM, Adam Langley <agl@imperialviolet.org>
> wrote:
> > 3) A much more minor change is that we now suggest a limit of 2^8 as
> > the maximum number of plaintexts encrypted with a single nonce. We
> > previously noted that AES-GCM-SIV with a fixed nonce is similar to
> > AES-GCM with a random nonce, and that NIST recommends a limit of 2^32
> > messages in that context.
>
> The actual text in the draft is "Thus with AES-GCM-SIV we recommend
> that, for a specific key, a nonce not be repeated more than 2^8
> times."
>
> Is this a meaningful recommendation? How would one go about following
> this recommendation in a practical implementation? In particular,
> AES-GCM-SIV is mostly interesting in implementations that cannot
> reliably and/or consistently save state, and it seems like any attempt
> to write code to enforce this relies on saving state in the manner. Is
> the idea here that one would, every 2^8 or so messages, force some
> kind of "sync state or force rekey" operation that would be too
> expensive to do on every message?
>
> Do we really need a 32-bit counter for this mode? Why not have a
> 16-bit counter? This would allow single messages up to 1MB. Then one
> could more safely use a 96-bit random + 16-bit fixed ID nonce or an
> 80-bit random + 32-bit fixed ID nonce. In general, super large
> messages don't work well with AEADs because it's hard to verify the
> integrity of a giant message before using the plaintext, so 32-bit
> counters seem excessive. I expect protocols would limit the maximum
> message length such that a ~16-bit counter would be sufficient.
>
> Cheers,
> Brian
> --
> https://briansmith.org/
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>

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<div dir=3D"rtl"><div dir=3D"ltr"><br></div><div dir=3D"ltr"><br></div><div=
 dir=3D"ltr">&gt;&gt;&gt;=C2=A0Is this a meaningful recommendation?=C2=A0</=
div><div dir=3D"ltr">&gt;&gt;&gt; How would one go about following this rec=
ommendation in a practical implementation?=C2=A0</div><div dir=3D"ltr"><br>=
</div><div dir=3D"ltr">This is a very valid question, that is answered in t=
he specification. But perhaps it is worth clarifying on the mailing list. I=
t is rather easy to adhere to the recommendation. Simply choose the 96-bit =
nonce uniformly at random. After, say, 2^{50} encryptions, what the probabi=
lity that a nonce repeated, even 5 times, can be bounded from above (see th=
e &quot;multibirthday&quot; reference in the spec) by 2^(-134).=C2=A0</div>=
<div dir=3D"ltr">(To this, you need to add occurrences where the keys also =
collide. All this analysis will be posted soon, together with the matching =
bounds).=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr"><br></div><=
div dir=3D"ltr">&gt;&gt;&gt;=C2=A0<span style=3D"font-size:11pt;font-family=
:calibri,sans-serif">Do we really need a 32-bit counter for this mode?=C2=
=A0</span></div><div dir=3D"ltr"><span style=3D"font-size:11pt;font-family:=
calibri,sans-serif">&gt;&gt;&gt; Why not have a 16-bit counter?=C2=A0</span=
><br>Also a very valid question.=C2=A0</div><div dir=3D"ltr">The answer is =
that you don&#39;t really need a 32-bit counter.=C2=A0</div><div dir=3D"ltr=
">It is possible for a usage to specify a shorter restriction on the allowe=
d message length. This will improve the security bounds, which are also a f=
unction of k, where 2^k is the largest number of blocks in a message. You c=
an choose any k &lt;=3D 32.=C2=A0</div><div dir=3D"ltr"><br></div><div dir=
=3D"ltr">Thanks, Shay=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr=
"><br></div><div class=3D"gmail_extra"><br><div class=3D"gmail_quote"><div =
dir=3D"ltr">2017-01-18 12:51 GMT-08:00 Brian Smith <span dir=3D"ltr">&lt;<a=
 href=3D"mailto:brian@briansmith.org" target=3D"_blank">brian@briansmith.or=
g</a>&gt;</span>:</div><blockquote class=3D"gmail_quote" style=3D"margin:0p=
x 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><s=
pan class=3D"gmail-m_7894771622141357201m_500321693258236033gmail-">On Wed,=
 Jan 18, 2017 at 7:34 AM, Adam Langley &lt;<a href=3D"mailto:agl@imperialvi=
olet.org" target=3D"_blank">agl@imperialviolet.org</a>&gt; wrote:<br>
&gt; 3) A much more minor change is that we now suggest a limit of 2^8 as<b=
r>
&gt; the maximum number of plaintexts encrypted with a single nonce. We<br>
&gt; previously noted that AES-GCM-SIV with a fixed nonce is similar to<br>
&gt; AES-GCM with a random nonce, and that NIST recommends a limit of 2^32<=
br>
&gt; messages in that context.<br>
<br>
</span>The actual text in the draft is &quot;Thus with AES-GCM-SIV we recom=
mend<br>
that, for a specific key, a nonce not be repeated more than 2^8<br>
times.&quot;<br>
<br>
Is this a meaningful recommendation? How would one go about following<br>
this recommendation in a practical implementation? In particular,<br>
AES-GCM-SIV is mostly interesting in implementations that cannot<br>
reliably and/or consistently save state, and it seems like any attempt<br>
to write code to enforce this relies on saving state in the manner. Is<br>
the idea here that one would, every 2^8 or so messages, force some<br>
kind of &quot;sync state or force rekey&quot; operation that would be too<b=
r>
expensive to do on every message?<br>
<br>
Do we really need a 32-bit counter for this mode? Why not have a<br>
16-bit counter? This would allow single messages up to 1MB. Then one<br>
could more safely use a 96-bit random + 16-bit fixed ID nonce or an<br>
80-bit random + 32-bit fixed ID nonce. In general, super large<br>
messages don&#39;t work well with AEADs because it&#39;s hard to verify the=
<br>
integrity of a giant message before using the plaintext, so 32-bit<br>
counters seem excessive. I expect protocols would limit the maximum<br>
message length such that a ~16-bit counter would be sufficient.<br>
<br>
Cheers,<br>
Brian<br>
<span class=3D"gmail-m_7894771622141357201m_500321693258236033gmail-HOEnZb"=
><font color=3D"#888888">--<br>
<a href=3D"https://briansmith.org/" rel=3D"noreferrer" target=3D"_blank">ht=
tps://briansmith.org/</a><br>
</font></span><div class=3D"gmail-m_7894771622141357201m_500321693258236033=
gmail-HOEnZb"><div class=3D"gmail-m_7894771622141357201m_500321693258236033=
gmail-h5"><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>
</div></div></blockquote></div><br></div></div>

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Subject: Re: [Cfrg] AES GCM SIV analysis
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On Wed, Jan 18, 2017 at 12:51 PM, Brian Smith <brian@briansmith.org> wrote:
> On Wed, Jan 18, 2017 at 7:34 AM, Adam Langley <agl@imperialviolet.org> wrote:
>> 3) A much more minor change is that we now suggest a limit of 2^8 as
>> the maximum number of plaintexts encrypted with a single nonce. We
>> previously noted that AES-GCM-SIV with a fixed nonce is similar to
>> AES-GCM with a random nonce, and that NIST recommends a limit of 2^32
>> messages in that context.
>
> The actual text in the draft is "Thus with AES-GCM-SIV we recommend
> that, for a specific key, a nonce not be repeated more than 2^8
> times."
>
> Is this a meaningful recommendation? How would one go about following
> this recommendation in a practical implementation? In particular,
> AES-GCM-SIV is mostly interesting in implementations that cannot
> reliably and/or consistently save state, and it seems like any attempt
> to write code to enforce this relies on saving state in the manner. Is
> the idea here that one would, every 2^8 or so messages, force some
> kind of "sync state or force rekey" operation that would be too
> expensive to do on every message?

No, nothing like that. Perhaps this part of the document isn't clear.

Basically, before we noted that AES-GCM-SIV with a fixed nonce like
like AES-GCM with a random nonce (except that it also leaks when
plaintexts are equal). We noted that NIST recommends no more than 2^32
messages be encrypted with a given key in that context.

So someone could, not completely unreasonably, say that they're not
worried about leaking when plaintexts are equal and use AES-GCM-SIV
with a fixed nonce for 2^32 messages.

We're now clearly saying that's not a great idea. Instead, generate
nonces at random. With a random, 96-bit nonce you don't have to worry
about the probability of having repeated a single value > 2^8 times
until you have a staggering number of plaintexts: greater than 2^100
of them. Since that vastly exceeds our current recommendation for
number of plaintexts per key (2^50), it's basically not a concern.

If that makes sense, what could we have written to be clearer?

> Do we really need a 32-bit counter for this mode? Why not have a
> 16-bit counter? This would allow single messages up to 1MB. Then one
> could more safely use a 96-bit random + 16-bit fixed ID nonce or an
> 80-bit random + 32-bit fixed ID nonce. In general, super large
> messages don't work well with AEADs because it's hard to verify the
> integrity of a giant message before using the plaintext, so 32-bit
> counters seem excessive. I expect protocols would limit the maximum
> message length such that a ~16-bit counter would be sufficient.

I agree that large AEAD messages have several problems. But I don't
think that we have any need for a larger nonce (see above). (And the
nonce is used with a counter only in the KDF phase, so it's unrelated
to the maximum plaintext size.)


Cheers

AGL

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


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From: Brian Smith <brian@briansmith.org>
Date: Wed, 18 Jan 2017 13:46:14 -1000
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> There's also a htmlized version available at:
> https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03

The intro defines nonce-misuse-resistant AEADS as ones that are
safe(r) to use when "two distinct messages are encrypted with the same
nonce". However, in reality we usually don't care only about the case
where *two* (==2) distinct messages are encrypted with the same (key,
nonce), but rather we care about the case where *multiple* (>=2)
messages are encrypted with the same (key, nonce). In particular the
new draft makes a distinction between encrypting <2^8 vs >=2^8
messages with the same (key, nonce), not a distinction between 1 vs 2
messages with the same (key, nonce).

The practical motivation for POLYVAL is unclear. In an email message
in an earlier mailing list thread, Shay said "We chose to use POLYVAL
so that 128-bit blocks can be viewed as field elements and as AES
ciphertexts in a consistent way (with respect to the order of the bits
inside each byte))," and I think that this should be included in the
spec, along with a more plain explanation that this is done (IIUC)
simply to avoid byte byteswapping on little-endian systems that GHASH
requires.

It isn't clear how the nonce length of 96 bits was chosen. I can see
some advantages, e.g. it is more of a drop-in replacement for AES-GCM,
which is almost exclusively used with 96-bit nonces in IETF protocols,
but is there any other reason? Since nonce-misuse-resistance is not a
binary property, but rather a gradiant, it seems better to optimize
for minimizing the chance of accidental nonce misuse, or minimizing
the number of times a nonce is likely to be misused, which AFAICT
means choosing a nonce length that is as long as is practical. The
rationale in the other thread says "In order to make room for the
counter, the nonce size has been reduced to 96 bits," but the counter
for the key derivation only needs to be 3 bits long, IIUC, so it seems
like the nonce length was reduced more than necessary?

The email also said "We now generate keys by using counter mode and
discarding half of each ciphertext block." The motivation for
discarding half of each ciphertext block should be added to the draft
(maybe in security considerations), along with a reference of how
discarding half of each ciphertext block achieves that goal.

The draft makes an argument about safety when "nonces are selected
uniformly at random." However, isn't a key motivation for AES-GCM-SIV
our lack of confidence in our ability to select nonces uniformly at
random? I personally would like to see discussion of the case where we
can't assume nonces are selected uniformly at random. (While I can't
come up with one off the top of my head right now, it seems likely
that there would be simpler and less invasive ways of defining a
nonce-misuse-resistant AEAD based on AES-GCM if we can also assume we
have a good random number generator and we're willing to accept the
birthday bound analysis in the draft. Thus, based on intuition it
seems like AES-GCM-SIV must be useful in contexts where nonces aren't
chosen uniformly at random in order to justify its complexity.)

Cheers,
Brian
--
https://briansmith.org/


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Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt
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On Wed, Jan 18, 2017 at 1:05 PM, John Mattsson
<john.mattsson@ericsson.com> wrote:
> - In addition to listing the performance penalty compared to GCM. The
>   draft should also mention that compared to GCM, some nice properties
>   disappear:
>   - Neither Encryption nor Decryption is online as encryption/decryption
>     cannot start before the whole plaintext/ciphertext is known.

I agree that this is true for encryption, but I don't believe that
AES-GCM should be *de*crypted in a streaming fashion, but rather that
records should be sized so that this isn't a problem. (At which point
the benefit for streaming encryption becomes small or moot.)

I've a long spiel about the dangers of processing unauthenticated
ciphertext which I'll spare you :) But, even for small machines, the
memory needed to safely buffer the decrypted plaintext to avoid
releasing it before it's authenticated is equal to the memory to
buffer the ciphertext followed by decrypting in-place.

So I actually quite like that the tag is at the end of the message
with AES-GCM-SIV because it makes it harder to do what I think is the
"wrong" thing.

>   - GCM-SIV removes the possibility to preprocess static headers (AAD).

Indeed.

(I wasn't sure where to put these points in the spec so, for the
moment, I've added an appendix for "Additional comparisons with
AES-GCM". I'm collecting changes in GitHub before making a new
version. For this message, see
https://github.com/agl/gcmsiv/commit/c6c7fd388dd122251264222b7491c6212e8183=
19.)

> - =E2=80=9CThe result of the encryption is the resulting ciphertext (trun=
cated
>    to the length of the plaintext) followed by the tag."
>
>   I suggest that the tag is placed first instead of last in the
>   ciphertext. This makes decryption online, which makes a large
>   difference. Suggestion:
>
>   =E2=80=9CThe result of the encryption is the tag followed by the cipher=
text
>    (truncated to the length of the plaintext)"

(See above.)

>
>
> - "within 5% of the speed of AES-GCM."
>   Should state when this is the case, e.g. long plaintext/aad.

Done.

>
> - I think the draft should give performance data also for short
>   plaintexts/aad or even better list the performance in number of
>   operations:
>
>   GCM:
>     Block Cipher Operations =3D p + 1
>     GF(2^128) Multiplications =3D p + a + 1
>
>   GCM-SIV-128
>     Block Cipher Operations =3D p + 5
>     GF(2^128) Multiplications =3D p + a + 1
>
>   GCM-SIV-256
>     Block Cipher Operations =3D p + 7
>     GF(2^128) Multiplications =3D p + a + 1
>
>   (if I got it right...)

I think that's correct and I've added that to the new appendix.

>   Where p is the block length of the plaintext and a is the block length
>   of the additional authenticated data,
>
>   I doubt that encryption of short messages are anywhere near 5% of GCM.
>
> - The "++" and "[:8]" operation should probably be defined.

Done.

>
> - What it the security/performance tradeoff with truncation in the key
>   derivation? What would the security properties be if "[:8]" was
>   removed?

I'll have to let Shay answer this, but the rough idea is that, since
AES is a permutation, not two ciphertexts can be equal given that
we're encrypting different plaintexts using the KDF phase. However,
ideally we would want a PRF where outputs can be the same. By taking
only the first eight bytes of each ciphertext block, we better
approximate a PRF.

> - The definition of U32LE seems unnecessary and only adds complexity.
>   I suggest:
>     OLD "U32LE(3) ++ nonce"
>     NEW "03 ++ 000000 ++ nonce

Good point.

>
> - The term K1 is only used in Test Vectors. I guess it is an old term
>   that should be removed.

Done.

> Some editorials:

Thank you for all these. They should be taken care of.

> - OLD "The record-authentication key is 128-bit and the
>        record-authentication key"
>   NEW "The record-authentication key is 128-bit and the
>        record-encryption key"
>
> - "} else if bytelen(key-generating-key) =3D=3D 32 {
>      record-encryption-key =3D AES128(key =3D key-generating-key,"
>
>   Should be AES256

Indeed, and record-authentication-key is wrong too!

> - Spacing around "+" and "*" are not consistent.
>
> - "the the"
>
> - yeilds
>
> - remainding
>
> - RFC7322 says "A comma is used before the last item of a series"

I think I've leave this one to the RFC Editor!



Cheers

AGL


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On Wed, Jan 18, 2017 at 3:46 PM, Brian Smith <brian@briansmith.org> wrote:
> The intro defines nonce-misuse-resistant AEADS as ones that are
> safe(r) to use when "two distinct messages are encrypted with the same
> nonce". However, in reality we usually don't care only about the case
> where *two* (==2) distinct messages are encrypted with the same (key,
> nonce), but rather we care about the case where *multiple* (>=2)
> messages are encrypted with the same (key, nonce). In particular the
> new draft makes a distinction between encrypting <2^8 vs >=2^8
> messages with the same (key, nonce), not a distinction between 1 vs 2
> messages with the same (key, nonce).

You're correct that the problem is multiple messages (potentially)
encrypted with the same (key, nonce) pair. But the number is very
small since the number of random nonces that need to be sampled from a
96-bit space in order to expect at least one to appear > x times,
rises *very* fast with x. As noted in the draft, for x=256, it's about
2^102.

The main thrust of that section in the spec is to say "pick nonces at
random". The 2^8 number was picked out of the aim to emphasize this
over fixing a specific nonce and not encrypting too many messages.

> The practical motivation for POLYVAL is unclear. In an email message
> in an earlier mailing list thread, Shay said "We chose to use POLYVAL
> so that 128-bit blocks can be viewed as field elements and as AES
> ciphertexts in a consistent way (with respect to the order of the bits
> inside each byte))," and I think that this should be included in the
> spec, along with a more plain explanation that this is done (IIUC)
> simply to avoid byte byteswapping on little-endian systems that GHASH
> requires.

I'll let Shay add something about this if he wishes, but I think the
bit ordering in GHASH is weird and it''s not just a big/little endian
thing. I know, having spoken to other people who have dealt with
GHASH, but I'm not unique in this either.

POLYVAL straightens this out :)

> It isn't clear how the nonce length of 96 bits was chosen. I can see
> some advantages, e.g. it is more of a drop-in replacement for AES-GCM,
> which is almost exclusively used with 96-bit nonces in IETF protocols,
> but is there any other reason?

It used to be 128 bits, but we wanted to change the KDF to use counter
mode. Thus we needed three bits for the counter. However, a 125-bit
nonce would be too weird so we rounded down to 96 bits.

An analysis of the probabilities of repeats shows that, even with 96
bits, there is a vast security margin so we're happy with that length.

> The email also said "We now generate keys by using counter mode and
> discarding half of each ciphertext block." The motivation for
> discarding half of each ciphertext block should be added to the draft
> (maybe in security considerations), along with a reference of how
> discarding half of each ciphertext block achieves that goal.

Agreed and I'm hoping that a more concrete comparison of how the new
KDF affects the bounds will come from Shay and Yehuda soon :)

> The draft makes an argument about safety when "nonces are selected
> uniformly at random." However, isn't a key motivation for AES-GCM-SIV
> our lack of confidence in our ability to select nonces uniformly at
> random?

No. The motivation is that selecting nonces at random with AES-GCM
isn't very comforting. NIST recommends a limit of 2^32 plaintexts for
a given key in this case, and that still has a 2^-33 chance of serious
failure.

> I personally would like to see discussion of the case where we
> can't assume nonces are selected uniformly at random. (While I can't
> come up with one off the top of my head right now, it seems likely
> that there would be simpler and less invasive ways of defining a
> nonce-misuse-resistant AEAD based on AES-GCM if we can also assume we
> have a good random number generator and we're willing to accept the
> birthday bound analysis in the draft. Thus, based on intuition it
> seems like AES-GCM-SIV must be useful in contexts where nonces aren't
> chosen uniformly at random in order to justify its complexity.)

Off the top of my head, I think we would need a cipher with a 256-bit
block in order for a scheme that doesn't depend on nonces being
(mostly) distinct to have comfortable security margins. AES-GCM-SIV is
not such a scheme.


Cheers

AGL

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


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References: <148476063144.1938.2025448065922517313.idtracker@ietfa.amsl.com> <D4A59386.5822C%john.mattsson@ericsson.com> <CAMfhd9XQSi17mLKE1AFUa2ZG8nJq4MfccMomFm+0ctsKm_Ab9w@mail.gmail.com>
From: Shay Gueron <shay.gueron@gmail.com>
Date: Wed, 18 Jan 2017 17:05:05 -0800
Message-ID: <CAHP81y-6j9uE6t+axwej=Rd8cGxthcVHQ1jqALNAP30za2VKYw@mail.gmail.com>
To: Adam Langley <agl@imperialviolet.org>
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Cc: "cfrg@ietf.org" <cfrg@ietf.org>
Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt
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Hello everyone,


I will try to address, really briefly, two of the points raised here and
deferred to me.

The definition of POLYVAL: there is an inherent discrepancy in the
definition of AES-GCM. 128-bit blocks need to be viewed as polynomials, and
also as 16 bytes for input/output for AES (AES is defined over bytes). The
way that the polynomials are defined leads to bytes that have the reverse
order of bits, compared to how AES views a bytes. I will publish a
 detailed paper on this issue. For now, there is some explanation in my
talk at RWC 2011 [1].
POLYVAL is defined in a way that is consistent with AES.

The other topic is why truncate the AES (throw away half of the bits) when
generating per-nonce keys. The idea is to get indistinguishabilityle bounds
that do not have a term that is quadratic in the number of queries (like
the ones we would get if we used all of the bits). Roughly speaking the
truncation gets us a term that looks like q/2^(96) instead of q^2/2^{129}.
The bounds and discussion can be seen at  [2].

Anyway an organized paper with a statement on the security bounds, is going
to come out in a paper that we are working on these very days. We will post
it soon.

Thank you, Shay

[1] https://crypto.stanford.edu/RealWorldCrypto/slides/gueron.pdf

[2] S. Gilboa, S. Gueron, =E2=80=9CThe Advantage of Truncated Permutations=
=E2=80=9D,
https://arxiv.org/abs/1610.02518   (submitted on 8 Oct 2016).

2017-01-18 16:13 GMT-08:00 Adam Langley <agl@imperialviolet.org>:

> On Wed, Jan 18, 2017 at 1:05 PM, John Mattsson
> <john.mattsson@ericsson.com> wrote:
> > - In addition to listing the performance penalty compared to GCM. The
> >   draft should also mention that compared to GCM, some nice properties
> >   disappear:
> >   - Neither Encryption nor Decryption is online as encryption/decryptio=
n
> >     cannot start before the whole plaintext/ciphertext is known.
>
> I agree that this is true for encryption, but I don't believe that
> AES-GCM should be *de*crypted in a streaming fashion, but rather that
> records should be sized so that this isn't a problem. (At which point
> the benefit for streaming encryption becomes small or moot.)
>
> I've a long spiel about the dangers of processing unauthenticated
> ciphertext which I'll spare you :) But, even for small machines, the
> memory needed to safely buffer the decrypted plaintext to avoid
> releasing it before it's authenticated is equal to the memory to
> buffer the ciphertext followed by decrypting in-place.
>
> So I actually quite like that the tag is at the end of the message
> with AES-GCM-SIV because it makes it harder to do what I think is the
> "wrong" thing.
>
> >   - GCM-SIV removes the possibility to preprocess static headers (AAD).
>
> Indeed.
>
> (I wasn't sure where to put these points in the spec so, for the
> moment, I've added an appendix for "Additional comparisons with
> AES-GCM". I'm collecting changes in GitHub before making a new
> version. For this message, see
> https://github.com/agl/gcmsiv/commit/c6c7fd388dd122251264222b7491c6
> 212e818319.)
>
> > - =E2=80=9CThe result of the encryption is the resulting ciphertext (tr=
uncated
> >    to the length of the plaintext) followed by the tag."
> >
> >   I suggest that the tag is placed first instead of last in the
> >   ciphertext. This makes decryption online, which makes a large
> >   difference. Suggestion:
> >
> >   =E2=80=9CThe result of the encryption is the tag followed by the ciph=
ertext
> >    (truncated to the length of the plaintext)"
>
> (See above.)
>
> >
> >
> > - "within 5% of the speed of AES-GCM."
> >   Should state when this is the case, e.g. long plaintext/aad.
>
> Done.
>
> >
> > - I think the draft should give performance data also for short
> >   plaintexts/aad or even better list the performance in number of
> >   operations:
> >
> >   GCM:
> >     Block Cipher Operations =3D p + 1
> >     GF(2^128) Multiplications =3D p + a + 1
> >
> >   GCM-SIV-128
> >     Block Cipher Operations =3D p + 5
> >     GF(2^128) Multiplications =3D p + a + 1
> >
> >   GCM-SIV-256
> >     Block Cipher Operations =3D p + 7
> >     GF(2^128) Multiplications =3D p + a + 1
> >
> >   (if I got it right...)
>
> I think that's correct and I've added that to the new appendix.
>
> >   Where p is the block length of the plaintext and a is the block lengt=
h
> >   of the additional authenticated data,
> >
> >   I doubt that encryption of short messages are anywhere near 5% of GCM=
.
> >
> > - The "++" and "[:8]" operation should probably be defined.
>
> Done.
>
> >
> > - What it the security/performance tradeoff with truncation in the key
> >   derivation? What would the security properties be if "[:8]" was
> >   removed?
>
> I'll have to let Shay answer this, but the rough idea is that, since
> AES is a permutation, not two ciphertexts can be equal given that
> we're encrypting different plaintexts using the KDF phase. However,
> ideally we would want a PRF where outputs can be the same. By taking
> only the first eight bytes of each ciphertext block, we better
> approximate a PRF.
>
> > - The definition of U32LE seems unnecessary and only adds complexity.
> >   I suggest:
> >     OLD "U32LE(3) ++ nonce"
> >     NEW "03 ++ 000000 ++ nonce
>
> Good point.
>
> >
> > - The term K1 is only used in Test Vectors. I guess it is an old term
> >   that should be removed.
>
> Done.
>
> > Some editorials:
>
> Thank you for all these. They should be taken care of.
>
> > - OLD "The record-authentication key is 128-bit and the
> >        record-authentication key"
> >   NEW "The record-authentication key is 128-bit and the
> >        record-encryption key"
> >
> > - "} else if bytelen(key-generating-key) =3D=3D 32 {
> >      record-encryption-key =3D AES128(key =3D key-generating-key,"
> >
> >   Should be AES256
>
> Indeed, and record-authentication-key is wrong too!
>
> > - Spacing around "+" and "*" are not consistent.
> >
> > - "the the"
> >
> > - yeilds
> >
> > - remainding
> >
> > - RFC7322 says "A comma is used before the last item of a series"
>
> I think I've leave this one to the RFC Editor!
>
>
>
> Cheers
>
> AGL
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>

--f403045dc5d2b0efc90546681f85
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

<div dir=3D"rtl"><div dir=3D"ltr">Hello everyone,=C2=A0</div><div dir=3D"lt=
r"><br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">I will try to addr=
ess, really briefly, two of the points raised here and deferred to me.=C2=
=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">The definition of POLY=
VAL: there is an inherent discrepancy in the definition of AES-GCM. 128-bit=
 blocks need to be viewed as polynomials, and also as 16 bytes for input/ou=
tput for AES (AES is defined over bytes). The way that the polynomials are =
defined leads to bytes that have the reverse order of bits, compared to how=
 AES views a bytes. I will publish a =C2=A0detailed paper on this issue. Fo=
r now, there is some explanation in my talk at RWC 2011 [1].=C2=A0</div><di=
v dir=3D"ltr">POLYVAL is defined in a way that is consistent with AES.=C2=
=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">The other topic is why=
 truncate the AES (throw away half of the bits) when generating per-nonce k=
eys. The idea is to get indistinguishabilityle bounds that do not have a te=
rm that is quadratic in the number of queries (like the ones we would get i=
f we used all of the bits). Roughly speaking the truncation gets us a term =
that looks like q/2^(96) instead of q^2/2^{129}. The bounds and discussion =
can be seen at =C2=A0[2].=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D=
"ltr">Anyway an organized paper with a statement on the security bounds, is=
 going to come out in a paper that we are working on these very days. We wi=
ll post it soon.=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">Tha=
nk you, Shay=C2=A0</div><div><br></div><div dir=3D"ltr">[1] <a href=3D"http=
s://crypto.stanford.edu/RealWorldCrypto/slides/gueron.pdf">https://crypto.s=
tanford.edu/RealWorldCrypto/slides/gueron.pdf</a><br></div><div dir=3D"ltr"=
><br></div><div dir=3D"ltr">[2] S. Gilboa, S. Gueron, =E2=80=9CThe Advantag=
e of Truncated Permutations=E2=80=9D,=C2=A0</div><div dir=3D"ltr"><a href=
=3D"https://arxiv.org/abs/1610.02518">https://arxiv.org/abs/1610.02518</a> =
=C2=A0 (submitted on 8 Oct 2016).=C2=A0</div></div><div class=3D"gmail_extr=
a"><br><div class=3D"gmail_quote"><div dir=3D"ltr">2017-01-18 16:13 GMT-08:=
00 Adam Langley <span dir=3D"ltr">&lt;<a href=3D"mailto:agl@imperialviolet.=
org" target=3D"_blank">agl@imperialviolet.org</a>&gt;</span>:</div><blockqu=
ote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc s=
olid;padding-left:1ex"><span class=3D"">On Wed, Jan 18, 2017 at 1:05 PM, Jo=
hn Mattsson<br>
&lt;<a href=3D"mailto:john.mattsson@ericsson.com">john.mattsson@ericsson.co=
m</a>&gt; wrote:<br>
&gt; - In addition to listing the performance penalty compared to GCM. The<=
br>
&gt;=C2=A0 =C2=A0draft should also mention that compared to GCM, some nice =
properties<br>
&gt;=C2=A0 =C2=A0disappear:<br>
&gt;=C2=A0 =C2=A0- Neither Encryption nor Decryption is online as encryptio=
n/decryption<br>
&gt;=C2=A0 =C2=A0 =C2=A0cannot start before the whole plaintext/ciphertext =
is known.<br>
<br>
</span>I agree that this is true for encryption, but I don&#39;t believe th=
at<br>
AES-GCM should be *de*crypted in a streaming fashion, but rather that<br>
records should be sized so that this isn&#39;t a problem. (At which point<b=
r>
the benefit for streaming encryption becomes small or moot.)<br>
<br>
I&#39;ve a long spiel about the dangers of processing unauthenticated<br>
ciphertext which I&#39;ll spare you :) But, even for small machines, the<br=
>
memory needed to safely buffer the decrypted plaintext to avoid<br>
releasing it before it&#39;s authenticated is equal to the memory to<br>
buffer the ciphertext followed by decrypting in-place.<br>
<br>
So I actually quite like that the tag is at the end of the message<br>
with AES-GCM-SIV because it makes it harder to do what I think is the<br>
&quot;wrong&quot; thing.<br>
<span class=3D""><br>
&gt;=C2=A0 =C2=A0- GCM-SIV removes the possibility to preprocess static hea=
ders (AAD).<br>
<br>
</span>Indeed.<br>
<br>
(I wasn&#39;t sure where to put these points in the spec so, for the<br>
moment, I&#39;ve added an appendix for &quot;Additional comparisons with<br=
>
AES-GCM&quot;. I&#39;m collecting changes in GitHub before making a new<br>
version. For this message, see<br>
<a href=3D"https://github.com/agl/gcmsiv/commit/c6c7fd388dd122251264222b749=
1c6212e818319" rel=3D"noreferrer" target=3D"_blank">https://github.com/agl/=
gcmsiv/<wbr>commit/<wbr>c6c7fd388dd122251264222b7491c6<wbr>212e818319</a>.)=
<br>
<span class=3D""><br>
&gt; - =E2=80=9CThe result of the encryption is the resulting ciphertext (t=
runcated<br>
&gt;=C2=A0 =C2=A0 to the length of the plaintext) followed by the tag.&quot=
;<br>
&gt;<br>
&gt;=C2=A0 =C2=A0I suggest that the tag is placed first instead of last in =
the<br>
&gt;=C2=A0 =C2=A0ciphertext. This makes decryption online, which makes a la=
rge<br>
&gt;=C2=A0 =C2=A0difference. Suggestion:<br>
&gt;<br>
&gt;=C2=A0 =C2=A0=E2=80=9CThe result of the encryption is the tag followed =
by the ciphertext<br>
&gt;=C2=A0 =C2=A0 (truncated to the length of the plaintext)&quot;<br>
<br>
</span>(See above.)<br>
<span class=3D""><br>
&gt;<br>
&gt;<br>
&gt; - &quot;within 5% of the speed of AES-GCM.&quot;<br>
&gt;=C2=A0 =C2=A0Should state when this is the case, e.g. long plaintext/aa=
d.<br>
<br>
</span>Done.<br>
<span class=3D""><br>
&gt;<br>
&gt; - I think the draft should give performance data also for short<br>
&gt;=C2=A0 =C2=A0plaintexts/aad or even better list the performance in numb=
er of<br>
&gt;=C2=A0 =C2=A0operations:<br>
&gt;<br>
&gt;=C2=A0 =C2=A0GCM:<br>
&gt;=C2=A0 =C2=A0 =C2=A0Block Cipher Operations =3D p + 1<br>
&gt;=C2=A0 =C2=A0 =C2=A0GF(2^128) Multiplications =3D p + a + 1<br>
&gt;<br>
&gt;=C2=A0 =C2=A0GCM-SIV-128<br>
&gt;=C2=A0 =C2=A0 =C2=A0Block Cipher Operations =3D p + 5<br>
&gt;=C2=A0 =C2=A0 =C2=A0GF(2^128) Multiplications =3D p + a + 1<br>
&gt;<br>
&gt;=C2=A0 =C2=A0GCM-SIV-256<br>
&gt;=C2=A0 =C2=A0 =C2=A0Block Cipher Operations =3D p + 7<br>
&gt;=C2=A0 =C2=A0 =C2=A0GF(2^128) Multiplications =3D p + a + 1<br>
&gt;<br>
&gt;=C2=A0 =C2=A0(if I got it right...)<br>
<br>
</span>I think that&#39;s correct and I&#39;ve added that to the new append=
ix.<br>
<span class=3D""><br>
&gt;=C2=A0 =C2=A0Where p is the block length of the plaintext and a is the =
block length<br>
&gt;=C2=A0 =C2=A0of the additional authenticated data,<br>
&gt;<br>
&gt;=C2=A0 =C2=A0I doubt that encryption of short messages are anywhere nea=
r 5% of GCM.<br>
&gt;<br>
&gt; - The &quot;++&quot; and &quot;[:8]&quot; operation should probably be=
 defined.<br>
<br>
</span>Done.<br>
<span class=3D""><br>
&gt;<br>
&gt; - What it the security/performance tradeoff with truncation in the key=
<br>
&gt;=C2=A0 =C2=A0derivation? What would the security properties be if &quot=
;[:8]&quot; was<br>
&gt;=C2=A0 =C2=A0removed?<br>
<br>
</span>I&#39;ll have to let Shay answer this, but the rough idea is that, s=
ince<br>
AES is a permutation, not two ciphertexts can be equal given that<br>
we&#39;re encrypting different plaintexts using the KDF phase. However,<br>
ideally we would want a PRF where outputs can be the same. By taking<br>
only the first eight bytes of each ciphertext block, we better<br>
approximate a PRF.<br>
<span class=3D""><br>
&gt; - The definition of U32LE seems unnecessary and only adds complexity.<=
br>
&gt;=C2=A0 =C2=A0I suggest:<br>
&gt;=C2=A0 =C2=A0 =C2=A0OLD &quot;U32LE(3) ++ nonce&quot;<br>
&gt;=C2=A0 =C2=A0 =C2=A0NEW &quot;03 ++ 000000 ++ nonce<br>
<br>
</span>Good point.<br>
<span class=3D""><br>
&gt;<br>
&gt; - The term K1 is only used in Test Vectors. I guess it is an old term<=
br>
&gt;=C2=A0 =C2=A0that should be removed.<br>
<br>
</span>Done.<br>
<br>
&gt; Some editorials:<br>
<br>
Thank you for all these. They should be taken care of.<br>
<span class=3D""><br>
&gt; - OLD &quot;The record-authentication key is 128-bit and the<br>
&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 record-authentication key&quot;<br>
&gt;=C2=A0 =C2=A0NEW &quot;The record-authentication key is 128-bit and the=
<br>
&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 record-encryption key&quot;<br>
&gt;<br>
&gt; - &quot;} else if bytelen(key-generating-key) =3D=3D 32 {<br>
&gt;=C2=A0 =C2=A0 =C2=A0 record-encryption-key =3D AES128(key =3D key-gener=
ating-key,&quot;<br>
&gt;<br>
&gt;=C2=A0 =C2=A0Should be AES256<br>
<br>
</span>Indeed, and record-authentication-key is wrong too!<br>
<span class=3D""><br>
&gt; - Spacing around &quot;+&quot; and &quot;*&quot; are not consistent.<b=
r>
&gt;<br>
&gt; - &quot;the the&quot;<br>
&gt;<br>
&gt; - yeilds<br>
&gt;<br>
&gt; - remainding<br>
&gt;<br>
&gt; - RFC7322 says &quot;A comma is used before the last item of a series&=
quot;<br>
<br>
</span>I think I&#39;ve leave this one to the RFC Editor!<br>
<br>
<br>
<br>
Cheers<br>
<br>
AGL<br>
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From: Brian Smith <brian@briansmith.org>
Date: Wed, 18 Jan 2017 17:53:09 -1000
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To: Adam Langley <agl@imperialviolet.org>
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Subject: Re: [Cfrg] AES GCM SIV analysis
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Adam Langley <agl@imperialviolet.org> wrote:
> Brian Smith <brian@briansmith.org> wrote:
>> The actual text in the draft is "Thus with AES-GCM-SIV we recommend
>> that, for a specific key, a nonce not be repeated more than 2^8
>> times."
>>
>> Is this a meaningful recommendation? How would one go about following
>> this recommendation in a practical implementation? In particular,
>> AES-GCM-SIV is mostly interesting in implementations that cannot
>> reliably and/or consistently save state, and it seems like any attempt
>> to write code to enforce this relies on saving state [snip]

> [snip] With a random, 96-bit nonce you don't have to worry
> about the probability of having repeated a single value > 2^8 times
> until you have a staggering number of plaintexts: greater than 2^100
> of them. Since that vastly exceeds our current recommendation for
> number of plaintexts per key (2^50), it's basically not a concern.
>
> If that makes sense, what could we have written to be clearer?

Perhaps: "We recommend instead that an implementation try to avoid
repeating a nonce for a specific key, just like it would it would do
for an AEAD that isn't nonce-misuse-resistant." This shifts the
emphasis away from the 2^8 number to where it belongs, IMO. Note that
"256" and how it is derived and why it is safe is explained in the
next paragraph anyway.

> I agree that large AEAD messages have several problems. But I don't
> think that we have any need for a larger nonce (see above). (And the
> nonce is used with a counter only in the KDF phase, so it's unrelated
> to the maximum plaintext size.)

Is there any way that a larger nonce (e.g. 120 bits) hurts, other than
being inconsistent with existing IETF AEADs?

Cheers,
Brian
-- 
https://briansmith.org/


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From: John Mattsson <john.mattsson@ericsson.com>
To: Brian Smith <brian@briansmith.org>, Adam Langley <agl@imperialviolet.org>
Thread-Topic: [Cfrg] AES GCM SIV analysis
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Just sitting here on the sidelines, but already my complexity meter has =
gone into the infra red.
__outer


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From: John Mattsson <john.mattsson@ericsson.com>
To: Adam Langley <agl@imperialviolet.org>
Thread-Topic: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt
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From: "Stanislav V. Smyshlyaev" <smyshsv@gmail.com>
Date: Thu, 19 Jan 2017 13:50:17 +0300
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Subject: Re: [Cfrg] Fwd: Rev RFC 7539?
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Document: draft-nir-cfrg-rfc7539bis-00
Reviewer: Stanislav Smyshlyaev
Review Date: 2017-01-19

The purpose of the document is to address a set of of errata for RFC 7539.
It has been done systematically and correctly - all errata have been
addressed.

RFC 7539 is an extremely important document providing some
(optional/"standby") diversity, so, I totally support the work and the
adoption of the new rfc7539bis as a CFRG document.

My only concerns related to the changes are the following (these two have
already been spotted by Russ Housley and John Mattsson):
- there are no changes in the Security Considerations section, while the
abstract says they should be.
- Capital "T" in the beginning of the second sentence of the abstract.

Also in the updated version I'd prefer to see an updated list of the papers
on ChaCha:
the ideology of the RFC is to give the alternative (e.g. as a standby
cipher) to AES in the protocols, so an up-to-date relevant list of
publications on the alternative algorithms would be helpful. Maybe the
authors have
thought on this and have come to a conclusion that no update is needed
though.

Some editorial comments, related to the original RFC:
1) "Professor Bernstein's paper" -> "[ChaCha]".
2) Section 2.5: do we really need a c-code (together with #include...)
instead of pseudocode here?
3) To add to the Russ Housley's list of unnecessary bullets and line
numbers: are "@@@" needed in A.5?
4) For "+", "^" and "<<<" definitions are given and for "|" (again -
already spotted by Russ) and for "&" they are not - some revision here
would be helpful.

And one more minor comment: the statements in 2.7 about the PRFs may be
more accurate, if instead of (or in addition to) informal words (about HMAC
that are used as PRF and that Poly1305 should not) references to the formal
PRF property and papers with proofs of HMAC would be given.

Nevertheless, in my opinion, the document is very close to being ready and
should be adopted by CFRG (after these minor corrections).

Best regards,
Stanislav V. Smyshlyaev, Ph.D.,
Head of Information Security Department,
CryptoPro LLC


2017-01-18 21:30 GMT+03:00 Russ Housley <housley@vigilsec.com>:

> Document: draft-nir-cfrg-rfc7539bis-00
> Reviewer: Russ Housley
> Review Date: 2017-01-19
>
> Summary: Almost Ready
>
> Major Concerns:
>
> The Abstract says that there are additions to the Security
> Considerations; however, I do not see a difference between the
> Security Considerations in this document and RFC 7539.
>
>
> Minor Concerns:
>
> In Section 2.3.1, please add a sentence to define the "|" operator
> in a manner similar to the definition for "+" in Section 2.1.
>
>
> Nits:
>
> Abstract: s/any new crypto/any new cryptographic mechanisms/
>
> Section 2.1 uses "rotation" and "roll" to describe the same operation.
> Please pick one term.
>
> In Sections 2.1 and 2.3, I do not think that the line numbers aid the
> reader. I think that simple indention would be better.
>
> In Sections 2.1 and 2.1.1, I do not think that the bullets aid the
> reader.  I think that simple indention would be better.
>
> Section 2.5.1 includes: r = (le_bytes_to_num(key[0..15]).
> I think you want to drop the leading parenthesis.
>
> In Author's address, please capitalize "st."
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>

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

<div dir=3D"ltr"><div>Document: draft-nir-cfrg-rfc7539bis-00</div><div>Revi=
ewer: Stanislav Smyshlyaev</div><div>Review Date: 2017-01-19</div><div><br>=
</div><div>The purpose of the document is to address a set of of errata for=
 RFC 7539. It has been done systematically and correctly - all errata have =
been addressed.</div><div><br></div><div>RFC 7539 is an extremely important=
 document providing some (optional/&quot;standby&quot;) diversity, so, I to=
tally support the work and the adoption of the new rfc7539bis as a CFRG doc=
ument.</div><div><br></div><div>My only concerns related to the changes are=
 the following (these two have already been spotted by Russ Housley and Joh=
n Mattsson):</div><div>- there are no changes in the Security Consideration=
s section, while the abstract says they should be.</div><div>- Capital &quo=
t;T&quot; in the beginning of the second sentence of the abstract.</div><di=
v><br></div><div>Also in the updated version I&#39;d prefer to see an updat=
ed list of the papers on ChaCha:=C2=A0</div><div>the ideology of the RFC is=
 to give the alternative (e.g. as a standby cipher) to AES in the protocols=
, so an up-to-date relevant list of publications on the alternative algorit=
hms would be helpful. Maybe the authors have=C2=A0</div><div>thought on thi=
s and have come to a conclusion that no update is needed though.</div><div>=
<br></div><div>Some editorial comments, related to the original RFC:</div><=
div>1) &quot;Professor Bernstein&#39;s paper&quot; -&gt; &quot;[ChaCha]&quo=
t;.</div><div>2) Section 2.5: do we really need a c-code (together with #in=
clude...) instead of pseudocode here?</div><div>3) To add to the Russ Housl=
ey&#39;s list of unnecessary bullets and line numbers: are &quot;@@@&quot; =
needed in A.5?</div><div>4) For &quot;+&quot;, &quot;^&quot; and &quot;&lt;=
&lt;&lt;&quot; definitions are given and for &quot;|&quot; (again - already=
 spotted by Russ) and for &quot;&amp;&quot; they are not - some revision he=
re would be helpful.</div><div><br></div><div>And one more minor comment: t=
he statements in 2.7 about the PRFs may be more accurate, if instead of (or=
 in addition to) informal words (about HMAC that are used as PRF and that P=
oly1305 should not) references to the formal PRF property and papers with p=
roofs of HMAC would be given.</div><div><br></div><div>Nevertheless, in my =
opinion, the document is very close to being ready and should be adopted by=
 CFRG (after these minor corrections).</div><div><br></div><div>Best regard=
s,</div><div>Stanislav V. Smyshlyaev, Ph.D.,</div><div>Head of Information =
Security Department,</div><div>CryptoPro LLC</div><div class=3D"gmail_extra=
"><div><div class=3D"gmail_signature" data-smartmail=3D"gmail_signature"><d=
iv dir=3D"ltr"><p><br></p></div></div></div><div class=3D"gmail_quote">2017=
-01-18 21:30 GMT+03:00 Russ Housley <span dir=3D"ltr">&lt;<a href=3D"mailto=
:housley@vigilsec.com" target=3D"_blank">housley@vigilsec.com</a>&gt;</span=
>:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-l=
eft:1px #ccc solid;padding-left:1ex">Document: draft-nir-cfrg-rfc7539bis-00=
<br>
Reviewer: Russ Housley<br>
Review Date: 2017-01-19<br>
<br>
Summary: Almost Ready<br>
<br>
Major Concerns:<br>
<br>
The Abstract says that there are additions to the Security<br>
Considerations; however, I do not see a difference between the<br>
Security Considerations in this document and RFC 7539.<br>
<br>
<br>
Minor Concerns:<br>
<br>
In Section 2.3.1, please add a sentence to define the &quot;|&quot; operato=
r<br>
in a manner similar to the definition for &quot;+&quot; in Section 2.1.<br>
<br>
<br>
Nits:<br>
<br>
Abstract: s/any new crypto/any new cryptographic mechanisms/<br>
<br>
Section 2.1 uses &quot;rotation&quot; and &quot;roll&quot; to describe the =
same operation.<br>
Please pick one term.<br>
<br>
In Sections 2.1 and 2.3, I do not think that the line numbers aid the<br>
reader. I think that simple indention would be better.<br>
<br>
In Sections 2.1 and 2.1.1, I do not think that the bullets aid the<br>
reader.=C2=A0 I think that simple indention would be better.<br>
<br>
Section 2.5.1 includes: r =3D (le_bytes_to_num(key[0..15]).<br>
I think you want to drop the leading parenthesis.<br>
<br>
In Author&#39;s address, please capitalize &quot;st.&quot;<br>
<div class=3D"HOEnZb"><div class=3D"h5"><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></div></div>

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Thread-Topic: [Cfrg] Fwd: Rev RFC 7539?
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<html><head></head><body lang=3D"en-US" style=3D"background-color: rgb(255,=
 255, 255); line-height: initial;">                                        =
                                              <div style=3D"width: 100%; fo=
nt-size: initial; font-family: Calibri, 'Slate Pro', sans-serif, sans-serif=
; color: rgb(31, 73, 125); text-align: initial; background-color: rgb(255, =
255, 255);">To answer one minor point: yes we do want C code (that can run =
and produce measurable output regardless of =E2=80=8Ethe level of understan=
ding of those who compile it :) rather that (or at worst - in addition to) =
pseudocode that people were known to interpret and implement wrongly now an=
d then.</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; ba=
ckground-color: rgb(255, 255, 255);"><br></div>                            =
                                                                           =
                                                                           =
                 <div style=3D"font-size: initial; font-family: Calibri, 'S=
late Pro', sans-serif, sans-serif; color: rgb(31, 73, 125); text-align: ini=
tial; background-color: rgb(255, 255, 255);">Sent&nbsp;from&nbsp;my&nbsp;Bl=
ackBerry&nbsp;10&nbsp;smartphone&nbsp;on&nbsp;the&nbsp;Verizon&nbsp;Wireles=
s&nbsp;4G&nbsp;LTE&nbsp;network.</div>                                     =
                                                                           =
                                                                  <table wi=
dth=3D"100%" style=3D"background-color:white;border-spacing:0px;"> <tbody><=
tr><td colspan=3D"2" style=3D"font-size: initial; text-align: initial; back=
ground-color: rgb(255, 255, 255);">                           <div style=3D=
"border-style: solid none none; border-top-color: rgb(181, 196, 223); borde=
r-top-width: 1pt; padding: 3pt 0in 0in; font-family: Tahoma, 'BB Alpha Sans=
', 'Slate Pro'; font-size: 10pt;">  <div><b>From: </b>Stanislav V. Smyshlya=
ev</div><div><b>Sent: </b>Thursday, January 19, 2017 05:50</div><div><b>To:=
 </b>IRTF CFRG</div><div><b>Subject: </b>Re: [Cfrg] Fwd: Rev RFC 7539?</div=
></div></td></tr></tbody></table><div style=3D"border-style: solid none non=
e; border-top-color: rgb(186, 188, 209); border-top-width: 1pt; font-size: =
initial; text-align: initial; background-color: rgb(255, 255, 255);"></div>=
<br><div id=3D"_originalContent" style=3D"">

<meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3Dutf-8">


<div dir=3D"ltr">
<div>Document: draft-nir-cfrg-rfc7539bis-00</div>
<div>Reviewer: Stanislav Smyshlyaev</div>
<div>Review Date: 2017-01-19</div>
<div><br>
</div>
<div>The purpose of the document is to address a set of of errata for RFC 7=
539. It has been done systematically and correctly - all errata have been a=
ddressed.</div>
<div><br>
</div>
<div>RFC 7539 is an extremely important document providing some (optional/"=
standby") diversity, so, I totally support the work and the adoption of the=
 new rfc7539bis as a CFRG document.</div>
<div><br>
</div>
<div>My only concerns related to the changes are the following (these two h=
ave already been spotted by Russ Housley and John Mattsson):</div>
<div>- there are no changes in the Security Considerations section, while t=
he abstract says they should be.</div>
<div>- Capital "T" in the beginning of the second sentence of the abstract.=
</div>
<div><br>
</div>
<div>Also in the updated version I'd prefer to see an updated list of the p=
apers on ChaCha:&nbsp;</div>
<div>the ideology of the RFC is to give the alternative (e.g. as a standby =
cipher) to AES in the protocols, so an up-to-date relevant list of publicat=
ions on the alternative algorithms would be helpful. Maybe the authors have=
&nbsp;</div>
<div>thought on this and have come to a conclusion that no update is needed=
 though.</div>
<div><br>
</div>
<div>Some editorial comments, related to the original RFC:</div>
<div>1) "Professor Bernstein's paper" -&gt; "[ChaCha]".</div>
<div>2) Section 2.5: do we really need a c-code (together with #include...)=
 instead of pseudocode here?</div>
<div>3) To add to the Russ Housley's list of unnecessary bullets and line n=
umbers: are "@@@" needed in A.5?</div>
<div>4) For "+", "^" and "&lt;&lt;&lt;" definitions are given and for "|" (=
again - already spotted by Russ) and for "&amp;" they are not - some revisi=
on here would be helpful.</div>
<div><br>
</div>
<div>And one more minor comment: the statements in 2.7 about the PRFs may b=
e more accurate, if instead of (or in addition to) informal words (about HM=
AC that are used as PRF and that Poly1305 should not) references to the for=
mal PRF property and papers with
 proofs of HMAC would be given.</div>
<div><br>
</div>
<div>Nevertheless, in my opinion, the document is very close to being ready=
 and should be adopted by CFRG (after these minor corrections).</div>
<div><br>
</div>
<div>Best regards,</div>
<div>Stanislav V. Smyshlyaev, Ph.D.,</div>
<div>Head of Information Security Department,</div>
<div>CryptoPro LLC</div>
<div class=3D"gmail_extra">
<div>
<div class=3D"gmail_signature">
<div dir=3D"ltr">
<p><br>
</p>
</div>
</div>
</div>
<div class=3D"gmail_quote">2017-01-18 21:30 GMT+03:00 Russ Housley <span di=
r=3D"ltr">
&lt;<a href=3D"mailto:housley@vigilsec.com">housley@vigilsec.com</a>&gt;</s=
pan>:<br>
<blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex; border-left:1=
px #ccc solid; padding-left:1ex">
Document: draft-nir-cfrg-rfc7539bis-00<br>
Reviewer: Russ Housley<br>
Review Date: 2017-01-19<br>
<br>
Summary: Almost Ready<br>
<br>
Major Concerns:<br>
<br>
The Abstract says that there are additions to the Security<br>
Considerations; however, I do not see a difference between the<br>
Security Considerations in this document and RFC 7539.<br>
<br>
<br>
Minor Concerns:<br>
<br>
In Section 2.3.1, please add a sentence to define the "|" operator<br>
in a manner similar to the definition for "+" in Section 2.1.<br>
<br>
<br>
Nits:<br>
<br>
Abstract: s/any new crypto/any new cryptographic mechanisms/<br>
<br>
Section 2.1 uses "rotation" and "roll" to describe the same operation.<br>
Please pick one term.<br>
<br>
In Sections 2.1 and 2.3, I do not think that the line numbers aid the<br>
reader. I think that simple indention would be better.<br>
<br>
In Sections 2.1 and 2.1.1, I do not think that the bullets aid the<br>
reader.&nbsp; I think that simple indention would be better.<br>
<br>
Section 2.5.1 includes: r =3D (le_bytes_to_num(key[0..15]).<br>
I think you want to drop the leading parenthesis.<br>
<br>
In Author's address, please capitalize "st."<br>
<div class=3D"HOEnZb">
<div class=3D"h5"><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>
</div>
</div>


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From: Shay Gueron <shay.gueron@gmail.com>
Date: Thu, 19 Jan 2017 05:50:06 -0800
Message-ID: <CAHP81y-wYHmVyGtrtkoW9nYWtpub=UOE-TzU89B8TeJZZopF-g@mail.gmail.com>
To: John Mattsson <john.mattsson@ericsson.com>
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Cc: Adam Langley <agl@imperialviolet.org>, "cfrg@ietf.org" <cfrg@ietf.org>
Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt
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Dear John,

The bounds in the reference that I pointed to (re. the KDF) bound with the
max between the quadratic and linear term (and 1).

I agree with your comment about q=3D3. If a usage is supposed to send q=3D3
messages (i.e., q=3D3 different nonces) with one key, it makes no point to
have a KDF before GCM-SIV (regardless of its design). Better use GCM-SIV
directly (the one described in the CCS15 paper).

In fact, even for a usage that has only very short messages (e.g., key
wrapping), GCM-SIV can be used directly (no KDF) and with a fixed nonce.

However, AES-GCM-SIV is constructed by a KDF step before the GCM-SIV
processing, with the intention to extend the lifetime of a given key,
beyond 2^{32}, (as it is with GCM-SIV, as explained in the text). In such
cases, it is useful to have a KDF with a small bound on the distinguishing
advantage. We chose the one that is described in the spec.

Thanks, Shay


2017-01-19 0:22 GMT-08:00 John Mattsson <john.mattsson@ericsson.com>:

> Thanks Shay,
>
> See reply inline.
>
> Cheers,
> John
>
>
> From: Shay Gueron <shay.gueron@gmail.com>
> Date: Thursday, 19 January 2017 at 02:05
> To: Adam Langley <agl@imperialviolet.org>
> Cc: John Mattsson2 <john.mattsson@ericsson.com>, "cfrg@ietf.org" <
> cfrg@ietf.org>, Shay Gueron <shay.gueron@gmail.com>
> Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt
>
> Hello everyone,
>
>
> I will try to address, really briefly, two of the points raised here and
> deferred to me.
>
> The definition of POLYVAL: there is an inherent discrepancy in the
> definition of AES-GCM. 128-bit blocks need to be viewed as polynomials, a=
nd
> also as 16 bytes for input/output for AES (AES is defined over bytes). Th=
e
> way that the polynomials are defined leads to bytes that have the reverse
> order of bits, compared to how AES views a bytes. I will publish a
>  detailed paper on this issue. For now, there is some explanation in my
> talk at RWC 2011 [1].
> POLYVAL is defined in a way that is consistent with AES.
>
>
> The other topic is why truncate the AES (throw away half of the bits) whe=
n
> generating per-nonce keys. The idea is to get indistinguishabilityle boun=
ds
> that do not have a term that is quadratic in the number of queries (like
> the ones we would get if we used all of the bits). Roughly speaking the
> truncation gets us a term that looks like q/2^(96) instead of q^2/2^{129}=
.
> The bounds and discussion can be seen at  [2].
>
>
> Asymptotically yes, but in this case we have q=3D2 and q=3D3 and any
> disadvantage of using a PRP should be negligible.
> In fact, if the above terms were true for small q (which they are likely
> not) the the then quadratic term is preferable as  2^2/2^{129} =3D 1/2^{1=
27}
> << 2/2^{96} =3D 1/2^{95}
> Feels like doubling the amount of AES operations may be overkill and not
> worth the negligible security increase. GCM is popular for its performanc=
e,
> not for high security bounds.
>
>
>
> Anyway an organized paper with a statement on the security bounds, is
> going to come out in a paper that we are working on these very days. We
> will post it soon.
>
> Thank you, Shay
>
> [1] https://crypto.stanford.edu/RealWorldCrypto/slides/gueron.pdf
>
> [2] S. Gilboa, S. Gueron, =E2=80=9CThe Advantage of Truncated Permutation=
s=E2=80=9D,
> https://arxiv.org/abs/1610.02518   (submitted on 8 Oct 2016).
>
> 2017-01-18 16:13 GMT-08:00 Adam Langley <agl@imperialviolet.org>:
>
>> On Wed, Jan 18, 2017 at 1:05 PM, John Mattsson
>> <john.mattsson@ericsson.com> wrote:
>> > - In addition to listing the performance penalty compared to GCM. The
>> >   draft should also mention that compared to GCM, some nice properties
>> >   disappear:
>> >   - Neither Encryption nor Decryption is online as encryption/decrypti=
on
>> >     cannot start before the whole plaintext/ciphertext is known.
>>
>> I agree that this is true for encryption, but I don't believe that
>> AES-GCM should be *de*crypted in a streaming fashion, but rather that
>> records should be sized so that this isn't a problem. (At which point
>> the benefit for streaming encryption becomes small or moot.)
>>
>> I've a long spiel about the dangers of processing unauthenticated
>> ciphertext which I'll spare you :) But, even for small machines, the
>> memory needed to safely buffer the decrypted plaintext to avoid
>> releasing it before it's authenticated is equal to the memory to
>> buffer the ciphertext followed by decrypting in-place.
>>
>> So I actually quite like that the tag is at the end of the message
>> with AES-GCM-SIV because it makes it harder to do what I think is the
>> "wrong" thing.
>>
>> >   - GCM-SIV removes the possibility to preprocess static headers (AAD)=
.
>>
>> Indeed.
>>
>> (I wasn't sure where to put these points in the spec so, for the
>> moment, I've added an appendix for "Additional comparisons with
>> AES-GCM". I'm collecting changes in GitHub before making a new
>> version. For this message, see
>> https://github.com/agl/gcmsiv/commit/c6c7fd388dd122251264222
>> b7491c6212e818319.)
>>
>> > - =E2=80=9CThe result of the encryption is the resulting ciphertext (t=
runcated
>> >    to the length of the plaintext) followed by the tag."
>> >
>> >   I suggest that the tag is placed first instead of last in the
>> >   ciphertext. This makes decryption online, which makes a large
>> >   difference. Suggestion:
>> >
>> >   =E2=80=9CThe result of the encryption is the tag followed by the cip=
hertext
>> >    (truncated to the length of the plaintext)"
>>
>> (See above.)
>>
>> >
>> >
>> > - "within 5% of the speed of AES-GCM."
>> >   Should state when this is the case, e.g. long plaintext/aad.
>>
>> Done.
>>
>> >
>> > - I think the draft should give performance data also for short
>> >   plaintexts/aad or even better list the performance in number of
>> >   operations:
>> >
>> >   GCM:
>> >     Block Cipher Operations =3D p + 1
>> >     GF(2^128) Multiplications =3D p + a + 1
>> >
>> >   GCM-SIV-128
>> >     Block Cipher Operations =3D p + 5
>> >     GF(2^128) Multiplications =3D p + a + 1
>> >
>> >   GCM-SIV-256
>> >     Block Cipher Operations =3D p + 7
>> >     GF(2^128) Multiplications =3D p + a + 1
>> >
>> >   (if I got it right...)
>>
>> I think that's correct and I've added that to the new appendix.
>>
>> >   Where p is the block length of the plaintext and a is the block leng=
th
>> >   of the additional authenticated data,
>> >
>> >   I doubt that encryption of short messages are anywhere near 5% of GC=
M.
>> >
>> > - The "++" and "[:8]" operation should probably be defined.
>>
>> Done.
>>
>> >
>> > - What it the security/performance tradeoff with truncation in the key
>> >   derivation? What would the security properties be if "[:8]" was
>> >   removed?
>>
>> I'll have to let Shay answer this, but the rough idea is that, since
>> AES is a permutation, not two ciphertexts can be equal given that
>> we're encrypting different plaintexts using the KDF phase. However,
>> ideally we would want a PRF where outputs can be the same. By taking
>> only the first eight bytes of each ciphertext block, we better
>> approximate a PRF.
>>
>> > - The definition of U32LE seems unnecessary and only adds complexity.
>> >   I suggest:
>> >     OLD "U32LE(3) ++ nonce"
>> >     NEW "03 ++ 000000 ++ nonce
>>
>> Good point.
>>
>> >
>> > - The term K1 is only used in Test Vectors. I guess it is an old term
>> >   that should be removed.
>>
>> Done.
>>
>> > Some editorials:
>>
>> Thank you for all these. They should be taken care of.
>>
>> > - OLD "The record-authentication key is 128-bit and the
>> >        record-authentication key"
>> >   NEW "The record-authentication key is 128-bit and the
>> >        record-encryption key"
>> >
>> > - "} else if bytelen(key-generating-key) =3D=3D 32 {
>> >      record-encryption-key =3D AES128(key =3D key-generating-key,"
>> >
>> >   Should be AES256
>>
>> Indeed, and record-authentication-key is wrong too!
>>
>> > - Spacing around "+" and "*" are not consistent.
>> >
>> > - "the the"
>> >
>> > - yeilds
>> >
>> > - remainding
>> >
>> > - RFC7322 says "A comma is used before the last item of a series"
>>
>> I think I've leave this one to the RFC Editor!
>>
>>
>>
>> Cheers
>>
>> AGL
>>
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org
>> https://www.irtf.org/mailman/listinfo/cfrg
>>
>
>

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Content-Type: text/html; charset=UTF-8
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<div dir=3D"rtl"><div dir=3D"ltr">Dear John,=C2=A0<br></div><div dir=3D"ltr=
"><br></div><div dir=3D"ltr">The bounds in the reference that I pointed to =
(re. the KDF) bound with the max between the quadratic and linear term (and=
 1).=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">I agree with yo=
ur comment about q=3D3. If a usage is supposed to send q=3D3 messages (i.e.=
, q=3D3 different nonces) with one key, it makes no point to have a KDF bef=
ore GCM-SIV (regardless of its design). Better use GCM-SIV directly (the on=
e described in the CCS15 paper).=C2=A0</div><div dir=3D"ltr"><br></div><div=
 dir=3D"ltr">In fact, even for a usage that has only very short messages (e=
.g., key wrapping), GCM-SIV can be used directly (no KDF) and with a fixed =
nonce.=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">However, AES-=
GCM-SIV is constructed by a KDF step before the GCM-SIV processing, with th=
e intention to extend the lifetime of a given key, beyond 2^{32}, (as it is=
 with GCM-SIV, as explained in the text). In such cases, it is useful to ha=
ve a KDF with a small bound on the distinguishing advantage. We chose the o=
ne that is described in the spec.=C2=A0</div><div dir=3D"ltr"><br></div><di=
v dir=3D"ltr">Thanks, Shay</div><div dir=3D"ltr"><br></div><div class=3D"gm=
ail_extra"><br><div class=3D"gmail_quote"><div dir=3D"ltr">2017-01-19 0:22 =
GMT-08:00 John Mattsson <span dir=3D"ltr">&lt;<a href=3D"mailto:john.mattss=
on@ericsson.com" target=3D"_blank">john.mattsson@ericsson.com</a>&gt;</span=
>:</div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0.8ex;border-=
left:1px solid rgb(204,204,204);border-right:1px solid rgb(204,204,204);pad=
ding-left:1ex;padding-right:1ex">



<div style=3D"word-wrap:break-word;color:rgb(0,0,0);font-size:14px;font-fam=
ily:calibri,sans-serif">
<div>
<div>Thanks Shay,</div>
<div><br>
</div>
<div>See reply inline.</div>
<div><br>
</div>
<div>Cheers,</div>
<div>John</div>
<div>
<div>
<p class=3D"MsoNormal" style=3D"font-size:11pt;margin:0cm 0cm 0.0001pt"><u>=
</u>=C2=A0<u></u></p>
</div>
</div>
</div>
<span id=3D"gmail-m_2063633427090501980OLK_SRC_BODY_SECTION">
<div style=3D"font-family:calibri;font-size:11pt;text-align:left;color:blac=
k;border-width:1pt medium medium;border-style:solid none none;border-bottom=
-color:initial;border-left-color:initial;padding:3pt 0in 0in;border-top-col=
or:rgb(181,196,223);border-right-color:initial">
<span style=3D"font-weight:bold">From: </span>Shay Gueron &lt;<a href=3D"ma=
ilto:shay.gueron@gmail.com" target=3D"_blank">shay.gueron@gmail.com</a>&gt;=
<br>
<span style=3D"font-weight:bold">Date: </span>Thursday, 19 January 2017 at =
02:05<br>
<span style=3D"font-weight:bold">To: </span>Adam Langley &lt;<a href=3D"mai=
lto:agl@imperialviolet.org" target=3D"_blank">agl@imperialviolet.org</a>&gt=
;<br>
<span style=3D"font-weight:bold">Cc: </span>John Mattsson2 &lt;<a href=3D"m=
ailto:john.mattsson@ericsson.com" target=3D"_blank">john.mattsson@ericsson.=
com</a>&gt;, &quot;<a href=3D"mailto:cfrg@ietf.org" target=3D"_blank">cfrg@=
ietf.org</a>&quot; &lt;<a href=3D"mailto:cfrg@ietf.org" target=3D"_blank">c=
frg@ietf.org</a>&gt;, Shay Gueron &lt;<a href=3D"mailto:shay.gueron@gmail.c=
om" target=3D"_blank">shay.gueron@gmail.com</a>&gt;<span class=3D"gmail-"><=
br>
<span style=3D"font-weight:bold">Subject: </span>Re: [Cfrg] I-D Action: dra=
ft-irtf-cfrg-gcmsiv-03.txt<br>
</span></div><span class=3D"gmail-">
<div><br>
</div>
<blockquote id=3D"gmail-m_2063633427090501980MAC_OUTLOOK_ATTRIBUTION_BLOCKQ=
UOTE">
<div>
<div>
<div dir=3D"rtl">
<div dir=3D"ltr">Hello everyone,=C2=A0</div>
<div dir=3D"ltr"><br>
</div>
<div dir=3D"ltr"><br>
</div>
<div dir=3D"ltr">I will try to address, really briefly, two of the points r=
aised here and deferred to me.=C2=A0</div>
<div dir=3D"ltr"><br>
</div>
<div dir=3D"ltr">The definition of POLYVAL: there is an inherent discrepanc=
y in the definition of AES-GCM. 128-bit blocks need to be viewed as polynom=
ials, and also as 16 bytes for input/output for AES (AES is defined over by=
tes). The way that the polynomials
 are defined leads to bytes that have the reverse order of bits, compared t=
o how AES views a bytes. I will publish a =C2=A0detailed paper on this issu=
e. For now, there is some explanation in my talk at RWC 2011 [1].=C2=A0</di=
v>
<div dir=3D"ltr">POLYVAL is defined in a way that is consistent with AES.=
=C2=A0</div>
</div>
</div>
</div>
</blockquote>
</span></span><span class=3D"gmail-"><span id=3D"gmail-m_206363342709050198=
0OLK_SRC_BODY_SECTION">
<blockquote id=3D"gmail-m_2063633427090501980MAC_OUTLOOK_ATTRIBUTION_BLOCKQ=
UOTE">
<div>
<div>
<div dir=3D"rtl">
<div dir=3D"ltr"><br>
</div>
<div dir=3D"ltr">The other topic is why truncate the AES (throw away half o=
f the bits) when generating per-nonce keys. The idea is to get indistinguis=
habilityle bounds that do not have a term that is quadratic in the number o=
f queries (like the ones we would
 get if we used all of the bits). Roughly speaking the truncation gets us a=
 term that looks like q/2^(96) instead of q^2/2^{129}. The bounds and discu=
ssion can be seen at =C2=A0[2].</div>
</div>
</div>
</div>
</blockquote>
</span>
<div><br>
</div>
</span><div>
<div>Asymptotically yes, but in this case we have q=3D2 and q=3D3 and any d=
isadvantage of using a PRP should be negligible.</div>
<div>In fact, if the above terms were true for small q (which they are like=
ly not) the the then quadratic term is preferable as =C2=A02^2/2^{129} =3D =
1/2^{127} &lt;&lt; 2/2^{96} =3D 1/2^{95}</div>
<div>Feels like doubling the amount of AES operations may be overkill and n=
ot worth the=C2=A0negligible=C2=A0security increase. GCM is popular for its=
 performance, not for high security bounds.</div>
</div><div><div class=3D"gmail-h5">
<div><br>
</div>
<span id=3D"gmail-m_2063633427090501980OLK_SRC_BODY_SECTION">
<blockquote id=3D"gmail-m_2063633427090501980MAC_OUTLOOK_ATTRIBUTION_BLOCKQ=
UOTE">
<div>
<div>
<div dir=3D"rtl">
<div dir=3D"ltr">=C2=A0</div>
<div dir=3D"ltr"><br>
</div>
<div dir=3D"ltr">Anyway an organized paper with a statement on the security=
 bounds, is going to come out in a paper that we are working on these very =
days. We will post it soon.=C2=A0</div>
<div dir=3D"ltr"><br>
</div>
<div dir=3D"ltr">Thank you, Shay=C2=A0</div>
<div><br>
</div>
<div dir=3D"ltr">[1] <a href=3D"https://crypto.stanford.edu/RealWorldCrypto=
/slides/gueron.pdf" target=3D"_blank">
https://crypto.stanford.edu/<wbr>RealWorldCrypto/slides/gueron.<wbr>pdf</a>=
<br>
</div>
<div dir=3D"ltr"><br>
</div>
<div dir=3D"ltr">[2] S. Gilboa, S. Gueron, =E2=80=9CThe Advantage of Trunca=
ted Permutations=E2=80=9D,=C2=A0</div>
<div dir=3D"ltr"><a href=3D"https://arxiv.org/abs/1610.02518" target=3D"_bl=
ank">https://arxiv.org/abs/1610.<wbr>02518</a> =C2=A0 (submitted on 8 Oct 2=
016).=C2=A0</div>
</div>
<div class=3D"gmail_extra"><br>
<div class=3D"gmail_quote">
<div dir=3D"ltr">2017-01-18 16:13 GMT-08:00 Adam Langley <span dir=3D"ltr">=
&lt;<a href=3D"mailto:agl@imperialviolet.org" target=3D"_blank">agl@imperia=
lviolet.org</a>&gt;</span>:</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">
<span>On Wed, Jan 18, 2017 at 1:05 PM, John Mattsson<br>
&lt;<a href=3D"mailto:john.mattsson@ericsson.com" target=3D"_blank">john.ma=
ttsson@ericsson.com</a>&gt; wrote:<br>
&gt; - In addition to listing the performance penalty compared to GCM. The<=
br>
&gt;=C2=A0 =C2=A0draft should also mention that compared to GCM, some nice =
properties<br>
&gt;=C2=A0 =C2=A0disappear:<br>
&gt;=C2=A0 =C2=A0- Neither Encryption nor Decryption is online as encryptio=
n/decryption<br>
&gt;=C2=A0 =C2=A0 =C2=A0cannot start before the whole plaintext/ciphertext =
is known.<br>
<br>
</span>I agree that this is true for encryption, but I don&#39;t believe th=
at<br>
AES-GCM should be *de*crypted in a streaming fashion, but rather that<br>
records should be sized so that this isn&#39;t a problem. (At which point<b=
r>
the benefit for streaming encryption becomes small or moot.)<br>
<br>
I&#39;ve a long spiel about the dangers of processing unauthenticated<br>
ciphertext which I&#39;ll spare you :) But, even for small machines, the<br=
>
memory needed to safely buffer the decrypted plaintext to avoid<br>
releasing it before it&#39;s authenticated is equal to the memory to<br>
buffer the ciphertext followed by decrypting in-place.<br>
<br>
So I actually quite like that the tag is at the end of the message<br>
with AES-GCM-SIV because it makes it harder to do what I think is the<br>
&quot;wrong&quot; thing.<br>
<span><br>
&gt;=C2=A0 =C2=A0- GCM-SIV removes the possibility to preprocess static hea=
ders (AAD).<br>
<br>
</span>Indeed.<br>
<br>
(I wasn&#39;t sure where to put these points in the spec so, for the<br>
moment, I&#39;ve added an appendix for &quot;Additional comparisons with<br=
>
AES-GCM&quot;. I&#39;m collecting changes in GitHub before making a new<br>
version. For this message, see<br>
<a href=3D"https://github.com/agl/gcmsiv/commit/c6c7fd388dd122251264222b749=
1c6212e818319" rel=3D"noreferrer" target=3D"_blank">https://github.com/agl/=
gcmsiv/<wbr>commit/c6c7fd388dd122251264222<wbr>b7491c6212e818319</a>.)<br>
<span><br>
&gt; - =E2=80=9CThe result of the encryption is the resulting ciphertext (t=
runcated<br>
&gt;=C2=A0 =C2=A0 to the length of the plaintext) followed by the tag.&quot=
;<br>
&gt;<br>
&gt;=C2=A0 =C2=A0I suggest that the tag is placed first instead of last in =
the<br>
&gt;=C2=A0 =C2=A0ciphertext. This makes decryption online, which makes a la=
rge<br>
&gt;=C2=A0 =C2=A0difference. Suggestion:<br>
&gt;<br>
&gt;=C2=A0 =C2=A0=E2=80=9CThe result of the encryption is the tag followed =
by the ciphertext<br>
&gt;=C2=A0 =C2=A0 (truncated to the length of the plaintext)&quot;<br>
<br>
</span>(See above.)<br>
<span><br>
&gt;<br>
&gt;<br>
&gt; - &quot;within 5% of the speed of AES-GCM.&quot;<br>
&gt;=C2=A0 =C2=A0Should state when this is the case, e.g. long plaintext/aa=
d.<br>
<br>
</span>Done.<br>
<span><br>
&gt;<br>
&gt; - I think the draft should give performance data also for short<br>
&gt;=C2=A0 =C2=A0plaintexts/aad or even better list the performance in numb=
er of<br>
&gt;=C2=A0 =C2=A0operations:<br>
&gt;<br>
&gt;=C2=A0 =C2=A0GCM:<br>
&gt;=C2=A0 =C2=A0 =C2=A0Block Cipher Operations =3D p + 1<br>
&gt;=C2=A0 =C2=A0 =C2=A0GF(2^128) Multiplications =3D p + a + 1<br>
&gt;<br>
&gt;=C2=A0 =C2=A0GCM-SIV-128<br>
&gt;=C2=A0 =C2=A0 =C2=A0Block Cipher Operations =3D p + 5<br>
&gt;=C2=A0 =C2=A0 =C2=A0GF(2^128) Multiplications =3D p + a + 1<br>
&gt;<br>
&gt;=C2=A0 =C2=A0GCM-SIV-256<br>
&gt;=C2=A0 =C2=A0 =C2=A0Block Cipher Operations =3D p + 7<br>
&gt;=C2=A0 =C2=A0 =C2=A0GF(2^128) Multiplications =3D p + a + 1<br>
&gt;<br>
&gt;=C2=A0 =C2=A0(if I got it right...)<br>
<br>
</span>I think that&#39;s correct and I&#39;ve added that to the new append=
ix.<br>
<span><br>
&gt;=C2=A0 =C2=A0Where p is the block length of the plaintext and a is the =
block length<br>
&gt;=C2=A0 =C2=A0of the additional authenticated data,<br>
&gt;<br>
&gt;=C2=A0 =C2=A0I doubt that encryption of short messages are anywhere nea=
r 5% of GCM.<br>
&gt;<br>
&gt; - The &quot;++&quot; and &quot;[:8]&quot; operation should probably be=
 defined.<br>
<br>
</span>Done.<br>
<span><br>
&gt;<br>
&gt; - What it the security/performance tradeoff with truncation in the key=
<br>
&gt;=C2=A0 =C2=A0derivation? What would the security properties be if &quot=
;[:8]&quot; was<br>
&gt;=C2=A0 =C2=A0removed?<br>
<br>
</span>I&#39;ll have to let Shay answer this, but the rough idea is that, s=
ince<br>
AES is a permutation, not two ciphertexts can be equal given that<br>
we&#39;re encrypting different plaintexts using the KDF phase. However,<br>
ideally we would want a PRF where outputs can be the same. By taking<br>
only the first eight bytes of each ciphertext block, we better<br>
approximate a PRF.<br>
<span><br>
&gt; - The definition of U32LE seems unnecessary and only adds complexity.<=
br>
&gt;=C2=A0 =C2=A0I suggest:<br>
&gt;=C2=A0 =C2=A0 =C2=A0OLD &quot;U32LE(3) ++ nonce&quot;<br>
&gt;=C2=A0 =C2=A0 =C2=A0NEW &quot;03 ++ 000000 ++ nonce<br>
<br>
</span>Good point.<br>
<span><br>
&gt;<br>
&gt; - The term K1 is only used in Test Vectors. I guess it is an old term<=
br>
&gt;=C2=A0 =C2=A0that should be removed.<br>
<br>
</span>Done.<br>
<br>
&gt; Some editorials:<br>
<br>
Thank you for all these. They should be taken care of.<br>
<span><br>
&gt; - OLD &quot;The record-authentication key is 128-bit and the<br>
&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 record-authentication key&quot;<br>
&gt;=C2=A0 =C2=A0NEW &quot;The record-authentication key is 128-bit and the=
<br>
&gt;=C2=A0 =C2=A0 =C2=A0 =C2=A0 record-encryption key&quot;<br>
&gt;<br>
&gt; - &quot;} else if bytelen(key-generating-key) =3D=3D 32 {<br>
&gt;=C2=A0 =C2=A0 =C2=A0 record-encryption-key =3D AES128(key =3D key-gener=
ating-key,&quot;<br>
&gt;<br>
&gt;=C2=A0 =C2=A0Should be AES256<br>
<br>
</span>Indeed, and record-authentication-key is wrong too!<br>
<span><br>
&gt; - Spacing around &quot;+&quot; and &quot;*&quot; are not consistent.<b=
r>
&gt;<br>
&gt; - &quot;the the&quot;<br>
&gt;<br>
&gt; - yeilds<br>
&gt;<br>
&gt; - remainding<br>
&gt;<br>
&gt; - RFC7322 says &quot;A comma is used before the last item of a series&=
quot;<br>
<br>
</span>I think I&#39;ve leave this one to the RFC Editor!<br>
<br>
<br>
<br>
Cheers<br>
<br>
AGL<br>
<div class=3D"gmail-m_2063633427090501980HOEnZb">
<div class=3D"gmail-m_2063633427090501980h5"><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>
</div>
</div>
</blockquote>
</div>
<br>
</div>
</div>
</div>
</blockquote>
</span>
</div></div></div>

</blockquote></div><br></div></div>

--001a114e72b2a40c34054672cf88--


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From: "Paterson, Kenny" <Kenny.Paterson@rhul.ac.uk>
To: Leonard den Ottolander <leonard-lists@den.ottolander.nl>, "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] A little room for AES-192 in TLS?
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Subject: Re: [Cfrg] A little room for AES-192 in TLS?
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From: Shay Gueron <shay.gueron@gmail.com>
Date: Wed, 18 Jan 2017 09:55:19 -0800
Message-ID: <CAHP81y_EWwK57cHkN7_rLreHWJ5fvjKL9FhqnRsCpKFp3H=SOg@mail.gmail.com>
To: Adam Langley <agl@imperialviolet.org>
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Cc: "Cooley, Dorothy E" <decoole@nsa.gov>, Yehuda Lindell <Yehuda.Lindell@biu.ac.il>, "cfrg@irtf.org" <cfrg@irtf.org>
Subject: Re: [Cfrg] AES GCM SIV analysis
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Dear CFRG,

In the interests of keeping things on the working-group mailing list, I am
including the two follow-ups that we sent, previously, in response to this

(note: the discussion with  "NSA Information Assurance Standards" team took
place in two  back-and-forth iterations. Hence we sent two replies, which
are attached here).

Due to the limit on the size of a posting, the two files will be
transmitted in two separate mails.

This attachment: Reply 1

Thank you, Shay Gueron


2017-01-18 9:46 GMT-08:00 Shay Gueron <shay.gueron@gmail.com>:

> Dear CFRG,
>
>
> In the interests of keeping things on the working-group mailing list, I am
> including the two follow-ups that we sent, previously, in response to this
>
>
> (note: the discussion with  "NSA Information Assurance Standards" team
> took place in two  back-and-forth iterations. Hence we sent two replies,
> which are attached here).
>
>
> Thank you, Shay Gueron
>
>
>
> 2017-01-18 9:34 GMT-08:00 Adam Langley <agl@imperialviolet.org>:
>
>> On Wed, Jan 18, 2017 at 8:49 AM, Cooley, Dorothy E <decoole@nsa.gov>
>> wrote:
>> > NSA's Information Assurance organization did some analysis of
>> AES-GCM-SIV,
>> > as described in "AES-GCM-SIV:  Nonce Misuse-Resistant Authenticated
>> > Encryption", dated August 29, 2016 [1].  We shared this analysis
>> privately
>> > with the three authors of AES-GCM-SIV, who requested that we post it to
>> the
>> > CFRG forum. The attachment describes the results of the analysis. We
>> believe
>> > the authors will be posting an update shortly.
>> >
>> >
>> >
>> > Any comments on this work can be directed to me.  But I will note that I
>> > didn't do the actual analysis (I can't claim to be a 'real'
>> cryptographer
>> > these days).
>> >
>> >
>> >
>> > Deb Cooley
>> >
>> > NSA Information Assurance Standards.
>> >
>> > decoole@nsa.gov
>>
>> Dear CFRG,
>>
>> We thank Deb Cooley's team very much for doing this analysis! As she
>> mentioned, they shared their results with us prior to posting here so
>> we already had an update ready and we've just posted
>> https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03.
>>
>> This update contains three noteworthy changes:
>>
>> 1) We now XOR the nonce into the result of POLYVAL before encrypting
>> to form the tag. This was in the original paper, it was even specified
>> for /decryption/ in -02, but it was omitted in the specification for
>> encryption. This was a mistake. Without it, an attacker can build a
>> lookup table of encryptions of zero under a variety of per-nonce keys
>> and then attack them in parallel (as pointed out in the comments from
>> the IAD), under a single-user-multi-key model.
>>
>> Draft -03 fixes this omission and reintroduces the nonce.
>>
>> 2) A different KDF. As I mentioned at the previous CFRG meeting (in
>> Seoul, 2016) , we had this design in mind but didn't feel that it
>> warranted a new version of the design. However, since we needed a
>> respin because of (1), we have included it.
>>
>> Previously, per-nonce key material was generated by repeated
>> encryption, E(nonce), E(E(nonce)), and so on. This cascade leads to
>> impractical but needling issues including those noted by IAD. We now
>> generate keys by using counter mode and discarding half of each
>> ciphertext block. This solves those issues and also gives improved
>> indistinguishability bounds.
>>
>> In order to make room for the counter, the nonce size has been reduced
>> to 96 bits.
>>
>> 3) A much more minor change is that we now suggest a limit of 2^8 as
>> the maximum number of plaintexts encrypted with a single nonce. We
>> previously noted that AES-GCM-SIV with a fixed nonce is similar to
>> AES-GCM with a random nonce, and that NIST recommends a limit of 2^32
>> messages in that context.
>>
>> Note that we do NOT recommend nonce reuse by choice even inside
>> AES-GCM-SIV. This is for two reasons. First, encrypting the same
>> message twice will be detected. Second, the security bounds when using
>> different nonces are better. For example, when encrypting 2^{32}
>> messages with the same nonce, the probability of a bad event is
>> 2^{-32}. However, as we have shown, when encryption with different
>> nonces, it is possible to go up to about 2^{50} messages without any
>> problem.
>>
>> If nonces repeat mistakenly, for which providing protection is the
>> main aim of this mode of operation, then very strong bounds are still
>> obtained for a large number of ciphertexts (much more than 2^32) as
>> long as a single nonce is not repeated more than say 2^8 times. In
>> practice, such an event is highly unlikely.
>>
>>
>>
>> Cheers
>>
>> AGL
>>
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org
>> https://www.irtf.org/mailman/listinfo/cfrg
>>
>
>

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

<div dir=3D"rtl"><div dir=3D"ltr"><div dir=3D"ltr">Dear CFRG,=C2=A0</div><d=
iv dir=3D"ltr"><br></div><div dir=3D"ltr">In the interests of keeping thing=
s on the working-group mailing list, I am including the two follow-ups that=
 we sent, previously, in response to this=C2=A0</div><div dir=3D"ltr"><br><=
/div><div dir=3D"ltr">(note: the discussion with =C2=A0&quot;NSA Informatio=
n Assurance Standards&quot; team took place in two =C2=A0back-and-forth ite=
rations. Hence we sent two replies, which are attached here).=C2=A0</div><d=
iv dir=3D"ltr"><br></div><div dir=3D"ltr">Due to the limit on the size of a=
 posting, the two files will be transmitted in two separate mails.=C2=A0</d=
iv><div dir=3D"ltr"><br></div><div dir=3D"ltr">This attachment: Reply 1</di=
v><div dir=3D"ltr"><br></div><div dir=3D"ltr">Thank you, Shay Gueron</div><=
div><br></div></div></div><div class=3D"gmail_extra"><div dir=3D"ltr"><br><=
div class=3D"gmail_quote">2017-01-18 9:46 GMT-08:00 Shay Gueron <span dir=
=3D"ltr">&lt;<a href=3D"mailto:shay.gueron@gmail.com" target=3D"_blank">sha=
y.gueron@gmail.com</a>&gt;</span>:<br><blockquote class=3D"gmail_quote" sty=
le=3D"margin:0 .8ex;border-left:1px #ccc solid;border-right:1px #ccc solid;=
padding-left:1ex;padding-right:1ex"><div dir=3D"rtl"><div dir=3D"ltr"><p cl=
ass=3D"MsoNormal">Dear CFRG,=C2=A0</p><p class=3D"MsoNormal"><br></p><p cla=
ss=3D"MsoNormal">In the interests of keeping things on the working-group
mailing list, I am including the two follow-ups that we sent, previously, i=
n
response to this=C2=A0</p><p class=3D"MsoNormal"><br></p><p class=3D"MsoNor=
mal">(note: the discussion with =C2=A0&quot;NSA Information Assurance Stand=
ards&quot; team took place in two =C2=A0back-and-forth iterations. Hence we=
 sent two replies, which are attached here).=C2=A0</p><p class=3D"MsoNormal=
"><br></p><p class=3D"MsoNormal">Thank you, Shay Gueron</p><p class=3D"MsoN=
ormal"><br></p></div></div><div class=3D"HOEnZb"><div class=3D"h5"><div cla=
ss=3D"gmail_extra"><br><div class=3D"gmail_quote"><div dir=3D"ltr">2017-01-=
18 9:34 GMT-08:00 Adam Langley <span dir=3D"ltr">&lt;<a href=3D"mailto:agl@=
imperialviolet.org" target=3D"_blank">agl@imperialviolet.org</a>&gt;</span>=
:</div><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-=
left:1px #ccc solid;padding-left:1ex"><span>On Wed, Jan 18, 2017 at 8:49 AM=
, Cooley, Dorothy E &lt;<a href=3D"mailto:decoole@nsa.gov" target=3D"_blank=
">decoole@nsa.gov</a>&gt; wrote:<br>
&gt; NSA&#39;s Information Assurance organization did some analysis of AES-=
GCM-SIV,<br>
&gt; as described in &quot;AES-GCM-SIV:=C2=A0 Nonce Misuse-Resistant Authen=
ticated<br>
&gt; Encryption&quot;, dated August 29, 2016 [1].=C2=A0 We shared this anal=
ysis privately<br>
&gt; with the three authors of AES-GCM-SIV, who requested that we post it t=
o the<br>
&gt; CFRG forum. The attachment describes the results of the analysis. We b=
elieve<br>
&gt; the authors will be posting an update shortly.<br>
&gt;<br>
&gt;<br>
&gt;<br>
&gt; Any comments on this work can be directed to me.=C2=A0 But I will note=
 that I<br>
&gt; didn&#39;t do the actual analysis (I can&#39;t claim to be a &#39;real=
&#39; cryptographer<br>
&gt; these days).<br>
&gt;<br>
&gt;<br>
&gt;<br>
&gt; Deb Cooley<br>
&gt;<br>
&gt; NSA Information Assurance Standards.<br>
&gt;<br>
&gt; <a href=3D"mailto:decoole@nsa.gov" target=3D"_blank">decoole@nsa.gov</=
a><br>
<br>
</span>Dear CFRG,<br>
<br>
We thank Deb Cooley&#39;s team very much for doing this analysis! As she<br=
>
mentioned, they shared their results with us prior to posting here so<br>
we already had an update ready and we&#39;ve just posted<br>
<a href=3D"https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03" rel=3D"no=
referrer" target=3D"_blank">https://tools.ietf.org/html/dr<wbr>aft-irtf-cfr=
g-gcmsiv-03</a>.<br>
<br>
This update contains three noteworthy changes:<br>
<br>
1) We now XOR the nonce into the result of POLYVAL before encrypting<br>
to form the tag. This was in the original paper, it was even specified<br>
for /decryption/ in -02, but it was omitted in the specification for<br>
encryption. This was a mistake. Without it, an attacker can build a<br>
lookup table of encryptions of zero under a variety of per-nonce keys<br>
and then attack them in parallel (as pointed out in the comments from<br>
the IAD), under a single-user-multi-key model.<br>
<br>
Draft -03 fixes this omission and reintroduces the nonce.<br>
<br>
2) A different KDF. As I mentioned at the previous CFRG meeting (in<br>
Seoul, 2016) , we had this design in mind but didn&#39;t feel that it<br>
warranted a new version of the design. However, since we needed a<br>
respin because of (1), we have included it.<br>
<br>
Previously, per-nonce key material was generated by repeated<br>
encryption, E(nonce), E(E(nonce)), and so on. This cascade leads to<br>
impractical but needling issues including those noted by IAD. We now<br>
generate keys by using counter mode and discarding half of each<br>
ciphertext block. This solves those issues and also gives improved<br>
indistinguishability bounds.<br>
<br>
In order to make room for the counter, the nonce size has been reduced<br>
to 96 bits.<br>
<br>
3) A much more minor change is that we now suggest a limit of 2^8 as<br>
the maximum number of plaintexts encrypted with a single nonce. We<br>
previously noted that AES-GCM-SIV with a fixed nonce is similar to<br>
AES-GCM with a random nonce, and that NIST recommends a limit of 2^32<br>
messages in that context.<br>
<br>
Note that we do NOT recommend nonce reuse by choice even inside<br>
AES-GCM-SIV. This is for two reasons. First, encrypting the same<br>
message twice will be detected. Second, the security bounds when using<br>
different nonces are better. For example, when encrypting 2^{32}<br>
messages with the same nonce, the probability of a bad event is<br>
2^{-32}. However, as we have shown, when encryption with different<br>
nonces, it is possible to go up to about 2^{50} messages without any<br>
problem.<br>
<br>
If nonces repeat mistakenly, for which providing protection is the<br>
main aim of this mode of operation, then very strong bounds are still<br>
obtained for a large number of ciphertexts (much more than 2^32) as<br>
long as a single nonce is not repeated more than say 2^8 times. In<br>
practice, such an event is highly unlikely.<br>
<br>
<br>
<br>
Cheers<br>
<br>
AGL<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>
</blockquote></div><br></div>
</div></div></blockquote></div></div></div>

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From: Shay Gueron <shay.gueron@gmail.com>
Date: Wed, 18 Jan 2017 10:06:33 -0800
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To: Adam Langley <agl@imperialviolet.org>
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Cc: "Cooley, Dorothy E" <decoole@nsa.gov>, Yehuda Lindell <Yehuda.Lindell@biu.ac.il>, "cfrg@irtf.org" <cfrg@irtf.org>
Subject: Re: [Cfrg] AES GCM SIV analysis
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Dear CFRG,

In the interests of keeping things on the working-group mailing list, I am
including the two follow-ups that we sent, previously, in response to this.


A note: the discussion with  "NSA Information Assurance Standards" team
took place in two  back-and-forth iterations. Hence we sent two replies,
which are attached here.

Thank you, Shay Gueron


2017-01-18 9:34 GMT-08:00 Adam Langley <agl@imperialviolet.org>:

> On Wed, Jan 18, 2017 at 8:49 AM, Cooley, Dorothy E <decoole@nsa.gov>
> wrote:
> > NSA's Information Assurance organization did some analysis of
> AES-GCM-SIV,
> > as described in "AES-GCM-SIV:  Nonce Misuse-Resistant Authenticated
> > Encryption", dated August 29, 2016 [1].  We shared this analysis
> privately
> > with the three authors of AES-GCM-SIV, who requested that we post it to
> the
> > CFRG forum. The attachment describes the results of the analysis. We
> believe
> > the authors will be posting an update shortly.
> >
> >
> >
> > Any comments on this work can be directed to me.  But I will note that I
> > didn't do the actual analysis (I can't claim to be a 'real' cryptographer
> > these days).
> >
> >
> >
> > Deb Cooley
> >
> > NSA Information Assurance Standards.
> >
> > decoole@nsa.gov
>
> Dear CFRG,
>
> We thank Deb Cooley's team very much for doing this analysis! As she
> mentioned, they shared their results with us prior to posting here so
> we already had an update ready and we've just posted
> https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03.
>
> This update contains three noteworthy changes:
>
> 1) We now XOR the nonce into the result of POLYVAL before encrypting
> to form the tag. This was in the original paper, it was even specified
> for /decryption/ in -02, but it was omitted in the specification for
> encryption. This was a mistake. Without it, an attacker can build a
> lookup table of encryptions of zero under a variety of per-nonce keys
> and then attack them in parallel (as pointed out in the comments from
> the IAD), under a single-user-multi-key model.
>
> Draft -03 fixes this omission and reintroduces the nonce.
>
> 2) A different KDF. As I mentioned at the previous CFRG meeting (in
> Seoul, 2016) , we had this design in mind but didn't feel that it
> warranted a new version of the design. However, since we needed a
> respin because of (1), we have included it.
>
> Previously, per-nonce key material was generated by repeated
> encryption, E(nonce), E(E(nonce)), and so on. This cascade leads to
> impractical but needling issues including those noted by IAD. We now
> generate keys by using counter mode and discarding half of each
> ciphertext block. This solves those issues and also gives improved
> indistinguishability bounds.
>
> In order to make room for the counter, the nonce size has been reduced
> to 96 bits.
>
> 3) A much more minor change is that we now suggest a limit of 2^8 as
> the maximum number of plaintexts encrypted with a single nonce. We
> previously noted that AES-GCM-SIV with a fixed nonce is similar to
> AES-GCM with a random nonce, and that NIST recommends a limit of 2^32
> messages in that context.
>
> Note that we do NOT recommend nonce reuse by choice even inside
> AES-GCM-SIV. This is for two reasons. First, encrypting the same
> message twice will be detected. Second, the security bounds when using
> different nonces are better. For example, when encrypting 2^{32}
> messages with the same nonce, the probability of a bad event is
> 2^{-32}. However, as we have shown, when encryption with different
> nonces, it is possible to go up to about 2^{50} messages without any
> problem.
>
> If nonces repeat mistakenly, for which providing protection is the
> main aim of this mode of operation, then very strong bounds are still
> obtained for a large number of ciphertexts (much more than 2^32) as
> long as a single nonce is not repeated more than say 2^8 times. In
> practice, such an event is highly unlikely.
>
>
>
> Cheers
>
> AGL
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>

--94eb2c0b8d1ef19e6e05466246c2
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

<div dir=3D"rtl"><div dir=3D"ltr">Dear CFRG,=C2=A0<br></div><div dir=3D"ltr=
"><div dir=3D"ltr"><br></div><div dir=3D"ltr">In the interests of keeping t=
hings on the working-group mailing list, I am including the two follow-ups =
that we sent, previously, in response to this. =C2=A0</div><div dir=3D"ltr"=
><br></div><div dir=3D"ltr">A note: the discussion with =C2=A0&quot;NSA Inf=
ormation Assurance Standards&quot; team took place in two =C2=A0back-and-fo=
rth iterations. Hence we sent two replies, which are attached here.=C2=A0</=
div><div dir=3D"ltr"><br></div><div dir=3D"ltr">Thank you, Shay Gueron</div=
><div><br></div></div></div><div class=3D"gmail_extra"><br><div class=3D"gm=
ail_quote"><div dir=3D"ltr">2017-01-18 9:34 GMT-08:00 Adam Langley <span di=
r=3D"ltr">&lt;<a href=3D"mailto:agl@imperialviolet.org" target=3D"_blank">a=
gl@imperialviolet.org</a>&gt;</span>:</div><blockquote class=3D"gmail_quote=
" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><=
span class=3D"">On Wed, Jan 18, 2017 at 8:49 AM, Cooley, Dorothy E &lt;<a h=
ref=3D"mailto:decoole@nsa.gov">decoole@nsa.gov</a>&gt; wrote:<br>
&gt; NSA&#39;s Information Assurance organization did some analysis of AES-=
GCM-SIV,<br>
&gt; as described in &quot;AES-GCM-SIV:=C2=A0 Nonce Misuse-Resistant Authen=
ticated<br>
&gt; Encryption&quot;, dated August 29, 2016 [1].=C2=A0 We shared this anal=
ysis privately<br>
&gt; with the three authors of AES-GCM-SIV, who requested that we post it t=
o the<br>
&gt; CFRG forum. The attachment describes the results of the analysis. We b=
elieve<br>
&gt; the authors will be posting an update shortly.<br>
&gt;<br>
&gt;<br>
&gt;<br>
&gt; Any comments on this work can be directed to me.=C2=A0 But I will note=
 that I<br>
&gt; didn&#39;t do the actual analysis (I can&#39;t claim to be a &#39;real=
&#39; cryptographer<br>
&gt; these days).<br>
&gt;<br>
&gt;<br>
&gt;<br>
&gt; Deb Cooley<br>
&gt;<br>
&gt; NSA Information Assurance Standards.<br>
&gt;<br>
&gt; <a href=3D"mailto:decoole@nsa.gov">decoole@nsa.gov</a><br>
<br>
</span>Dear CFRG,<br>
<br>
We thank Deb Cooley&#39;s team very much for doing this analysis! As she<br=
>
mentioned, they shared their results with us prior to posting here so<br>
we already had an update ready and we&#39;ve just posted<br>
<a href=3D"https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03" rel=3D"no=
referrer" target=3D"_blank">https://tools.ietf.org/html/<wbr>draft-irtf-cfr=
g-gcmsiv-03</a>.<br>
<br>
This update contains three noteworthy changes:<br>
<br>
1) We now XOR the nonce into the result of POLYVAL before encrypting<br>
to form the tag. This was in the original paper, it was even specified<br>
for /decryption/ in -02, but it was omitted in the specification for<br>
encryption. This was a mistake. Without it, an attacker can build a<br>
lookup table of encryptions of zero under a variety of per-nonce keys<br>
and then attack them in parallel (as pointed out in the comments from<br>
the IAD), under a single-user-multi-key model.<br>
<br>
Draft -03 fixes this omission and reintroduces the nonce.<br>
<br>
2) A different KDF. As I mentioned at the previous CFRG meeting (in<br>
Seoul, 2016) , we had this design in mind but didn&#39;t feel that it<br>
warranted a new version of the design. However, since we needed a<br>
respin because of (1), we have included it.<br>
<br>
Previously, per-nonce key material was generated by repeated<br>
encryption, E(nonce), E(E(nonce)), and so on. This cascade leads to<br>
impractical but needling issues including those noted by IAD. We now<br>
generate keys by using counter mode and discarding half of each<br>
ciphertext block. This solves those issues and also gives improved<br>
indistinguishability bounds.<br>
<br>
In order to make room for the counter, the nonce size has been reduced<br>
to 96 bits.<br>
<br>
3) A much more minor change is that we now suggest a limit of 2^8 as<br>
the maximum number of plaintexts encrypted with a single nonce. We<br>
previously noted that AES-GCM-SIV with a fixed nonce is similar to<br>
AES-GCM with a random nonce, and that NIST recommends a limit of 2^32<br>
messages in that context.<br>
<br>
Note that we do NOT recommend nonce reuse by choice even inside<br>
AES-GCM-SIV. This is for two reasons. First, encrypting the same<br>
message twice will be detected. Second, the security bounds when using<br>
different nonces are better. For example, when encrypting 2^{32}<br>
messages with the same nonce, the probability of a bad event is<br>
2^{-32}. However, as we have shown, when encryption with different<br>
nonces, it is possible to go up to about 2^{50} messages without any<br>
problem.<br>
<br>
If nonces repeat mistakenly, for which providing protection is the<br>
main aim of this mode of operation, then very strong bounds are still<br>
obtained for a large number of ciphertexts (much more than 2^32) as<br>
long as a single nonce is not repeated more than say 2^8 times. In<br>
practice, such an event is highly unlikely.<br>
<br>
<br>
<br>
Cheers<br>
<br>
AGL<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>
</blockquote></div><br></div>

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From: Adam Langley <agl@imperialviolet.org>
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Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt
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On Thu, Jan 19, 2017 at 2:19 AM, John Mattsson
<john.mattsson@ericsson.com> wrote:
> - The use of one-time authentication keys has the benefit that it
> mitigates Fergusson=E2=80=99s authentication key recovery attack on GCM i=
n the
> two-party case. In case of multicast the attack remains (but significantl=
y
> restricted). This makes GCM-SIV a little bit more suitable for truncated
> tags than GCM. I think these advantages should be mentioned.

Thanks. I've added a TODO locally to think about this. I'm not sure
that we want to mention truncating authentication tags because that
seems contrary to the general thrust of robustness here. I'll see
whether I can say something about the advantages of the one-time
authentication keys in general however.

>>So I actually quite like that the tag is at the end of the message
>>with AES-GCM-SIV because it makes it harder to do what I think is the
>>"wrong" thing.
>
> I would agree with you if placing the tag last actually improved anything=
,
> but the fact is that GCM-SIV actually forces processing of unauthenticate=
d
> ciphertext by design (a change from GCM). I cannot see any security
> benefits with (C, T) compared to (T, C). The only difference I can see is
> that (C, T) increases the latency for decryption on multicore.

I don't understand why AES-GCM-SIV forces the processing of
unauthenticated plaintext. I think we might have different
definitions.

To me, processing authenticated plaintext means that the crypto API
releases plaintext for other processing before it has authenticated
it. It doesn't mean that the plaintext cannot sit in memory during
decryption while the AEAD checks the tag. (Indeed, many GCM
implementations interleave decryption and calculation of the GHASH
value.)

So putting the tag at the end prevents such APIs from being written,
which I think is a benefit.

A second benefit to putting tags at the end is that it's generally
easier to have extra space at the end of a buffer than the beginning.
This is not precise and might be a result of my C/C++/Go-based
environment, but I'm going to claim that a (buf, len, max) pattern is
easier for people to do with in an API than a (buf,
initial-padding-length, len).

In a case where space at the end of a buffer is easier to deal with,
putting the tag at the end is nicer because, otherwise,
encryption-in-place has to write ciphertext blocks 16 bytes in advance
of where it read them. In order to avoid clobbering the next plaintext
block, that has to copied first. I admit it's only a minor problem.

On the other hand, I'm not sure that I see the benefits of putting the
tag first in terms of latency on multicore machines. The AEAD model is
that the whole ciphertext is in memory when the operation is called so
it's as easy to read the tag from the end as from the beginning.

I can see an advantage in cases where the system could start
decrypting while the remainder of the record was still being read. Was
that what you had in mind? At least for multicore machines, I don't
think records should be so large that it makes a difference though.



Cheers

AGL


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From: Adam Langley <agl@imperialviolet.org>
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Subject: Re: [Cfrg] AES GCM SIV analysis
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On Wed, Jan 18, 2017 at 7:53 PM, Brian Smith <brian@briansmith.org> wrote:
> Perhaps: "We recommend instead that an implementation try to avoid
> repeating a nonce for a specific key, just like it would it would do
> for an AEAD that isn't nonce-misuse-resistant." This shifts the
> emphasis away from the 2^8 number to where it belongs, IMO. Note that
> "256" and how it is derived and why it is safe is explained in the
> next paragraph anyway.

After some discussions on Twitter I've discovered that several people
(possibly including Brian) understand "nonce-misuse resistant" to mean
a stronger property than AES-GCM-SIV has. Namely they understood it to
mean that the value of the nonce is /irrelevant/ for security, except
that a fixed nonce discloses equality of plaintexts.

AES-GCM-SIV doesn't have this property. It is robust to random nonce
duplication but not designed for a fixed nonce. Specifically, after
2^n full-sized (i.e. 64MB) messages, there's ~2^(96-2n) chance that
two of the messages reused counter values and thus keystream. (The
bounds are better if messages are smaller.)

Consider a broken TLS implementation that always uses a zero nonce and
is sending 16KB records as fast as possible. By the time it has sent
2^40 records (44 TB) there's about a 2^-32 chance that two of those
records shared keystream bytes. (That's very rough and there might be
a few stray factors of two missing in there.)

That's a lot better than AES-GCM, but we're not saying that the nonces
are completely irrelevant to security.

Perhaps we need a different term to clarify this? Occasional nonce
duplication tolerant?

>> I agree that large AEAD messages have several problems. But I don't
>> think that we have any need for a larger nonce (see above). (And the
>> nonce is used with a counter only in the KDF phase, so it's unrelated
>> to the maximum plaintext size.)
>
> Is there any way that a larger nonce (e.g. 120 bits) hurts, other than
> being inconsistent with existing IETF AEADs?

With three bits for the counter, the largest the nonce could be is 125
bits. But I think a nonce that's not a whole number of bytes would be
too confusing.

The nonce could be 120 bits (15 bytes) but that has no practical
advantage over 96 bits. If you're picking nonces at random then the
change in bounds is trivial (see multibirthday reference in the spec).
If your nonce generation is broken and you're using a fixed value then
the size is irrelevant.

96 bits is a "rounder" number and might save some alignment problems
is all, really.


Cheers

AGL

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


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From: "Dang, Quynh (Fed)" <quynh.dang@nist.gov>
To: "shay@math.haifa.ac.il" <shay@math.haifa.ac.il>, "agl@google.com" <agl@google.com>, "Yehuda.Lindell@biu.ac.il" <Yehuda.Lindell@biu.ac.il>
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Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt
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Shay, Adam and Yehuda,


There are 2 things I hope to discuss in this email below.


1) The draft said that "We recommend a limit of 2^50 plaintexts encrypted w=
ith a given key. Past this point, AES-GCM-SIV may be distinguishable from a=
n ideal AEAD.  (This is based on standard assumptions about AES.)".


To keep the probability of having a collision among 128-bit blocks in the c=
iphtertexts below 1/2^32 (practically zero), it has been suggested that und=
er a given key, the amount of ciphertexts is not more than 2^48 128-bit blo=
cks for the GCM in TLS 1.3.


With 2^50 plaintexts (equivalent amount of ciphertexts) and each ciphertext=
 can be up to 2^32 128-bit blocks in the GCM-SIV draft, there can be collis=
ion situations.


A. When the ciphertext size is only 1 128-bit block, the probability for a =
collision is already higher than 1/2^32.

B. The probability for a collision gets bigger when the size of a ciphertex=
t gets bigger.


With the GCM-SIV, the collision issue is under multiple AES encryption keys=
 when the corresponding nonces are unique which is different from the colli=
sion situation described at the beginning for the GCM in TLS 1.3 which is u=
nder only one key.


I can't think of a damage to the data owner who sends their encrypted data =
over a TLS session caused by collision(s) among 128-bit blocks of the ciphe=
rtexts. So, I don't have an opinion here.


2) The draft said that " However, we feel that the 2^32 limit for AES-GCM i=
s too risky in a multi-key setting.  Thus with AES-GCM-SIV we recommend tha=
t, for a specific key, a nonce not be repeated more than 2^8 times.  (And, =
ideally, not be repeated at all.)" .


Currently, the GCM with 96-bit random nonces situation, NIST requires the n=
umber of encryptions to be not more than 2^32, so that the probability of a=
 repeat of a pair (key and nonce) is below 1/2^32, under a given key.


With m keys, the probability for a repeat of a pair of (key and nonce) is a=
bout m/2^32.


Therefore, it is best to use  96-bit counter-nonces for GCM.


With the GCM-SIV, when a nonce is repeated 2^8 times, the AES-128 encryptio=
n key is repeated 2^8 times. The 96-bit nonces for the AES counter mode enc=
ryption are practically (pseudo)-random nonces (derived from plaintexts and=
 the master key). The probability for a repeat of a pair of (key and nonce)=
 is about 2^16/2^96 =3D 2^(-80).


If someone cares about the multi-key situation such as the amount of keys b=
eing 2^50 (2^50 sessions),  call the number of sessions 2^x, the probabilit=
y for a repeat of a pair of (key and nonce) is about 2^(x - 80).


The actual break happens when a pair of (key and nonce) repeats AND at leas=
t one 32-bit counter value also repeats with this pair. This problem happen=
s  with 100% chance when the ciphertext size is (2^31 + 1) 128-bit blocks o=
r larger.


Call the size of a ciphertext 2^y 128-bit blocks, the probability for havin=
g at least one 32-bit counter value to repeat is about 2^(y + 1)/2^32 =3D 1=
/2^(31 - y) =3D 2^(y - 31).


So, the number 2^(x - 80) x 2^(y - 31) =3D 2^( x + y - 111) must be not gre=
ater than 2^(-32) in order to keep the probability for a complete break to =
be below 2^(-32).


2^( x + y - 111) <=3D 2^(-32)   <=3D=3D>  x + y <=3D 79.


When y =3D 32, x <=3D 79 - 32 =3D 47.


So, when plaintext/ciphetext size is 2^32 128-bit blocks, the GCM-SIV might=
 be not good enough for 2^47 (or more) sessions when each session has 2^8 r=
epeated nonce if a user's objective is to protect all of those 2^47 (or mor=
e) sessions.


In short, this condition "x + y <=3D 79" should be respected for the curren=
t GCM-SIV: draft 3 when the mode is used to protect a large number of sessi=
ons (multiple users).


To protect a lot more than 2^47 sessions when the ciphertext size is about =
2^32 128-bit blocks, maybe it would be good to require that nonce must not =
be repeated. A specific number of repetitions of a nonce allowed can be der=
ived from each pair of x and y if desired.


Best,

Quynh.

________________________________
From: Cfrg <cfrg-bounces@irtf.org> on behalf of internet-drafts@ietf.org <i=
nternet-drafts@ietf.org>
Sent: Wednesday, January 18, 2017 12:30:31 PM
To: i-d-announce@ietf.org
Cc: cfrg@ietf.org
Subject: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt


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

        Title           : AES-GCM-SIV: Nonce Misuse-Resistant Authenticated=
 Encryption
        Authors         : Shay Gueron
                          Adam Langley
                          Yehuda Lindell
        Filename        : draft-irtf-cfrg-gcmsiv-03.txt
        Pages           : 45
        Date            : 2017-01-18

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/
draft-irtf-cfrg-gcmsiv-02 - datatracker.ietf.org<https://datatracker.ietf.o=
rg/doc/draft-irtf-cfrg-gcmsiv/>
datatracker.ietf.org
AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption (Internet-Draf=
t, 2016)




There's also a htmlized version available at:
https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03

A diff from the previous version is available at:
https://www.ietf.org/rfcdiff?url2=3Ddraft-irtf-cfrg-gcmsiv-03


Please note that it may take a couple of minutes from the time of submissio=
n
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/

_______________________________________________
Cfrg mailing list
Cfrg@irtf.org
https://www.irtf.org/mailman/listinfo/cfrg

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<html>
<head>
<meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3Diso-8859-=
1">
<style type=3D"text/css" style=3D"display:none;"><!-- P {margin-top:0;margi=
n-bottom:0;} --></style>
</head>
<body dir=3D"ltr">
<div id=3D"divtagdefaultwrapper" dir=3D"ltr">
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<br>
</p>
<meta content=3D"text/html; charset=3DUTF-8">
<div dir=3D"ltr">
<div id=3D"x_divtagdefaultwrapper" dir=3D"ltr">
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
Shay, Adam and Yehuda,</p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<br>
</p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
There are 2 things I hope to discuss in this email below.&nbsp;</p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<br>
</p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
1) The draft said that &quot;<span style=3D"font-size:12pt">We recommend a =
limit of 2^50 plaintexts encrypted with a given key.&nbsp;</span><span styl=
e=3D"font-size:12pt">Past this point, AES-GCM-SIV may be distinguishable fr=
om an ideal&nbsp;</span><span style=3D"font-size:12pt">AEAD.&nbsp;
 (This is based on standard assumptions about AES.)&quot;.&nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">To keep the probability of having&nbsp;a col=
lision among 128-bit blocks in the ciphtertexts below 1/2^32 (practically z=
ero), it has been suggested that under a given key, the amount of ciphertex=
ts is not more than 2^48 128-bit blocks
 for the GCM in TLS 1.3. &nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">With 2^50 plaintexts (equivalent amount of c=
iphertexts) and each ciphertext can be up to 2^32 128-bit blocks in the GCM=
-SIV draft, there can be
</span>collision<span style=3D"font-size:12pt">&nbsp;situations.</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">A. When the ciphertext size is only 1 128-bi=
t block, the probability for a&nbsp;collision is already higher than 1/2^32=
.</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">B. The </span>probability<span style=3D"font=
-size:12pt">&nbsp;for a collision gets bigger when the size of a&nbsp;ciphe=
rtext gets bigger.&nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">With the&nbsp;</span><span style=3D"font-siz=
e:12pt">GCM-SIV, the collision issue is under multiple AES encryption keys =
when the corresponding nonces are unique which is different from the
</span>collision<span style=3D"font-size:12pt">&nbsp;situation </span>descr=
ibed<span style=3D"font-size:12pt">&nbsp;at the
</span>beginning<span style=3D"font-size:12pt">&nbsp;for the GCM in TLS 1.3=
 which is under only&nbsp;one key.&nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">I can't think of a damage to the data owner =
who sends their encrypted data over a TLS session caused by collision(s) am=
ong 128-bit blocks of the&nbsp;ciphertexts.&nbsp;So,&nbsp;I don't have an o=
pinion here. &nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">2) The draft said that &quot;&nbsp;</span><s=
pan style=3D"font-size:12pt">However, we feel that the 2^32 limit for AES-<=
/span><span style=3D"font-size:12pt">GCM is too risky in a multi-key settin=
g.&nbsp; Thus with AES-GCM-SIV we&nbsp;</span><span style=3D"font-size:12pt=
">recommend
 that, for a specific key, a nonce not be repeated more than&nbsp;</span><s=
pan style=3D"font-size:12pt">2^8 times.&nbsp; (And, ideally, not be repeate=
d at all.)</span><span style=3D"font-size:12pt">&quot; .&nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">Currently, the&nbsp;GCM with 96-bit random n=
onces situation, NIST requires the number of encryptions&nbsp;to be not mor=
e than 2^32, so that the probability of a repeat of a&nbsp;pair (key and no=
nce) is below 1/2^32, under a given key.&nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">With m keys, the probability for a repeat of=
 a pair of (key and nonce) is about m/2^32.</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">Therefore, it is best to use &nbsp;96-bit&nb=
sp;counter-nonces for GCM.&nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">With the GCM-SIV, when a nonce is repeated 2=
^8 times, the AES-128 encryption key is repeated 2^8 times. The 96-bit nonc=
es for the AES counter mode encryption are practically (pseudo)-random nonc=
es (derived from plaintexts and the
 master&nbsp;key). The probability for a repeat of a pair of (key and nonce=
) is about 2^16/2^96 =3D 2^(-80).</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">If someone cares about the&nbsp;</span><span=
 style=3D"font-size:12pt">multi-key situation such as the amount of keys be=
ing 2^50 (2^50 sessions)</span><span style=3D"font-size:12pt">, &nbsp;c</sp=
an>all the number of sessions 2^x, the probability&nbsp;for
 a repeat of a pair of (key and nonce) is about 2^(x - 80).</p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">The actual break happens when&nbsp;a pair of=
 (key and nonce) repeats AND at least one 32-bit&nbsp;counter value also re=
peats with this pair. This problem happens &nbsp;with&nbsp;100% chance&nbsp=
;when the ciphertext size is (2^31 &#43; 1) 128-bit blocks or larger.&nbsp;=
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">Call&nbsp;the size of a ciphertext 2^y 128-b=
it blocks, the probability for having at least one 32-bit counter value to =
repeat is about&nbsp;2^(y &#43; 1)/2^32 =3D 1/2^(31 - y) =3D 2^(y - 31).&nb=
sp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-size:12pt">So, the number&nbsp;</span>2^(x - 80) x&nbsp=
;2^(y - 31) =3D 2^( x &#43; y - 111) must be not greater than 2^(-32) in or=
der to keep the probability&nbsp;for a complete break to be below 2^(-32).&=
nbsp;</p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<br>
</p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px">2^( x &=
#43; y - 111) &lt;=3D 2^(-32) &nbsp; &lt;=3D=3D&gt; &nbsp;x &#43; y &lt;=3D=
 79.&nbsp;</span><br>
</p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px">When y =
=3D 32, x &lt;=3D 79 - 32 =3D 47.&nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px">So, whe=
n plaintext/ciphetext size is 2^32 128-bit blocks, the GCM-SIV might be not
 good enough for 2^47 (or more) sessions when each session has 2^8 repeated=
 nonce if a user's&nbsp;objective is to protect all of those 2^47 (or more)=
 sessions.&nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
In short, this condition&nbsp;&quot;<span style=3D"font-family:Calibri,Aria=
l,Helvetica,sans-serif,&quot;Apple Color Emoji&quot;,&quot;Segoe UI Emoji&q=
uot;,NotoColorEmoji,&quot;Segoe UI Symbol&quot;,&quot;Android Emoji&quot;,E=
mojiSymbols; font-size:16px">x &#43; y &lt;=3D 79&quot; should be respected=
 for the current&nbsp;GCM-SIV:
 draft 3 when the mode is used to protect a large number of&nbsp;sessions (=
multiple users).&nbsp;</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px"><br>
</span></p>
<p>To protect a lot more than 2^47 sessions when the ciphertext size is abo=
ut 2^32 128-bit blocks, maybe it would be good to require that nonce must n=
ot be repeated. A specific number of repetitions of a nonce allowed&nbsp;ca=
n be derived from each pair of x and
 y if desired.&nbsp;</p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-family: Calibri, Arial, Helvetica, sans-serif, &quot;Ap=
ple Color Emoji&quot;, &quot;Segoe UI Emoji&quot;, NotoColorEmoji, &quot;Se=
goe UI Symbol&quot;, &quot;Android Emoji&quot;, EmojiSymbols;"><br>
</span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-family: Calibri, Arial, Helvetica, sans-serif, &quot;Ap=
ple Color Emoji&quot;, &quot;Segoe UI Emoji&quot;, NotoColorEmoji, &quot;Se=
goe UI Symbol&quot;, &quot;Android Emoji&quot;, EmojiSymbols;">Best,&nbsp;<=
/span></p>
<p style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sa=
ns-serif; font-size: 12pt;">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px"></span>=
<span style=3D"font-family: Calibri, Arial, Helvetica, sans-serif, &quot;Ap=
ple Color Emoji&quot;, &quot;Segoe UI Emoji&quot;, NotoColorEmoji, &quot;Se=
goe UI Symbol&quot;, &quot;Android Emoji&quot;, EmojiSymbols;">Quynh.
 &nbsp;</span></p>
</div>
<hr tabindex=3D"-1" style=3D"color: rgb(0, 0, 0); font-family: Calibri, Ari=
al, Helvetica, sans-serif; font-size: 12pt; display: inline-block; width: 9=
8%;">
<div id=3D"x_divRplyFwdMsg" dir=3D"ltr" style=3D"color: rgb(0, 0, 0); font-=
family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;">
<font face=3D"Calibri, sans-serif" color=3D"#000000" style=3D"font-size:11p=
t"><b>From:</b> Cfrg &lt;cfrg-bounces@irtf.org&gt; on behalf of internet-dr=
afts@ietf.org &lt;internet-drafts@ietf.org&gt;<br>
<b>Sent:</b> Wednesday, January 18, 2017 12:30:31 PM<br>
<b>To:</b> i-d-announce@ietf.org<br>
<b>Cc:</b> cfrg@ietf.org<br>
<b>Subject:</b> [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt</font>
<div>&nbsp;</div>
</div>
</div>
<font size=3D"2" style=3D"color: rgb(0, 0, 0); font-family: Calibri, Arial,=
 Helvetica, sans-serif; font-size: 12pt;"><span style=3D"font-size:10pt">
<div class=3D"PlainText"><br>
A New Internet-Draft is available from the on-line Internet-Drafts director=
ies.<br>
This draft is a work item of the Crypto Forum of the IETF.<br>
<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Title&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; : AES-GCM-SIV: Nonce Misuse-Resistant Aut=
henticated Encryption<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Authors&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp; : Shay Gueron<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
 Adam Langley<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
 Yehuda Lindell<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Filename&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp; : draft-irtf-cfrg-gcmsiv-03.txt<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Pages&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; : 45<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Date&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; : 2017-01-18<br>
<br>
Abstract:<br>
&nbsp;&nbsp; This memo specifies two authenticated encryption algorithms th=
at are<br>
&nbsp;&nbsp; nonce misuse-resistant - that is that they do not fail<br>
&nbsp;&nbsp; catastrophically if a nonce is repeated.<br>
<br>
<br>
The IETF datatracker status page for this draft is:<br>
<a href=3D"https://datatracker.ietf.org/doc/draft-irtf-cfrg-gcmsiv/" id=3D"=
LPlnk127226" previewremoved=3D"true">https://datatracker.ietf.org/doc/draft=
-irtf-cfrg-gcmsiv/</a>
<div id=3D"LPBorder_GT_14851876727780.2981390626859044" style=3D"margin-bot=
tom:20px; overflow:auto; width:100%; text-indent:0px">
<table id=3D"LPContainer_14851876727760.5638155877889133" cellspacing=3D"0"=
 style=3D"width:90%; background-color:rgb(255,255,255); overflow:auto; padd=
ing-top:20px; padding-bottom:20px; margin-top:20px; border-top:1px dotted r=
gb(200,200,200); border-bottom:1px dotted rgb(200,200,200)">
<tbody>
<tr valign=3D"top" style=3D"border-spacing:0px">
<td id=3D"TextCell_14851876727760.9523046007123246" colspan=3D"2" style=3D"=
vertical-align: top; padding: 0px; display: table-cell; position: relative;=
">
<div id=3D"LPRemovePreviewContainer_14851876727770.13980665690839134"></div=
>
<div id=3D"LPTitle_14851876727770.07131646564122507" style=3D"top:0px; colo=
r:rgb(0,120,215); font-weight:normal; font-size:21px; font-family:wf_segoe-=
ui_light,&quot;Segoe UI Light&quot;,&quot;Segoe WP Light&quot;,&quot;Segoe =
UI&quot;,&quot;Segoe WP&quot;,Tahoma,Arial,sans-serif; line-height:21px">
<a id=3D"LPUrlAnchor_14851876727770.6733486941122127" href=3D"https://datat=
racker.ietf.org/doc/draft-irtf-cfrg-gcmsiv/" target=3D"_blank" style=3D"tex=
t-decoration:none">draft-irtf-cfrg-gcmsiv-02 - datatracker.ietf.org</a></di=
v>
<div id=3D"LPMetadata_14851876727770.4877856828459095" style=3D"margin:10px=
 0px 16px; color:rgb(102,102,102); font-weight:normal; font-family:wf_segoe=
-ui_normal,&quot;Segoe UI&quot;,&quot;Segoe WP&quot;,Tahoma,Arial,sans-seri=
f; font-size:14px; line-height:14px">
datatracker.ietf.org</div>
<div id=3D"LPDescription_14851876727780.4655758567440518" style=3D"display:=
block; color:rgb(102,102,102); font-weight:normal; font-family:wf_segoe-ui_=
normal,&quot;Segoe UI&quot;,&quot;Segoe WP&quot;,Tahoma,Arial,sans-serif; f=
ont-size:14px; line-height:20px; max-height:100px; overflow:hidden">
AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption (Internet-Draf=
t, 2016)</div>
</td>
</tr>
</tbody>
</table>
</div>
<br>
<br>
<br>
There's also a htmlized version available at:<br>
<a href=3D"https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03" id=3D"LPl=
nk570119" previewremoved=3D"true">https://tools.ietf.org/html/draft-irtf-cf=
rg-gcmsiv-03</a><br>
<br>
A diff from the previous version is available at:<br>
<a href=3D"https://www.ietf.org/rfcdiff?url2=3Ddraft-irtf-cfrg-gcmsiv-03" i=
d=3D"LPlnk686843" previewremoved=3D"true">https://www.ietf.org/rfcdiff?url2=
=3Ddraft-irtf-cfrg-gcmsiv-03</a><br>
<br>
<br>
Please note that it may take a couple of minutes from the time of submissio=
n<br>
until the htmlized version and diff are available at tools.ietf.org.<br>
<br>
Internet-Drafts are also available by anonymous FTP at:<br>
<a href=3D"ftp://ftp.ietf.org/internet-drafts/">ftp://ftp.ietf.org/internet=
-drafts/</a><br>
<br>
_______________________________________________<br>
Cfrg mailing list<br>
Cfrg@irtf.org<br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg">https://www.irtf.org=
/mailman/listinfo/cfrg</a><br>
</div>
</span></font></div>
</body>
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From: "Dang, Quynh (Fed)" <quynh.dang@nist.gov>
To: "shay@math.haifa.ac.il" <shay@math.haifa.ac.il>, "agl@google.com" <agl@google.com>, "Yehuda.Lindell@biu.ac.il" <Yehuda.Lindell@biu.ac.il>
Thread-Topic: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt
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One way to improve the misuse of repeated nonces situation is to derive the=
 AES encryption key from the S_s value, the nonce and the master key.


Quynh.




________________________________
From: Cfrg <cfrg-bounces@irtf.org> on behalf of Dang, Quynh (Fed) <quynh.da=
ng@nist.gov>
Sent: Monday, January 23, 2017 1:43 PM
To: shay@math.haifa.ac.il; agl@google.com; Yehuda.Lindell@biu.ac.il
Cc: cfrg@ietf.org
Subject: Re: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt



Shay, Adam and Yehuda,


There are 2 things I hope to discuss in this email below.


1) The draft said that "We recommend a limit of 2^50 plaintexts encrypted w=
ith a given key. Past this point, AES-GCM-SIV may be distinguishable from a=
n ideal AEAD.  (This is based on standard assumptions about AES.)".


To keep the probability of having a collision among 128-bit blocks in the c=
iphtertexts below 1/2^32 (practically zero), it has been suggested that und=
er a given key, the amount of ciphertexts is not more than 2^48 128-bit blo=
cks for the GCM in TLS 1.3.


With 2^50 plaintexts (equivalent amount of ciphertexts) and each ciphertext=
 can be up to 2^32 128-bit blocks in the GCM-SIV draft, there can be collis=
ion situations.


A. When the ciphertext size is only 1 128-bit block, the probability for a =
collision is already higher than 1/2^32.

B. The probability for a collision gets bigger when the size of a ciphertex=
t gets bigger.


With the GCM-SIV, the collision issue is under multiple AES encryption keys=
 when the corresponding nonces are unique which is different from the colli=
sion situation described at the beginning for the GCM in TLS 1.3 which is u=
nder only one key.


I can't think of a damage to the data owner who sends their encrypted data =
over a TLS session caused by collision(s) among 128-bit blocks of the ciphe=
rtexts. So, I don't have an opinion here.


2) The draft said that " However, we feel that the 2^32 limit for AES-GCM i=
s too risky in a multi-key setting.  Thus with AES-GCM-SIV we recommend tha=
t, for a specific key, a nonce not be repeated more than 2^8 times.  (And, =
ideally, not be repeated at all.)" .


Currently, the GCM with 96-bit random nonces situation, NIST requires the n=
umber of encryptions to be not more than 2^32, so that the probability of a=
 repeat of a pair (key and nonce) is below 1/2^32, under a given key.


With m keys, the probability for a repeat of a pair of (key and nonce) is a=
bout m/2^32.


Therefore, it is best to use  96-bit counter-nonces for GCM.


With the GCM-SIV, when a nonce is repeated 2^8 times, the AES-128 encryptio=
n key is repeated 2^8 times. The 96-bit nonces for the AES counter mode enc=
ryption are practically (pseudo)-random nonces (derived from plaintexts and=
 the master key). The probability for a repeat of a pair of (key and nonce)=
 is about 2^16/2^96 =3D 2^(-80).


If someone cares about the multi-key situation such as the amount of keys b=
eing 2^50 (2^50 sessions),  call the number of sessions 2^x, the probabilit=
y for a repeat of a pair of (key and nonce) is about 2^(x - 80).


The actual break happens when a pair of (key and nonce) repeats AND at leas=
t one 32-bit counter value also repeats with this pair. This problem happen=
s  with 100% chance when the ciphertext size is (2^31 + 1) 128-bit blocks o=
r larger.


Call the size of a ciphertext 2^y 128-bit blocks, the probability for havin=
g at least one 32-bit counter value to repeat is about 2^(y + 1)/2^32 =3D 1=
/2^(31 - y) =3D 2^(y - 31).


So, the number 2^(x - 80) x 2^(y - 31) =3D 2^( x + y - 111) must be not gre=
ater than 2^(-32) in order to keep the probability for a complete break to =
be below 2^(-32).


2^( x + y - 111) <=3D 2^(-32)   <=3D=3D>  x + y <=3D 79.


When y =3D 32, x <=3D 79 - 32 =3D 47.


So, when plaintext/ciphetext size is 2^32 128-bit blocks, the GCM-SIV might=
 be not good enough for 2^47 (or more) sessions when each session has 2^8 r=
epeated nonce if a user's objective is to protect all of those 2^47 (or mor=
e) sessions.


In short, this condition "x + y <=3D 79" should be respected for the curren=
t GCM-SIV: draft 3 when the mode is used to protect a large number of sessi=
ons (multiple users).


To protect a lot more than 2^47 sessions when the ciphertext size is about =
2^32 128-bit blocks, maybe it would be good to require that nonce must not =
be repeated. A specific number of repetitions of a nonce allowed can be der=
ived from each pair of x and y if desired.


Best,

Quynh.

________________________________
From: Cfrg <cfrg-bounces@irtf.org> on behalf of internet-drafts@ietf.org <i=
nternet-drafts@ietf.org>
Sent: Wednesday, January 18, 2017 12:30:31 PM
To: i-d-announce@ietf.org
Cc: cfrg@ietf.org
Subject: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt


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

        Title           : AES-GCM-SIV: Nonce Misuse-Resistant Authenticated=
 Encryption
        Authors         : Shay Gueron
                          Adam Langley
                          Yehuda Lindell
        Filename        : draft-irtf-cfrg-gcmsiv-03.txt
        Pages           : 45
        Date            : 2017-01-18

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/
draft-irtf-cfrg-gcmsiv-02 - datatracker.ietf.org<https://datatracker.ietf.o=
rg/doc/draft-irtf-cfrg-gcmsiv/>
datatracker.ietf.org
AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption (Internet-Draf=
t, 2016)




There's also a htmlized version available at:
https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03

A diff from the previous version is available at:
https://www.ietf.org/rfcdiff?url2=3Ddraft-irtf-cfrg-gcmsiv-03


Please note that it may take a couple of minutes from the time of submissio=
n
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/

_______________________________________________
Cfrg mailing list
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--_000_CY4PR09MB14647E9FAC808C6CEBA3BE9DF3750CY4PR09MB1464namp_
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<html>
<head>
<meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3Diso-8859-=
1">
<style type=3D"text/css" style=3D"display:none;"><!-- P {margin-top:0;margi=
n-bottom:0;} --></style>
</head>
<body dir=3D"ltr">
<div id=3D"divtagdefaultwrapper" style=3D"font-size:12pt;color:#000000;font=
-family:Calibri,Arial,Helvetica,sans-serif;" dir=3D"ltr">
<p>One way to improve the misuse of repeated nonces situation is to derive =
the AES encryption key from the S_s value, the&nbsp;nonce and the master ke=
y.</p>
<p><br>
</p>
<p>Quynh.&nbsp;</p>
<p><br>
</p>
<p><br>
</p>
<br>
<br>
<div style=3D"color: rgb(0, 0, 0);">
<hr tabindex=3D"-1" style=3D"display:inline-block; width:98%">
<div id=3D"divRplyFwdMsg" dir=3D"ltr"><font face=3D"Calibri, sans-serif" co=
lor=3D"#000000" style=3D"font-size:11pt"><b>From:</b> Cfrg &lt;cfrg-bounces=
@irtf.org&gt; on behalf of Dang, Quynh (Fed) &lt;quynh.dang@nist.gov&gt;<br=
>
<b>Sent:</b> Monday, January 23, 2017 1:43 PM<br>
<b>To:</b> shay@math.haifa.ac.il; agl@google.com; Yehuda.Lindell@biu.ac.il<=
br>
<b>Cc:</b> cfrg@ietf.org<br>
<b>Subject:</b> Re: [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt</font>
<div>&nbsp;</div>
</div>
<div>
<div id=3D"divtagdefaultwrapper" dir=3D"ltr">
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<br>
</p>
<meta content=3D"text/html; charset=3DUTF-8">
<div dir=3D"ltr">
<div id=3D"x_divtagdefaultwrapper" dir=3D"ltr">
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
Shay, Adam and Yehuda,</p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<br>
</p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
There are 2 things I hope to discuss in this email below.&nbsp;</p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<br>
</p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
1) The draft said that &quot;<span style=3D"font-size:12pt">We recommend a =
limit of 2^50 plaintexts encrypted with a given key.&nbsp;</span><span styl=
e=3D"font-size:12pt">Past this point, AES-GCM-SIV may be distinguishable fr=
om an ideal&nbsp;</span><span style=3D"font-size:12pt">AEAD.&nbsp;
 (This is based on standard assumptions about AES.)&quot;.&nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">To keep the probability of having&nbsp;a col=
lision among 128-bit blocks in the ciphtertexts below 1/2^32 (practically z=
ero), it has been suggested that under a given key, the amount of ciphertex=
ts is not more than 2^48 128-bit blocks
 for the GCM in TLS 1.3. &nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">With 2^50 plaintexts (equivalent amount of c=
iphertexts) and each ciphertext can be up to 2^32 128-bit blocks in the GCM=
-SIV draft, there can be
</span>collision<span style=3D"font-size:12pt">&nbsp;situations.</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">A. When the ciphertext size is only 1 128-bi=
t block, the probability for a&nbsp;collision is already higher than 1/2^32=
.</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">B. The </span>probability<span style=3D"font=
-size:12pt">&nbsp;for a collision gets bigger when the size of a&nbsp;ciphe=
rtext gets bigger.&nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">With the&nbsp;</span><span style=3D"font-siz=
e:12pt">GCM-SIV, the collision issue is under multiple AES encryption keys =
when the corresponding nonces are unique which is different from the
</span>collision<span style=3D"font-size:12pt">&nbsp;situation </span>descr=
ibed<span style=3D"font-size:12pt">&nbsp;at the
</span>beginning<span style=3D"font-size:12pt">&nbsp;for the GCM in TLS 1.3=
 which is under only&nbsp;one key.&nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">I can't think of a damage to the data owner =
who sends their encrypted data over a TLS session caused by collision(s) am=
ong 128-bit blocks of the&nbsp;ciphertexts.&nbsp;So,&nbsp;I don't have an o=
pinion here. &nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">2) The draft said that &quot;&nbsp;</span><s=
pan style=3D"font-size:12pt">However, we feel that the 2^32 limit for AES-<=
/span><span style=3D"font-size:12pt">GCM is too risky in a multi-key settin=
g.&nbsp; Thus with AES-GCM-SIV we&nbsp;</span><span style=3D"font-size:12pt=
">recommend
 that, for a specific key, a nonce not be repeated more than&nbsp;</span><s=
pan style=3D"font-size:12pt">2^8 times.&nbsp; (And, ideally, not be repeate=
d at all.)</span><span style=3D"font-size:12pt">&quot; .&nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">Currently, the&nbsp;GCM with 96-bit random n=
onces situation, NIST requires the number of encryptions&nbsp;to be not mor=
e than 2^32, so that the probability of a repeat of a&nbsp;pair (key and no=
nce) is below 1/2^32, under a given key.&nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">With m keys, the probability for a repeat of=
 a pair of (key and nonce) is about m/2^32.</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">Therefore, it is best to use &nbsp;96-bit&nb=
sp;counter-nonces for GCM.&nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">With the GCM-SIV, when a nonce is repeated 2=
^8 times, the AES-128 encryption key is repeated 2^8 times. The 96-bit nonc=
es for the AES counter mode encryption are practically (pseudo)-random nonc=
es (derived from plaintexts and the
 master&nbsp;key). The probability for a repeat of a pair of (key and nonce=
) is about 2^16/2^96 =3D 2^(-80).</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">If someone cares about the&nbsp;</span><span=
 style=3D"font-size:12pt">multi-key situation such as the amount of keys be=
ing 2^50 (2^50 sessions)</span><span style=3D"font-size:12pt">, &nbsp;c</sp=
an>all the number of sessions 2^x, the probability&nbsp;for
 a repeat of a pair of (key and nonce) is about 2^(x - 80).</p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">The actual break happens when&nbsp;a pair of=
 (key and nonce) repeats AND at least one 32-bit&nbsp;counter value also re=
peats with this pair. This problem happens &nbsp;with&nbsp;100% chance&nbsp=
;when the ciphertext size is (2^31 &#43; 1) 128-bit blocks or larger.&nbsp;=
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">Call&nbsp;the size of a ciphertext 2^y 128-b=
it blocks, the probability for having at least one 32-bit counter value to =
repeat is about&nbsp;2^(y &#43; 1)/2^32 =3D 1/2^(31 - y) =3D 2^(y - 31).&nb=
sp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-size:12pt">So, the number&nbsp;</span>2^(x - 80) x&nbsp=
;2^(y - 31) =3D 2^( x &#43; y - 111) must be not greater than 2^(-32) in or=
der to keep the probability&nbsp;for a complete break to be below 2^(-32).&=
nbsp;</p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<br>
</p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px">2^( x &=
#43; y - 111) &lt;=3D 2^(-32) &nbsp; &lt;=3D=3D&gt; &nbsp;x &#43; y &lt;=3D=
 79.&nbsp;</span><br>
</p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px">When y =
=3D 32, x &lt;=3D 79 - 32 =3D 47.&nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px">So, whe=
n plaintext/ciphetext size is 2^32 128-bit blocks, the GCM-SIV might be not
 good enough for 2^47 (or more) sessions when each session has 2^8 repeated=
 nonce if a user's&nbsp;objective is to protect all of those 2^47 (or more)=
 sessions.&nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
In short, this condition&nbsp;&quot;<span style=3D"font-family:Calibri,Aria=
l,Helvetica,sans-serif,&quot;Apple Color Emoji&quot;,&quot;Segoe UI Emoji&q=
uot;,NotoColorEmoji,&quot;Segoe UI Symbol&quot;,&quot;Android Emoji&quot;,E=
mojiSymbols; font-size:16px">x &#43; y &lt;=3D 79&quot; should be respected=
 for the current&nbsp;GCM-SIV:
 draft 3 when the mode is used to protect a large number of&nbsp;sessions (=
multiple users).&nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px"><br>
</span></p>
<p>To protect a lot more than 2^47 sessions when the ciphertext size is abo=
ut 2^32 128-bit blocks, maybe it would be good to require that nonce must n=
ot be repeated. A specific number of repetitions of a nonce allowed&nbsp;ca=
n be derived from each pair of x and
 y if desired.&nbsp;</p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols"><br>
</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols">Best,&nbsp;</span></p>
<p style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helvetica,sans-seri=
f; font-size:12pt">
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols; font-size:16px"></span>=
<span style=3D"font-family:Calibri,Arial,Helvetica,sans-serif,&quot;Apple C=
olor Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI S=
ymbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols">Quynh.
 &nbsp;</span></p>
</div>
<hr tabindex=3D"-1" style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,He=
lvetica,sans-serif; font-size:12pt; display:inline-block; width:98%">
<div id=3D"x_divRplyFwdMsg" dir=3D"ltr" style=3D"color:rgb(0,0,0); font-fam=
ily:Calibri,Arial,Helvetica,sans-serif; font-size:12pt">
<font face=3D"Calibri, sans-serif" color=3D"#000000" style=3D"font-size:11p=
t"><b>From:</b> Cfrg &lt;cfrg-bounces@irtf.org&gt; on behalf of internet-dr=
afts@ietf.org &lt;internet-drafts@ietf.org&gt;<br>
<b>Sent:</b> Wednesday, January 18, 2017 12:30:31 PM<br>
<b>To:</b> i-d-announce@ietf.org<br>
<b>Cc:</b> cfrg@ietf.org<br>
<b>Subject:</b> [Cfrg] I-D Action: draft-irtf-cfrg-gcmsiv-03.txt</font>
<div>&nbsp;</div>
</div>
</div>
<font size=3D"2" style=3D"color:rgb(0,0,0); font-family:Calibri,Arial,Helve=
tica,sans-serif; font-size:12pt"><span style=3D"font-size:10pt">
<div class=3D"PlainText"><br>
A New Internet-Draft is available from the on-line Internet-Drafts director=
ies.<br>
This draft is a work item of the Crypto Forum of the IETF.<br>
<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Title&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; : AES-GCM-SIV: Nonce Misuse-Resistant Aut=
henticated Encryption<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Authors&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp; : Shay Gueron<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
 Adam Langley<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
 Yehuda Lindell<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Filename&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp; : draft-irtf-cfrg-gcmsiv-03.txt<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Pages&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; : 45<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Date&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; : 2017-01-18<br>
<br>
Abstract:<br>
&nbsp;&nbsp; This memo specifies two authenticated encryption algorithms th=
at are<br>
&nbsp;&nbsp; nonce misuse-resistant - that is that they do not fail<br>
&nbsp;&nbsp; catastrophically if a nonce is repeated.<br>
<br>
<br>
The IETF datatracker status page for this draft is:<br>
<a href=3D"https://datatracker.ietf.org/doc/draft-irtf-cfrg-gcmsiv/" id=3D"=
LPlnk127226" previewremoved=3D"true">https://datatracker.ietf.org/doc/draft=
-irtf-cfrg-gcmsiv/</a>
<div id=3D"LPBorder_GT_14851876727780.2981390626859044" style=3D"margin-bot=
tom:20px; overflow:auto; width:100%; text-indent:0px">
<table id=3D"LPContainer_14851876727760.5638155877889133" cellspacing=3D"0"=
 style=3D"width:90%; background-color:rgb(255,255,255); overflow:auto; padd=
ing-top:20px; padding-bottom:20px; margin-top:20px; border-top:1px dotted r=
gb(200,200,200); border-bottom:1px dotted rgb(200,200,200)">
<tbody>
<tr valign=3D"top" style=3D"border-spacing:0px">
<td id=3D"TextCell_14851876727760.9523046007123246" colspan=3D"2" style=3D"=
vertical-align: top; padding: 0px; display: table-cell; position: relative;=
">
<div id=3D"LPRemovePreviewContainer_14851876727770.13980665690839134"></div=
>
<div id=3D"LPTitle_14851876727770.07131646564122507" style=3D"top:0px; colo=
r:rgb(0,120,215); font-weight:normal; font-size:21px; font-family:wf_segoe-=
ui_light,&quot;Segoe UI Light&quot;,&quot;Segoe WP Light&quot;,&quot;Segoe =
UI&quot;,&quot;Segoe WP&quot;,Tahoma,Arial,sans-serif; line-height:21px">
<a id=3D"LPUrlAnchor_14851876727770.6733486941122127" href=3D"https://datat=
racker.ietf.org/doc/draft-irtf-cfrg-gcmsiv/" target=3D"_blank" style=3D"tex=
t-decoration:none">draft-irtf-cfrg-gcmsiv-02 - datatracker.ietf.org</a></di=
v>
<div id=3D"LPMetadata_14851876727770.4877856828459095" style=3D"margin:10px=
 0px 16px; color:rgb(102,102,102); font-weight:normal; font-family:wf_segoe=
-ui_normal,&quot;Segoe UI&quot;,&quot;Segoe WP&quot;,Tahoma,Arial,sans-seri=
f; font-size:14px; line-height:14px">
datatracker.ietf.org</div>
<div id=3D"LPDescription_14851876727780.4655758567440518" style=3D"display:=
block; color:rgb(102,102,102); font-weight:normal; font-family:wf_segoe-ui_=
normal,&quot;Segoe UI&quot;,&quot;Segoe WP&quot;,Tahoma,Arial,sans-serif; f=
ont-size:14px; line-height:20px; max-height:100px; overflow:hidden">
AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption (Internet-Draf=
t, 2016)</div>
</td>
</tr>
</tbody>
</table>
</div>
<br>
<br>
<br>
There's also a htmlized version available at:<br>
<a href=3D"https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03" id=3D"LPl=
nk570119" previewremoved=3D"true">https://tools.ietf.org/html/draft-irtf-cf=
rg-gcmsiv-03</a><br>
<br>
A diff from the previous version is available at:<br>
<a href=3D"https://www.ietf.org/rfcdiff?url2=3Ddraft-irtf-cfrg-gcmsiv-03" i=
d=3D"LPlnk686843" previewremoved=3D"true">https://www.ietf.org/rfcdiff?url2=
=3Ddraft-irtf-cfrg-gcmsiv-03</a><br>
<br>
<br>
Please note that it may take a couple of minutes from the time of submissio=
n<br>
until the htmlized version and diff are available at tools.ietf.org.<br>
<br>
Internet-Drafts are also available by anonymous FTP at:<br>
<a href=3D"ftp://ftp.ietf.org/internet-drafts/">ftp://ftp.ietf.org/internet=
-drafts/</a><br>
<br>
_______________________________________________<br>
Cfrg mailing list<br>
Cfrg@irtf.org<br>
<a href=3D"https://www.irtf.org/mailman/listinfo/cfrg">https://www.irtf.org=
/mailman/listinfo/cfrg</a><br>
</div>
</span></font></div>
</div>
</div>
</div>
</body>
</html>

--_000_CY4PR09MB14647E9FAC808C6CEBA3BE9DF3750CY4PR09MB1464namp_--


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Subject: [Cfrg] RFC 8032 on Edwards-Curve Digital Signature Algorithm (EdDSA)
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A new Request for Comments is now available in online RFC libraries.

        
        RFC 8032

        Title:      Edwards-Curve Digital Signature Algorithm (EdDSA) 
        Author:     S. Josefsson, I. Liusvaara
        Status:     Informational
        Stream:     IRTF
        Date:       January 2017
        Mailbox:    simon@josefsson.org, 
                    ilariliusvaara@welho.com
        Pages:      60
        Characters: 103210
        Updates/Obsoletes/SeeAlso:   None

        I-D Tag:    draft-irtf-cfrg-eddsa-08.txt

        URL:        https://www.rfc-editor.org/info/rfc8032

        DOI:        10.17487/RFC8032

This document describes elliptic curve signature scheme Edwards-curve
Digital Signature Algorithm (EdDSA).  The algorithm is instantiated
with recommended parameters for the edwards25519 and edwards448
curves.  An example implementation and test vectors are provided.

This document is a product of the Crypto Forum Research Group of the IRTF.


INFORMATIONAL: This memo provides information for the Internet community.
It does not specify an Internet standard of any kind. Distribution of
this memo is unlimited.

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The RFC Editor Team
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From: Tony Arcieri <bascule@gmail.com>
Date: Tue, 24 Jan 2017 16:57:26 -0800
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Subject: Re: [Cfrg] [rfc-dist] RFC 8032 on Edwards-Curve Digital Signature Algorithm (EdDSA)
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Happy to finally see this published! Thanks to everyone who worked on it.

-- 
Tony Arcieri

--001a11446e289b1b040546e0b85f
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<div dir="ltr">Happy to finally see this published! Thanks to everyone who worked on it.<div class="gmail_extra"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature">Tony Arcieri<br></div>
</div></div>

--001a11446e289b1b040546e0b85f--


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Subject: [Cfrg] CFRG curves: yay! (was: Fwd: RFC 8032 on Edwards-Curve Digital Signature Algorithm (EdDSA))
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I'd just like to say thanks to all - authors, chairs,
commenters and all others on this list and off (active,
retired or otherwise;-) who contributed to CFRG documenting
and reviewing elliptic curves that IMO demonstrate that
the combination of academic cryptography and open-review
rough-consensus processes can do as well or better than
other sources of crypto.

And I really hope that CFG continue to be as or more
effective - this does seem to me to be the right way
to introduce and criticise new crypto for the Internet
community.

S.



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From: "Eggert, Lars" <lars@netapp.com>
To: Stephen Farrell <stephen.farrell@cs.tcd.ie>
Thread-Topic: [Cfrg] CFRG curves: yay! (was: Fwd: RFC 8032 on Edwards-Curve Digital Signature Algorithm (EdDSA))
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Subject: Re: [Cfrg] CFRG curves: yay! (was: Fwd: RFC 8032 on Edwards-Curve Digital Signature Algorithm (EdDSA))
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On 2017-1-25, at 10:21, Stephen Farrell <stephen.farrell@cs.tcd.ie> =
wrote:
> I'd just like to say thanks to all - authors, chairs,
> commenters and all others on this list and off (active,
> retired or otherwise;-) who contributed to CFRG documenting
> and reviewing elliptic curves that IMO demonstrate that
> the combination of academic cryptography and open-review
> rough-consensus processes can do as well or better than
> other sources of crypto.
>=20
> And I really hope that CFG continue to be as or more
> effective - this does seem to me to be the right way
> to introduce and criticise new crypto for the Internet
> community.

I'd like to echo this. This work is certainly amongst the largest =
concrete contributions the IRTF has made to the open standards process. =
Thank you all!

Lars

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From: Yoav Nir <ynir.ietf@gmail.com>
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To: Stephen Farrell <stephen.farrell@cs.tcd.ie>
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Subject: Re: [Cfrg] Help with the use of contexts
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>=20
>> On 17 Jan 2017, at 13:48, Stephen Farrell <stephen.farrell@cs.tcd.ie> =
wrote:
>>=20
>>=20
>> However, I really do wish that CFRG specs would not offer
>> both choices - that will simply lead to repeating this
>> discussion each time an IETF protocol wants to use the CFRG
>> spec. And of course, different decisions will be made over
>> time,
>=20
> Not over time. In the next few months the IESG is going to get =
documents about EdDSA signatures from TLS, IPsecME and curdle for =
signatures in TLS, IKE, and PKIX respectively.  If the decision is not =
the same in all of them, I think (hope) that the IESG would ask why.

So now that RFC 8032 is out and does include both choices, what is our =
advice to TLS, IPsecME and Curdle?  Contexts or no?

Yoav


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To: Adam Langley <agl@imperialviolet.org>, Brian Smith <brian@briansmith.org>
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From: Dan Harkins <dharkins@lounge.org>
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Subject: Re: [Cfrg] AES GCM SIV analysis
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   Hello,

On 1/19/17 9:33 AM, Adam Langley wrote:
> On Wed, Jan 18, 2017 at 7:53 PM, Brian Smith <brian@briansmith.org> wrote:
>> Perhaps: "We recommend instead that an implementation try to avoid
>> repeating a nonce for a specific key, just like it would it would do
>> for an AEAD that isn't nonce-misuse-resistant." This shifts the
>> emphasis away from the 2^8 number to where it belongs, IMO. Note that
>> "256" and how it is derived and why it is safe is explained in the
>> next paragraph anyway.
> After some discussions on Twitter I've discovered that several people
> (possibly including Brian) understand "nonce-misuse resistant" to mean
> a stronger property than AES-GCM-SIV has. Namely they understood it to
> mean that the value of the nonce is /irrelevant/ for security, except
> that a fixed nonce discloses equality of plaintexts.

   But that is the definition used in the seminal work on the matter, [1].
If you want to have a different notion concerning a lesser restriction on
nonce reuse then you should use a different term.

> AES-GCM-SIV doesn't have this property. It is robust to random nonce
> duplication but not designed for a fixed nonce. Specifically, after
> 2^n full-sized (i.e. 64MB) messages, there's ~2^(96-2n) chance that
> two of the messages reused counter values and thus keystream. (The
> bounds are better if messages are smaller.)
>
> Consider a broken TLS implementation that always uses a zero nonce and
> is sending 16KB records as fast as possible. By the time it has sent
> 2^40 records (44 TB) there's about a 2^-32 chance that two of those
> records shared keystream bytes. (That's very rough and there might be
> a few stray factors of two missing in there.)
>
> That's a lot better than AES-GCM, but we're not saying that the nonces
> are completely irrelevant to security.
>
> Perhaps we need a different term to clarify this? Occasional nonce
> duplication tolerant?

   Which brings up a question I've resisted asking: Why are you doing this?

   If you want to have an AEAD scheme that is nonce-misuse resistant that
can use a fast(er) authentication scheme then why not just do RFC 5297
with GHASH instead of AES-CMAC? You're defining a new irreducible
polynomial that, to my knowledge, is not in existing hardware the way
that PCLMULQDQ using x^128 + x^7 + x^2 + x + 1, is in Intel chips.
You're defining a(nother) KDF /inside/ the cipher mode itself instead of
just letting a KDF, which all users of AES-GCM-SIV will use, generate a
double-wide key. And I don't see the reason for either.

>>> I agree that large AEAD messages have several problems. But I don't
>>> think that we have any need for a larger nonce (see above). (And the
>>> nonce is used with a counter only in the KDF phase, so it's unrelated
>>> to the maximum plaintext size.)
>> Is there any way that a larger nonce (e.g. 120 bits) hurts, other than
>> being inconsistent with existing IETF AEADs?
> With three bits for the counter, the largest the nonce could be is 125
> bits. But I think a nonce that's not a whole number of bytes would be
> too confusing.
>
> The nonce could be 120 bits (15 bytes) but that has no practical
> advantage over 96 bits. If you're picking nonces at random then the
> change in bounds is trivial (see multibirthday reference in the spec).
> If your nonce generation is broken and you're using a fixed value then
> the size is irrelevant.
>
> 96 bits is a "rounder" number and might save some alignment problems
> is all, really.

   The size of the nonce should not matter to a generic misuse-resistant
cipher mode.

   regards,

   Dan.

   [1] https://eprint.iacr.org/2006/221.pdf

>
>
> Cheers
>
> AGL
>


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From: Adam Langley <agl@imperialviolet.org>
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Subject: Re: [Cfrg] AES GCM SIV analysis
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On Thu, Jan 26, 2017 at 6:26 PM, Dan Harkins <dharkins@lounge.org> wrote:
>   But that is the definition used in the seminal work on the matter, [1].
> If you want to have a different notion concerning a lesser restriction on
> nonce reuse then you should use a different term.

That paper formalises an advantage that an attacker might have over an
ideal scheme. In the same way that block ciphers aren't ideal PRFs,
nonce-misuse-resistant schemes aren't hitting that ideal either. RFC
5297 doesn't hit it, at minimum because it'll run out of counter-space
after enough messages. AES-GCM-SIV isn't hitting it either.

But that doesn't mean that they aren't practically useful.

I'm not sure what an ideal NMR AEAD would look like, but it's probably
quite different to both RFC 5297 and AES-GCM-SIV and probably looks
like a wide-block construction. If someone can point at something they
think does hit it, that would be interesting to me at least. (Although
perhaps it's well trodden ground for those who are more familiar with
the literature than I.)

>   Which brings up a question I've resisted asking: Why are you doing this?
>
>   If you want to have an AEAD scheme that is nonce-misuse resistant that
> can use a fast(er) authentication scheme then why not just do RFC 5297
> with GHASH instead of AES-CMAC?

AES-GCM has lead to a state of the world where our large machines,
which need to encrypt and decrypt lots of data, end up having hardware
support for AES and GF(128) operations. We would like to take
advantage of that because it's hard to beat the speed and power
efficiency of dedicated hardware, but sometimes we want not to have to
worry about nonces.

> You're defining a new irreducible
> polynomial that, to my knowledge, is not in existing hardware the way
> that PCLMULQDQ using x^128 + x^7 + x^2 + x + 1, is in Intel chips.

PCLMULQDQ (and other hardware implementations, to my knowledge) is not
specific to that polynomial. Also, the polynomial in AES-GCM-SIV is
that polynomial, just with some ordering oddities addressed. See
https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03#appendix-A.

> You're defining a(nother) KDF /inside/ the cipher mode itself instead of
> just letting a KDF, which all users of AES-GCM-SIV will use, generate a
> double-wide key. And I don't see the reason for either.

Our KDF is per-nonce; it's not the same as having a double-width key
and partitioning it internally. We do this in order to get better
bounds when encrypting very large numbers of messages.


Cheers

AGL


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From: Watson Ladd <watsonbladd@gmail.com>
Date: Sun, 29 Jan 2017 14:33:39 -0800
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Subject: Re: [Cfrg] Help with the use of contexts
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On Tue, Jan 24, 2017 at 11:02 PM, Yoav Nir <ynir.ietf@gmail.com> wrote:
>
>>
>>> On 17 Jan 2017, at 13:48, Stephen Farrell <stephen.farrell@cs.tcd.ie> w=
rote:
>>>
>>>
>>> However, I really do wish that CFRG specs would not offer
>>> both choices - that will simply lead to repeating this
>>> discussion each time an IETF protocol wants to use the CFRG
>>> spec. And of course, different decisions will be made over
>>> time,
>>
>> Not over time. In the next few months the IESG is going to get documents=
 about EdDSA signatures from TLS, IPsecME and curdle for signatures in TLS,=
 IKE, and PKIX respectively.  If the decision is not the same in all of the=
m, I think (hope) that the IESG would ask why.
>
> So now that RFC 8032 is out and does include both choices, what is our ad=
vice to TLS, IPsecME and Curdle?  Contexts or no?
>
> Yoav
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg

No contexts. Why did we ever include them?

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


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> On 30 Jan 2017, at 0:33, Watson Ladd <watsonbladd@gmail.com> wrote:
>=20
> On Tue, Jan 24, 2017 at 11:02 PM, Yoav Nir <ynir.ietf@gmail.com> =
wrote:
>>=20
>>>=20
>>>> On 17 Jan 2017, at 13:48, Stephen Farrell =
<stephen.farrell@cs.tcd.ie> wrote:
>>>>=20
>>>>=20
>>>> However, I really do wish that CFRG specs would not offer
>>>> both choices - that will simply lead to repeating this
>>>> discussion each time an IETF protocol wants to use the CFRG
>>>> spec. And of course, different decisions will be made over
>>>> time,
>>>=20
>>> Not over time. In the next few months the IESG is going to get =
documents about EdDSA signatures from TLS, IPsecME and curdle for =
signatures in TLS, IKE, and PKIX respectively.  If the decision is not =
the same in all of them, I think (hope) that the IESG would ask why.
>>=20
>> So now that RFC 8032 is out and does include both choices, what is =
our advice to TLS, IPsecME and Curdle?  Contexts or no?
>>=20
>> Yoav
>>=20
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org
>> https://www.irtf.org/mailman/listinfo/cfrg
>=20
> No contexts. Why did we ever include them?

Seemed like a good idea at the time. The thread begins here:

https://mailarchive.ietf.org/arch/msg/cfrg/GOPQ6lgJcfrXboexQmgNk_ZIZW8 =
<https://mailarchive.ietf.org/arch/msg/cfrg/GOPQ6lgJcfrXboexQmgNk_ZIZW8>

Regardless, ISTM that almost nobody is advocating for using contexts now =
for Ed448 in any of the above applications, or for using Ed25519ctx in =
there.=20

Yoav


--Apple-Mail=_0F5A10DD-469A-4F49-83F4-38DE8AD4E258
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<html><head><meta http-equiv=3D"Content-Type" content=3D"text/html =
charset=3Dus-ascii"></head><body style=3D"word-wrap: break-word; =
-webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" =
class=3D""><br class=3D""><div><blockquote type=3D"cite" class=3D""><div =
class=3D"">On 30 Jan 2017, at 0:33, Watson Ladd &lt;<a =
href=3D"mailto:watsonbladd@gmail.com" =
class=3D"">watsonbladd@gmail.com</a>&gt; wrote:</div><br =
class=3D"Apple-interchange-newline"><div class=3D""><div class=3D"">On =
Tue, Jan 24, 2017 at 11:02 PM, Yoav Nir &lt;<a =
href=3D"mailto:ynir.ietf@gmail.com" class=3D"">ynir.ietf@gmail.com</a>&gt;=
 wrote:<br class=3D""><blockquote type=3D"cite" class=3D""><br =
class=3D""><blockquote type=3D"cite" class=3D""><br class=3D""><blockquote=
 type=3D"cite" class=3D"">On 17 Jan 2017, at 13:48, Stephen Farrell =
&lt;<a href=3D"mailto:stephen.farrell@cs.tcd.ie" =
class=3D"">stephen.farrell@cs.tcd.ie</a>&gt; wrote:<br class=3D""><br =
class=3D""><br class=3D"">However, I really do wish that CFRG specs =
would not offer<br class=3D"">both choices - that will simply lead to =
repeating this<br class=3D"">discussion each time an IETF protocol wants =
to use the CFRG<br class=3D"">spec. And of course, different decisions =
will be made over<br class=3D"">time,<br class=3D""></blockquote><br =
class=3D"">Not over time. In the next few months the IESG is going to =
get documents about EdDSA signatures from TLS, IPsecME and curdle for =
signatures in TLS, IKE, and PKIX respectively. &nbsp;If the decision is =
not the same in all of them, I think (hope) that the IESG would ask =
why.<br class=3D""></blockquote><br class=3D"">So now that RFC 8032 is =
out and does include both choices, what is our advice to TLS, IPsecME =
and Curdle? &nbsp;Contexts or no?<br class=3D""><br class=3D"">Yoav<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"">https://www.irtf.org/mailman/listinfo/cfrg<br =
class=3D""></blockquote><br class=3D"">No contexts. Why did we ever =
include them?<br class=3D""></div></div></blockquote></div><br =
class=3D""><div class=3D"">Seemed like a good idea at the time. The =
thread begins here:</div><div class=3D""><br class=3D""></div><div =
class=3D""><a =
href=3D"https://mailarchive.ietf.org/arch/msg/cfrg/GOPQ6lgJcfrXboexQmgNk_Z=
IZW8" =
class=3D"">https://mailarchive.ietf.org/arch/msg/cfrg/GOPQ6lgJcfrXboexQmgN=
k_ZIZW8</a></div><div class=3D""><br class=3D""></div><div =
class=3D"">Regardless, ISTM that almost nobody is advocating for using =
contexts now for Ed448 in any of the above applications, or for using =
Ed25519ctx in there.&nbsp;</div><div class=3D""><br class=3D""></div><div =
class=3D"">Yoav</div><div class=3D""><br class=3D""></div></body></html>=

--Apple-Mail=_0F5A10DD-469A-4F49-83F4-38DE8AD4E258--


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To: Yoav Nir <ynir.ietf@gmail.com>, Watson Ladd <watsonbladd@gmail.com>
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From: Stephen Farrell <stephen.farrell@cs.tcd.ie>
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Date: Sun, 29 Jan 2017 23:37:34 +0000
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Subject: Re: [Cfrg] Help with the use of contexts
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On 29/01/17 23:24, Yoav Nir wrote:
> Regardless, ISTM that almost nobody is advocating for using contexts
> now for Ed448 in any of the above applications, or for using
> Ed25519ctx in there.

If cfrg decided to revisit the decision and eliminate contexts,
I don't think anyone would really suffer. (And any sufferer
can always write an RFC too if that's really needed.)

Cheers,
S.


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Subject: Re: [Cfrg] Help with the use of contexts
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From: Alex Cope <alexcope@google.com>
Date: Mon, 30 Jan 2017 13:58:50 -0800
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To: Adam Langley <agl@imperialviolet.org>
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Cc: "cfrg@irtf.org" <cfrg@irtf.org>
Subject: Re: [Cfrg] AES GCM SIV analysis
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I'm also unconvinced that defining POLYVAL as modulo x^128 + x^127 + x^126
+ x^121 + 1 is better than defining it modulo x^128 + x^7 + x^2 + x + 1.

My reasons for thinking that  x^128 + x^7 + x^2 + x + 1 is a better
reducing polynomial are:
1) On X86, no performant implementation of POLYVAL will reduce to GHASH, as
that would result in unnecessarily byte swapping twice then calling
PCLMULQDQ. The same seems true for any implementation in a little-endian
machine.
2) If the concern is making a less performance sensitive implantation of
GCM-SIV easier to write given a GCM implantation, the relationship between
POLYVAL as currently defined and GHASH does help slightly. However,
implementing finite field multiplication with POLYVAL'S byte ordering
modulo x^128 + x^7 + x^2 + x + 1 given a reference GHASH implementation is
quite easy*, and most accidental errors in such implementation will be
detected by test vectors.  Thus I don't think the current design choice
makes GCM-SIV substantially easier to implement correctly.
3) x^128 + x^7 + x^2 + x + 1 is more 'natural' as as the lexicography first
irreducible polynomial.  It seems likely that future work that relies on
finite field multiplication will opt to use the byte ordering of POLYVAL
because it makes the most sense on little endian machines, and will also
reduce modulo  x^128 + x^7 + x^2 + x + 1.  I doubt anyone else will want to
use GHASH as currently defined, but if it were defined modulo x^128 + x^7 +
x^2 + x + 1, the implementation could be nicely reused. I think that in the
long term this will lead to more code reuse than having POLYVAL as a one
off finite field representation.

If you are strongly concerned reusing dedicated hardware or big-endian
implementations of GHASH then the current design makes some sense as a
compromise, but I'm unaware of such requirements.

Regards
-Alex

*I did it recently for a table-based implementation. You can look at the
patch here: https://patchwork.kernel.org/patch/9428397/

On Fri, Jan 27, 2017 at 12:21 PM, Adam Langley <agl@imperialviolet.org>
wrote:

> On Thu, Jan 26, 2017 at 6:26 PM, Dan Harkins <dharkins@lounge.org> wrote:
> >   But that is the definition used in the seminal work on the matter, [1].
> > If you want to have a different notion concerning a lesser restriction on
> > nonce reuse then you should use a different term.
>
> That paper formalises an advantage that an attacker might have over an
> ideal scheme. In the same way that block ciphers aren't ideal PRFs,
> nonce-misuse-resistant schemes aren't hitting that ideal either. RFC
> 5297 doesn't hit it, at minimum because it'll run out of counter-space
> after enough messages. AES-GCM-SIV isn't hitting it either.
>
> But that doesn't mean that they aren't practically useful.
>
> I'm not sure what an ideal NMR AEAD would look like, but it's probably
> quite different to both RFC 5297 and AES-GCM-SIV and probably looks
> like a wide-block construction. If someone can point at something they
> think does hit it, that would be interesting to me at least. (Although
> perhaps it's well trodden ground for those who are more familiar with
> the literature than I.)
>
> >   Which brings up a question I've resisted asking: Why are you doing
> this?
> >
> >   If you want to have an AEAD scheme that is nonce-misuse resistant that
> > can use a fast(er) authentication scheme then why not just do RFC 5297
> > with GHASH instead of AES-CMAC?
>
> AES-GCM has lead to a state of the world where our large machines,
> which need to encrypt and decrypt lots of data, end up having hardware
> support for AES and GF(128) operations. We would like to take
> advantage of that because it's hard to beat the speed and power
> efficiency of dedicated hardware, but sometimes we want not to have to
> worry about nonces.
>
> > You're defining a new irreducible
> > polynomial that, to my knowledge, is not in existing hardware the way
> > that PCLMULQDQ using x^128 + x^7 + x^2 + x + 1, is in Intel chips.
>
> PCLMULQDQ (and other hardware implementations, to my knowledge) is not
> specific to that polynomial. Also, the polynomial in AES-GCM-SIV is
> that polynomial, just with some ordering oddities addressed. See
> https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03#appendix-A.
>
> > You're defining a(nother) KDF /inside/ the cipher mode itself instead of
> > just letting a KDF, which all users of AES-GCM-SIV will use, generate a
> > double-wide key. And I don't see the reason for either.
>
> Our KDF is per-nonce; it's not the same as having a double-width key
> and partitioning it internally. We do this in order to get better
> bounds when encrypting very large numbers of messages.
>
>
> Cheers
>
> AGL
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
> https://www.irtf.org/mailman/listinfo/cfrg
>

--001a114b2888b3a5b6054756eb24
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div>I&#39;m also unconvinced that defining POLYVAL as mod=
ulo x^128 + x^127 + x^126 + x^121 + 1 is better than defining it modulo x^1=
28 + x^7 + x^2 + x + 1.=C2=A0<br></div><div><br></div><div>My reasons for t=
hinking that =C2=A0x^128 + x^7 + x^2 + x + 1 is a better reducing polynomia=
l are:</div><div>1) On X86, no performant implementation of POLYVAL will re=
duce to GHASH, as that would result in unnecessarily byte swapping twice th=
en calling PCLMULQDQ. The same seems true for any implementation in a littl=
e-endian machine.</div><div>2) If the concern is making a less performance =
sensitive implantation of GCM-SIV easier to write given a GCM implantation,=
 the relationship between POLYVAL as currently defined and GHASH does help =
slightly. However, implementing finite field multiplication with POLYVAL&#3=
9;S byte ordering modulo x^128 + x^7 + x^2 + x + 1 given a reference GHASH =
implementation is quite easy*, and most accidental errors in such implement=
ation will be detected by test vectors.=C2=A0 Thus I don&#39;t think the cu=
rrent design choice makes GCM-SIV substantially easier to implement correct=
ly.</div><div>3) x^128 + x^7 + x^2 + x + 1 is more &#39;natural&#39; as as =
the lexicography first irreducible polynomial.=C2=A0 It seems likely that f=
uture work that relies on finite field multiplication will opt to use the b=
yte ordering of POLYVAL because it makes the most sense on little endian ma=
chines, and will also reduce modulo =C2=A0x^128 + x^7 + x^2 + x + 1.=C2=A0 =
I doubt anyone else will want to use GHASH as currently defined, but if it =
were defined modulo x^128 + x^7 + x^2 + x + 1, the implementation could be =
nicely reused. I think that in the long term this will lead to more code re=
use than having POLYVAL as a one off finite field representation.</div><div=
><br></div><div>If you are strongly concerned reusing dedicated hardware or=
 big-endian implementations of GHASH then the current design makes some sen=
se as a compromise, but I&#39;m unaware of such requirements.</div><div><br=
></div><div>Regards</div><div>-Alex</div><div><font color=3D"#000000"><span=
 style=3D"font-size:13.3333px"><br></span></font></div><div><font color=3D"=
#000000"><span style=3D"font-size:13.3333px">*I did it recently for a table=
-based implementation. You can look at the patch here:=C2=A0<a href=3D"http=
s://patchwork.kernel.org/patch/9428397/">https://patchwork.kernel.org/patch=
/9428397/</a></span></font></div></div><div class=3D"gmail_extra"><br><div =
class=3D"gmail_quote">On Fri, Jan 27, 2017 at 12:21 PM, Adam Langley <span =
dir=3D"ltr">&lt;<a href=3D"mailto:agl@imperialviolet.org" target=3D"_blank"=
>agl@imperialviolet.org</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"><span class=3D"">On Thu, Jan 26, 2017 at 6:26 PM, Dan Harkins &lt;<a h=
ref=3D"mailto:dharkins@lounge.org">dharkins@lounge.org</a>&gt; wrote:<br>
&gt;=C2=A0 =C2=A0But that is the definition used in the seminal work on the=
 matter, [1].<br>
&gt; If you want to have a different notion concerning a lesser restriction=
 on<br>
&gt; nonce reuse then you should use a different term.<br>
<br>
</span>That paper formalises an advantage that an attacker might have over =
an<br>
ideal scheme. In the same way that block ciphers aren&#39;t ideal PRFs,<br>
nonce-misuse-resistant schemes aren&#39;t hitting that ideal either. RFC<br=
>
5297 doesn&#39;t hit it, at minimum because it&#39;ll run out of counter-sp=
ace<br>
after enough messages. AES-GCM-SIV isn&#39;t hitting it either.<br>
<br>
But that doesn&#39;t mean that they aren&#39;t practically useful.<br>
<br>
I&#39;m not sure what an ideal NMR AEAD would look like, but it&#39;s proba=
bly<br>
quite different to both RFC 5297 and AES-GCM-SIV and probably looks<br>
like a wide-block construction. If someone can point at something they<br>
think does hit it, that would be interesting to me at least. (Although<br>
perhaps it&#39;s well trodden ground for those who are more familiar with<b=
r>
the literature than I.)<br>
<span class=3D""><br>
&gt;=C2=A0 =C2=A0Which brings up a question I&#39;ve resisted asking: Why a=
re you doing this?<br>
&gt;<br>
&gt;=C2=A0 =C2=A0If you want to have an AEAD scheme that is nonce-misuse re=
sistant that<br>
&gt; can use a fast(er) authentication scheme then why not just do RFC 5297=
<br>
&gt; with GHASH instead of AES-CMAC?<br>
<br>
</span>AES-GCM has lead to a state of the world where our large machines,<b=
r>
which need to encrypt and decrypt lots of data, end up having hardware<br>
support for AES and GF(128) operations. We would like to take<br>
advantage of that because it&#39;s hard to beat the speed and power<br>
efficiency of dedicated hardware, but sometimes we want not to have to<br>
worry about nonces.<br>
<span class=3D""><br>
&gt; You&#39;re defining a new irreducible<br>
&gt; polynomial that, to my knowledge, is not in existing hardware the way<=
br>
&gt; that PCLMULQDQ using x^128 + x^7 + x^2 + x + 1, is in Intel chips.<br>
<br>
</span>PCLMULQDQ (and other hardware implementations, to my knowledge) is n=
ot<br>
specific to that polynomial. Also, the polynomial in AES-GCM-SIV is<br>
that polynomial, just with some ordering oddities addressed. See<br>
<a href=3D"https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03#appendix-A=
" rel=3D"noreferrer" target=3D"_blank">https://tools.ietf.org/html/<wbr>dra=
ft-irtf-cfrg-gcmsiv-03#<wbr>appendix-A</a>.<br>
<span class=3D""><br>
&gt; You&#39;re defining a(nother) KDF /inside/ the cipher mode itself inst=
ead of<br>
&gt; just letting a KDF, which all users of AES-GCM-SIV will use, generate =
a<br>
&gt; double-wide key. And I don&#39;t see the reason for either.<br>
<br>
</span>Our KDF is per-nonce; it&#39;s not the same as having a double-width=
 key<br>
and partitioning it internally. We do this in order to get better<br>
bounds when encrypting very large numbers of messages.<br>
<div class=3D"HOEnZb"><div class=3D"h5"><br>
<br>
Cheers<br>
<br>
AGL<br>
<br>
______________________________<wbr>_________________<br>
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<a href=3D"mailto:Cfrg@irtf.org">Cfrg@irtf.org</a><br>
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</div></div></blockquote></div><br></div>

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From: Watson Ladd <watsonbladd@gmail.com>
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Subject: Re: [Cfrg] AES GCM SIV analysis
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On Mon, Jan 30, 2017 at 1:58 PM, Alex Cope <alexcope@google.com> wrote:
> I'm also unconvinced that defining POLYVAL as modulo x^128 + x^127 + x^126 +
> x^121 + 1 is better than defining it modulo x^128 + x^7 + x^2 + x + 1.
>
> My reasons for thinking that  x^128 + x^7 + x^2 + x + 1 is a better reducing
> polynomial are:
> 1) On X86, no performant implementation of POLYVAL will reduce to GHASH, as
> that would result in unnecessarily byte swapping twice then calling
> PCLMULQDQ. The same seems true for any implementation in a little-endian
> machine.

I think it is important to look at how endianness matters in
polynomial arithmetic. GHASH takes the least
significant bit of a byte to be x^7, then takes a sequence of bytes
(a_0, a_1, \ldots a_15) to represent
a_0+a_1*x^8+a_2*x^16+\ldots+a_15*x^120. This is "little-endian": the
least significant byte is lowest. However,
it is an independent choice from the representation and layout of
words in memory.

Intel's implementation of GHASH does not reflect bytes, nor is byte
reflection sufficient in a naive implementation. For
details see: https://software.intel.com/sites/default/files/m/4/1/2/2/c/1230-Carry-Less-Multiplication-and-The-GCM-Mode_WP_.pdf

It's true that the specified polynomial doesn't have a Barret friendly
form. But the division by 128 naturally falls out of a Montgomery
based approach: precompute H*x^-8, then perform a multiplication add a
multiple of p(x) to clear out from x^0 to x^120, then shift down by a
whole number of bytes. The
multiplication by p(x) can be written as (x^8+x^7+x^6+x^1)*x^120+1 to
show that we don't need that many invocations of multiply. (Also, the
operations are linear: there are many ways to reduce the number of
reductions).

> 2) If the concern is making a less performance sensitive implantation of
> GCM-SIV easier to write given a GCM implantation, the relationship between
> POLYVAL as currently defined and GHASH does help slightly. However,
> implementing finite field multiplication with POLYVAL'S byte ordering modulo
> x^128 + x^7 + x^2 + x + 1 given a reference GHASH implementation is quite
> easy*, and most accidental errors in such implementation will be detected by
> test vectors.  Thus I don't think the current design choice makes GCM-SIV
> substantially easier to implement correctly.
> 3) x^128 + x^7 + x^2 + x + 1 is more 'natural' as as the lexicography first
> irreducible polynomial.  It seems likely that future work that relies on
> finite field multiplication will opt to use the byte ordering of POLYVAL
> because it makes the most sense on little endian machines, and will also
> reduce modulo  x^128 + x^7 + x^2 + x + 1.  I doubt anyone else will want to
> use GHASH as currently defined, but if it were defined modulo x^128 + x^7 +
> x^2 + x + 1, the implementation could be nicely reused. I think that in the
> long term this will lead to more code reuse than having POLYVAL as a one off
> finite field representation.
>
> If you are strongly concerned reusing dedicated hardware or big-endian
> implementations of GHASH then the current design makes some sense as a
> compromise, but I'm unaware of such requirements.

I don't know what "big-endian" is supposed to mean here. But yes,
reusing polynomial and field specific hardware is important on devices
which aren't Intel chips, many of which will want to use hardcoded
keys and may not be able to generate nonces effectively.

>
> Regards
> -Alex
>
> *I did it recently for a table-based implementation. You can look at the
> patch here: https://patchwork.kernel.org/patch/9428397/
>
> On Fri, Jan 27, 2017 at 12:21 PM, Adam Langley <agl@imperialviolet.org>
> wrote:
>>
>> On Thu, Jan 26, 2017 at 6:26 PM, Dan Harkins <dharkins@lounge.org> wrote:
>> >   But that is the definition used in the seminal work on the matter,
>> > [1].
>> > If you want to have a different notion concerning a lesser restriction
>> > on
>> > nonce reuse then you should use a different term.
>>
>> That paper formalises an advantage that an attacker might have over an
>> ideal scheme. In the same way that block ciphers aren't ideal PRFs,
>> nonce-misuse-resistant schemes aren't hitting that ideal either. RFC
>> 5297 doesn't hit it, at minimum because it'll run out of counter-space
>> after enough messages. AES-GCM-SIV isn't hitting it either.
>>
>> But that doesn't mean that they aren't practically useful.
>>
>> I'm not sure what an ideal NMR AEAD would look like, but it's probably
>> quite different to both RFC 5297 and AES-GCM-SIV and probably looks
>> like a wide-block construction. If someone can point at something they
>> think does hit it, that would be interesting to me at least. (Although
>> perhaps it's well trodden ground for those who are more familiar with
>> the literature than I.)
>>
>> >   Which brings up a question I've resisted asking: Why are you doing
>> > this?
>> >
>> >   If you want to have an AEAD scheme that is nonce-misuse resistant that
>> > can use a fast(er) authentication scheme then why not just do RFC 5297
>> > with GHASH instead of AES-CMAC?
>>
>> AES-GCM has lead to a state of the world where our large machines,
>> which need to encrypt and decrypt lots of data, end up having hardware
>> support for AES and GF(128) operations. We would like to take
>> advantage of that because it's hard to beat the speed and power
>> efficiency of dedicated hardware, but sometimes we want not to have to
>> worry about nonces.
>>
>> > You're defining a new irreducible
>> > polynomial that, to my knowledge, is not in existing hardware the way
>> > that PCLMULQDQ using x^128 + x^7 + x^2 + x + 1, is in Intel chips.
>>
>> PCLMULQDQ (and other hardware implementations, to my knowledge) is not
>> specific to that polynomial. Also, the polynomial in AES-GCM-SIV is
>> that polynomial, just with some ordering oddities addressed. See
>> https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03#appendix-A.
>>
>> > You're defining a(nother) KDF /inside/ the cipher mode itself instead of
>> > just letting a KDF, which all users of AES-GCM-SIV will use, generate a
>> > double-wide key. And I don't see the reason for either.
>>
>> Our KDF is per-nonce; it's not the same as having a double-width key
>> and partitioning it internally. We do this in order to get better
>> bounds when encrypting very large numbers of messages.
>>
>>
>> Cheers
>>
>> AGL
>>
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org
>> https://www.irtf.org/mailman/listinfo/cfrg
>
>
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org
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>



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


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From: Shay Gueron <shay.gueron@gmail.com>
Date: Tue, 31 Jan 2017 03:04:06 +0200
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Cc: Adam Langley <agl@imperialviolet.org>, "cfrg@irtf.org" <cfrg@irtf.org>
Subject: Re: [Cfrg] AES GCM SIV analysis
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>>> 1) On X86, no performant implementation of POLYVAL will reduce to
>>> GHASH, as that would result in unnecessarily byte swapping twice
>>> then calling PCLMULQDQ.

I suggest to count the number of byte swaps done with AES-GCM-SIV optimized
implementation on X86 (see the code in my guthub, for example), and the
number of bye swaps done with AES-GCM (take the OpenSSL example).
The answers are: 0 for AES-GCM-SIV and 1 per each block (of the message and
the AAD +1) in OpenSSL.

The identity provided in the spec, relating GHASH and POLYVAL is provided
for convenience, in case someone chooses to re-use software (or hardware).
It is not suggesting that the fastest way to compute POLYVAL is through
GHASH.

The reason is (again) the order of bits inside the bytes. The definition of
AES-GCM which has this order reversed with respect to the order of bits in
the bytes of AES input/output.

In fact, although many would think that AES-GCM operates natively in
GF(2^128) with the reduction polynomial is x^128 + x^7 + x^2 + x + 1, this
is not the case (unless you are reversing the bits in the bytes of each
block). AES-GCM is operating in the field represented by the reduction
polynomial x^128 + x^127 + x^126 + x^121 + 1.

There will be explained in detail in a paper that I will post soon. But
perhaps the slides in my RWC talk could explain this for now (
https://crypto.stanford.edu/RealWorldCrypto/slides/gueron.pdf)

Regards, Shay


2017-01-30 23:58 GMT+02:00 Alex Cope <alexcope@google.com>:

> I'm also unconvinced that defining POLYVAL as modulo x^128 + x^127 + x^126
> + x^121 + 1 is better than defining it modulo x^128 + x^7 + x^2 + x + 1.
>
> My reasons for thinking that  x^128 + x^7 + x^2 + x + 1 is a better
> reducing polynomial are:
> 1) On X86, no performant implementation of POLYVAL will reduce to GHASH,
> as that would result in unnecessarily byte swapping twice then calling
> PCLMULQDQ. The same seems true for any implementation in a little-endian
> machine.
> 2) If the concern is making a less performance sensitive implantation of
> GCM-SIV easier to write given a GCM implantation, the relationship between
> POLYVAL as currently defined and GHASH does help slightly. However,
> implementing finite field multiplication with POLYVAL'S byte ordering
> modulo x^128 + x^7 + x^2 + x + 1 given a reference GHASH implementation is
> quite easy*, and most accidental errors in such implementation will be
> detected by test vectors.  Thus I don't think the current design choice
> makes GCM-SIV substantially easier to implement correctly.
> 3) x^128 + x^7 + x^2 + x + 1 is more 'natural' as as the lexicography
> first irreducible polynomial.  It seems likely that future work that relies
> on finite field multiplication will opt to use the byte ordering of POLYVAL
> because it makes the most sense on little endian machines, and will also
> reduce modulo  x^128 + x^7 + x^2 + x + 1.  I doubt anyone else will want to
> use GHASH as currently defined, but if it were defined modulo x^128 + x^7 +
> x^2 + x + 1, the implementation could be nicely reused. I think that in the
> long term this will lead to more code reuse than having POLYVAL as a one
> off finite field representation.
>
> If you are strongly concerned reusing dedicated hardware or big-endian
> implementations of GHASH then the current design makes some sense as a
> compromise, but I'm unaware of such requirements.
>
> Regards
> -Alex
>
> *I did it recently for a table-based implementation. You can look at the
> patch here: https://patchwork.kernel.org/patch/9428397/
>
> On Fri, Jan 27, 2017 at 12:21 PM, Adam Langley <agl@imperialviolet.org>
> wrote:
>
>> On Thu, Jan 26, 2017 at 6:26 PM, Dan Harkins <dharkins@lounge.org> wrote:
>> >   But that is the definition used in the seminal work on the matter,
>> [1].
>> > If you want to have a different notion concerning a lesser restriction
>> on
>> > nonce reuse then you should use a different term.
>>
>> That paper formalises an advantage that an attacker might have over an
>> ideal scheme. In the same way that block ciphers aren't ideal PRFs,
>> nonce-misuse-resistant schemes aren't hitting that ideal either. RFC
>> 5297 doesn't hit it, at minimum because it'll run out of counter-space
>> after enough messages. AES-GCM-SIV isn't hitting it either.
>>
>> But that doesn't mean that they aren't practically useful.
>>
>> I'm not sure what an ideal NMR AEAD would look like, but it's probably
>> quite different to both RFC 5297 and AES-GCM-SIV and probably looks
>> like a wide-block construction. If someone can point at something they
>> think does hit it, that would be interesting to me at least. (Although
>> perhaps it's well trodden ground for those who are more familiar with
>> the literature than I.)
>>
>> >   Which brings up a question I've resisted asking: Why are you doing
>> this?
>> >
>> >   If you want to have an AEAD scheme that is nonce-misuse resistant that
>> > can use a fast(er) authentication scheme then why not just do RFC 5297
>> > with GHASH instead of AES-CMAC?
>>
>> AES-GCM has lead to a state of the world where our large machines,
>> which need to encrypt and decrypt lots of data, end up having hardware
>> support for AES and GF(128) operations. We would like to take
>> advantage of that because it's hard to beat the speed and power
>> efficiency of dedicated hardware, but sometimes we want not to have to
>> worry about nonces.
>>
>> > You're defining a new irreducible
>> > polynomial that, to my knowledge, is not in existing hardware the way
>> > that PCLMULQDQ using x^128 + x^7 + x^2 + x + 1, is in Intel chips.
>>
>> PCLMULQDQ (and other hardware implementations, to my knowledge) is not
>> specific to that polynomial. Also, the polynomial in AES-GCM-SIV is
>> that polynomial, just with some ordering oddities addressed. See
>> https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03#appendix-A.
>>
>> > You're defining a(nother) KDF /inside/ the cipher mode itself instead of
>> > just letting a KDF, which all users of AES-GCM-SIV will use, generate a
>> > double-wide key. And I don't see the reason for either.
>>
>> Our KDF is per-nonce; it's not the same as having a double-width key
>> and partitioning it internally. We do this in order to get better
>> bounds when encrypting very large numbers of messages.
>>
>>
>> Cheers
>>
>> AGL
>>
>> _______________________________________________
>> 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
>
>

--f403045dc5d24f7b3805475982a5
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

<div dir=3D"rtl"><div dir=3D"ltr">&gt;&gt;&gt; 1) On X86, no performant imp=
lementation of POLYVAL will reduce to=C2=A0<br></div><div dir=3D"ltr">&gt;&=
gt;&gt; GHASH, as that would result in unnecessarily byte swapping twice=C2=
=A0</div><div dir=3D"ltr">&gt;&gt;&gt; then calling PCLMULQDQ.=C2=A0</div><=
div dir=3D"ltr"><br></div><div dir=3D"ltr">I suggest to count the number of=
 byte swaps done with AES-GCM-SIV optimized implementation on X86 (see the =
code in my guthub, for example), and the number of bye swaps done with AES-=
GCM (take the OpenSSL example).=C2=A0</div><div dir=3D"ltr">The answers are=
: 0 for AES-GCM-SIV and 1 per each block (of the message and the AAD +1) in=
 OpenSSL.=C2=A0<br></div><div dir=3D"ltr"><br></div><div dir=3D"ltr">The id=
entity provided in the spec, relating GHASH and POLYVAL is provided for con=
venience, in case someone chooses to re-use software (or hardware). It is n=
ot suggesting that the fastest way to compute POLYVAL is through GHASH.=C2=
=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">The reason is (again) =
the order of bits inside the bytes. The definition of AES-GCM which has thi=
s order reversed with respect to the order of bits in the bytes of AES inpu=
t/output.=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">In fact, a=
lthough many would think that AES-GCM operates natively in GF(2^128) with t=
he reduction polynomial is x^128 + x^7 + x^2 + x + 1, this is not the case =
(unless you are reversing the bits in the bytes of each block). AES-GCM is =
operating in the field represented by the reduction polynomial x^128 + x^12=
7 + x^126 + x^121 + 1.=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D"lt=
r">There will be explained in detail in a paper that I will post soon. But =
perhaps the slides in my RWC talk could explain this for now (<a href=3D"ht=
tps://crypto.stanford.edu/RealWorldCrypto/slides/gueron.pdf">https://crypto=
.stanford.edu/RealWorldCrypto/slides/gueron.pdf</a>)</div><div dir=3D"ltr">=
<br></div><div dir=3D"ltr">Regards, Shay =C2=A0</div><div dir=3D"ltr"><br><=
/div><div class=3D"gmail_extra"><br><div class=3D"gmail_quote"><div dir=3D"=
ltr">2017-01-30 23:58 GMT+02:00 Alex Cope <span dir=3D"ltr">&lt;<a href=3D"=
mailto:alexcope@google.com" target=3D"_blank">alexcope@google.com</a>&gt;</=
span>:</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"l=
tr"><div>I&#39;m also unconvinced that defining POLYVAL as modulo x^128 + x=
^127 + x^126 + x^121 + 1 is better than defining it modulo x^128 + x^7 + x^=
2 + x + 1.=C2=A0<br></div><div><br></div><div>My reasons for thinking that =
=C2=A0x^128 + x^7 + x^2 + x + 1 is a better reducing polynomial are:</div><=
div>1) On X86, no performant implementation of POLYVAL will reduce to GHASH=
, as that would result in unnecessarily byte swapping twice then calling PC=
LMULQDQ. The same seems true for any implementation in a little-endian mach=
ine.</div><div>2) If the concern is making a less performance sensitive imp=
lantation of GCM-SIV easier to write given a GCM implantation, the relation=
ship between POLYVAL as currently defined and GHASH does help slightly. How=
ever, implementing finite field multiplication with POLYVAL&#39;S byte orde=
ring modulo x^128 + x^7 + x^2 + x + 1 given a reference GHASH implementatio=
n is quite easy*, and most accidental errors in such implementation will be=
 detected by test vectors.=C2=A0 Thus I don&#39;t think the current design =
choice makes GCM-SIV substantially easier to implement correctly.</div><div=
>3) x^128 + x^7 + x^2 + x + 1 is more &#39;natural&#39; as as the lexicogra=
phy first irreducible polynomial.=C2=A0 It seems likely that future work th=
at relies on finite field multiplication will opt to use the byte ordering =
of POLYVAL because it makes the most sense on little endian machines, and w=
ill also reduce modulo =C2=A0x^128 + x^7 + x^2 + x + 1.=C2=A0 I doubt anyon=
e else will want to use GHASH as currently defined, but if it were defined =
modulo x^128 + x^7 + x^2 + x + 1, the implementation could be nicely reused=
. I think that in the long term this will lead to more code reuse than havi=
ng POLYVAL as a one off finite field representation.</div><div><br></div><d=
iv>If you are strongly concerned reusing dedicated hardware or big-endian i=
mplementations of GHASH then the current design makes some sense as a compr=
omise, but I&#39;m unaware of such requirements.</div><div><br></div><div>R=
egards</div><div>-Alex</div><div><font color=3D"#000000"><span style=3D"fon=
t-size:13.3333px"><br></span></font></div><div><font color=3D"#000000"><spa=
n style=3D"font-size:13.3333px">*I did it recently for a table-based implem=
entation. You can look at the patch here:=C2=A0<a href=3D"https://patchwork=
.kernel.org/patch/9428397/" target=3D"_blank">https://patchwork.<wbr>kernel=
.org/patch/9428397/</a></span></font></div></div><div class=3D"gmail-HOEnZb=
"><div class=3D"gmail-h5"><div class=3D"gmail_extra"><br><div class=3D"gmai=
l_quote">On Fri, Jan 27, 2017 at 12:21 PM, Adam Langley <span dir=3D"ltr">&=
lt;<a href=3D"mailto:agl@imperialviolet.org" target=3D"_blank">agl@imperial=
violet.org</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"><span>On Thu, Jan 26, 2017 at 6:26 PM, Dan Harkins &lt;<a href=
=3D"mailto:dharkins@lounge.org" target=3D"_blank">dharkins@lounge.org</a>&g=
t; wrote:<br>
&gt;=C2=A0 =C2=A0But that is the definition used in the seminal work on the=
 matter, [1].<br>
&gt; If you want to have a different notion concerning a lesser restriction=
 on<br>
&gt; nonce reuse then you should use a different term.<br>
<br>
</span>That paper formalises an advantage that an attacker might have over =
an<br>
ideal scheme. In the same way that block ciphers aren&#39;t ideal PRFs,<br>
nonce-misuse-resistant schemes aren&#39;t hitting that ideal either. RFC<br=
>
5297 doesn&#39;t hit it, at minimum because it&#39;ll run out of counter-sp=
ace<br>
after enough messages. AES-GCM-SIV isn&#39;t hitting it either.<br>
<br>
But that doesn&#39;t mean that they aren&#39;t practically useful.<br>
<br>
I&#39;m not sure what an ideal NMR AEAD would look like, but it&#39;s proba=
bly<br>
quite different to both RFC 5297 and AES-GCM-SIV and probably looks<br>
like a wide-block construction. If someone can point at something they<br>
think does hit it, that would be interesting to me at least. (Although<br>
perhaps it&#39;s well trodden ground for those who are more familiar with<b=
r>
the literature than I.)<br>
<span><br>
&gt;=C2=A0 =C2=A0Which brings up a question I&#39;ve resisted asking: Why a=
re you doing this?<br>
&gt;<br>
&gt;=C2=A0 =C2=A0If you want to have an AEAD scheme that is nonce-misuse re=
sistant that<br>
&gt; can use a fast(er) authentication scheme then why not just do RFC 5297=
<br>
&gt; with GHASH instead of AES-CMAC?<br>
<br>
</span>AES-GCM has lead to a state of the world where our large machines,<b=
r>
which need to encrypt and decrypt lots of data, end up having hardware<br>
support for AES and GF(128) operations. We would like to take<br>
advantage of that because it&#39;s hard to beat the speed and power<br>
efficiency of dedicated hardware, but sometimes we want not to have to<br>
worry about nonces.<br>
<span><br>
&gt; You&#39;re defining a new irreducible<br>
&gt; polynomial that, to my knowledge, is not in existing hardware the way<=
br>
&gt; that PCLMULQDQ using x^128 + x^7 + x^2 + x + 1, is in Intel chips.<br>
<br>
</span>PCLMULQDQ (and other hardware implementations, to my knowledge) is n=
ot<br>
specific to that polynomial. Also, the polynomial in AES-GCM-SIV is<br>
that polynomial, just with some ordering oddities addressed. See<br>
<a href=3D"https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03#appendix-A=
" rel=3D"noreferrer" target=3D"_blank">https://tools.ietf.org/html/dr<wbr>a=
ft-irtf-cfrg-gcmsiv-03#append<wbr>ix-A</a>.<br>
<span><br>
&gt; You&#39;re defining a(nother) KDF /inside/ the cipher mode itself inst=
ead of<br>
&gt; just letting a KDF, which all users of AES-GCM-SIV will use, generate =
a<br>
&gt; double-wide key. And I don&#39;t see the reason for either.<br>
<br>
</span>Our KDF is per-nonce; it&#39;s not the same as having a double-width=
 key<br>
and partitioning it internally. We do this in order to get better<br>
bounds when encrypting very large numbers of messages.<br>
<div class=3D"gmail-m_-5268966438158733069HOEnZb"><div class=3D"gmail-m_-52=
68966438158733069h5"><br>
<br>
Cheers<br>
<br>
AGL<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>
</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></div>

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Date: Mon, 30 Jan 2017 17:45:49 -0800
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Subject: Re: [Cfrg] AES GCM SIV analysis
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Thanks for the quick responses to my comments. I should have more carefully
proofread my first message, as I confused bit and byte reflection at
several points, my bad.

I'm in agreement that the bit ordering in POLYVAL is far more better, and
after looking into Montgomery multiplication a bit more, working
modulo x^128 + x^127 + x^126 + x^121 + 1 makes more sense. Consider me
convinced.

-Alex


On Mon, Jan 30, 2017 at 5:04 PM, Shay Gueron <shay.gueron@gmail.com> wrote:

> >>> 1) On X86, no performant implementation of POLYVAL will reduce to
> >>> GHASH, as that would result in unnecessarily byte swapping twice
> >>> then calling PCLMULQDQ.
>
> I suggest to count the number of byte swaps done with AES-GCM-SIV
> optimized implementation on X86 (see the code in my guthub, for example),
> and the number of bye swaps done with AES-GCM (take the OpenSSL example).
> The answers are: 0 for AES-GCM-SIV and 1 per each block (of the message
> and the AAD +1) in OpenSSL.
>
> The identity provided in the spec, relating GHASH and POLYVAL is provided
> for convenience, in case someone chooses to re-use software (or hardware).
> It is not suggesting that the fastest way to compute POLYVAL is through
> GHASH.
>
> The reason is (again) the order of bits inside the bytes. The definition
> of AES-GCM which has this order reversed with respect to the order of bits
> in the bytes of AES input/output.
>
> In fact, although many would think that AES-GCM operates natively in
> GF(2^128) with the reduction polynomial is x^128 + x^7 + x^2 + x + 1, this
> is not the case (unless you are reversing the bits in the bytes of each
> block). AES-GCM is operating in the field represented by the reduction
> polynomial x^128 + x^127 + x^126 + x^121 + 1.
>
> There will be explained in detail in a paper that I will post soon. But
> perhaps the slides in my RWC talk could explain this for now (
> https://crypto.stanford.edu/RealWorldCrypto/slides/gueron.pdf)
>
> Regards, Shay
>
>
> 2017-01-30 23:58 GMT+02:00 Alex Cope <alexcope@google.com>:
>
>> I'm also unconvinced that defining POLYVAL as modulo x^128 + x^127 +
>> x^126 + x^121 + 1 is better than defining it modulo x^128 + x^7 + x^2 + x +
>> 1.
>>
>> My reasons for thinking that  x^128 + x^7 + x^2 + x + 1 is a better
>> reducing polynomial are:
>> 1) On X86, no performant implementation of POLYVAL will reduce to GHASH,
>> as that would result in unnecessarily byte swapping twice then calling
>> PCLMULQDQ. The same seems true for any implementation in a little-endian
>> machine.
>> 2) If the concern is making a less performance sensitive implantation of
>> GCM-SIV easier to write given a GCM implantation, the relationship between
>> POLYVAL as currently defined and GHASH does help slightly. However,
>> implementing finite field multiplication with POLYVAL'S byte ordering
>> modulo x^128 + x^7 + x^2 + x + 1 given a reference GHASH implementation is
>> quite easy*, and most accidental errors in such implementation will be
>> detected by test vectors.  Thus I don't think the current design choice
>> makes GCM-SIV substantially easier to implement correctly.
>> 3) x^128 + x^7 + x^2 + x + 1 is more 'natural' as as the lexicography
>> first irreducible polynomial.  It seems likely that future work that relies
>> on finite field multiplication will opt to use the byte ordering of POLYVAL
>> because it makes the most sense on little endian machines, and will also
>> reduce modulo  x^128 + x^7 + x^2 + x + 1.  I doubt anyone else will want to
>> use GHASH as currently defined, but if it were defined modulo x^128 + x^7 +
>> x^2 + x + 1, the implementation could be nicely reused. I think that in the
>> long term this will lead to more code reuse than having POLYVAL as a one
>> off finite field representation.
>>
>> If you are strongly concerned reusing dedicated hardware or big-endian
>> implementations of GHASH then the current design makes some sense as a
>> compromise, but I'm unaware of such requirements.
>>
>> Regards
>> -Alex
>>
>> *I did it recently for a table-based implementation. You can look at the
>> patch here: https://patchwork.kernel.org/patch/9428397/
>>
>> On Fri, Jan 27, 2017 at 12:21 PM, Adam Langley <agl@imperialviolet.org>
>> wrote:
>>
>>> On Thu, Jan 26, 2017 at 6:26 PM, Dan Harkins <dharkins@lounge.org>
>>> wrote:
>>> >   But that is the definition used in the seminal work on the matter,
>>> [1].
>>> > If you want to have a different notion concerning a lesser restriction
>>> on
>>> > nonce reuse then you should use a different term.
>>>
>>> That paper formalises an advantage that an attacker might have over an
>>> ideal scheme. In the same way that block ciphers aren't ideal PRFs,
>>> nonce-misuse-resistant schemes aren't hitting that ideal either. RFC
>>> 5297 doesn't hit it, at minimum because it'll run out of counter-space
>>> after enough messages. AES-GCM-SIV isn't hitting it either.
>>>
>>> But that doesn't mean that they aren't practically useful.
>>>
>>> I'm not sure what an ideal NMR AEAD would look like, but it's probably
>>> quite different to both RFC 5297 and AES-GCM-SIV and probably looks
>>> like a wide-block construction. If someone can point at something they
>>> think does hit it, that would be interesting to me at least. (Although
>>> perhaps it's well trodden ground for those who are more familiar with
>>> the literature than I.)
>>>
>>> >   Which brings up a question I've resisted asking: Why are you doing
>>> this?
>>> >
>>> >   If you want to have an AEAD scheme that is nonce-misuse resistant
>>> that
>>> > can use a fast(er) authentication scheme then why not just do RFC 5297
>>> > with GHASH instead of AES-CMAC?
>>>
>>> AES-GCM has lead to a state of the world where our large machines,
>>> which need to encrypt and decrypt lots of data, end up having hardware
>>> support for AES and GF(128) operations. We would like to take
>>> advantage of that because it's hard to beat the speed and power
>>> efficiency of dedicated hardware, but sometimes we want not to have to
>>> worry about nonces.
>>>
>>> > You're defining a new irreducible
>>> > polynomial that, to my knowledge, is not in existing hardware the way
>>> > that PCLMULQDQ using x^128 + x^7 + x^2 + x + 1, is in Intel chips.
>>>
>>> PCLMULQDQ (and other hardware implementations, to my knowledge) is not
>>> specific to that polynomial. Also, the polynomial in AES-GCM-SIV is
>>> that polynomial, just with some ordering oddities addressed. See
>>> https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03#appendix-A.
>>>
>>> > You're defining a(nother) KDF /inside/ the cipher mode itself instead
>>> of
>>> > just letting a KDF, which all users of AES-GCM-SIV will use, generate a
>>> > double-wide key. And I don't see the reason for either.
>>>
>>> Our KDF is per-nonce; it's not the same as having a double-width key
>>> and partitioning it internally. We do this in order to get better
>>> bounds when encrypting very large numbers of messages.
>>>
>>>
>>> Cheers
>>>
>>> AGL
>>>
>>> _______________________________________________
>>> 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
>>
>>
>

--001a113c06d477de1e05475a1778
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_extra">Thanks for the quick responses =
to my comments. I should have more carefully proofread my first message, as=
 I confused bit and byte reflection at several points, my bad.</div><div cl=
ass=3D"gmail_extra"><br></div><div class=3D"gmail_extra">I&#39;m in agreeme=
nt that the bit ordering in POLYVAL is far more better, and after looking i=
nto=C2=A0<span style=3D"font-size:12.8px">Montgomery multiplication=C2=A0a =
bit more, working modulo=C2=A0x^128 + x^127 + x^126 + x^121 + 1 makes more =
sense. Consider me convinced.</span></div><div class=3D"gmail_extra"><span =
style=3D"font-size:12.8px"><br></span></div><div class=3D"gmail_extra"><spa=
n style=3D"font-size:12.8px">-Alex</span></div><div class=3D"gmail_extra"><=
br></div><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">On Mon, =
Jan 30, 2017 at 5:04 PM, Shay Gueron <span dir=3D"ltr">&lt;<a href=3D"mailt=
o:shay.gueron@gmail.com" target=3D"_blank">shay.gueron@gmail.com</a>&gt;</s=
pan> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0p=
x 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir=
=3D"rtl"><span class=3D"gmail-"><div dir=3D"ltr">&gt;&gt;&gt; 1) On X86, no=
 performant implementation of POLYVAL will reduce to=C2=A0<br></div><div di=
r=3D"ltr">&gt;&gt;&gt; GHASH, as that would result in unnecessarily byte sw=
apping twice=C2=A0</div><div dir=3D"ltr">&gt;&gt;&gt; then calling PCLMULQD=
Q.=C2=A0</div><div dir=3D"ltr"><br></div></span><div dir=3D"ltr">I suggest =
to count the number of byte swaps done with AES-GCM-SIV optimized implement=
ation on X86 (see the code in my guthub, for example), and the number of by=
e swaps done with AES-GCM (take the OpenSSL example).=C2=A0</div><div dir=
=3D"ltr">The answers are: 0 for AES-GCM-SIV and 1 per each block (of the me=
ssage and the AAD +1) in OpenSSL.=C2=A0<br></div><div dir=3D"ltr"><br></div=
><div dir=3D"ltr">The identity provided in the spec, relating GHASH and POL=
YVAL is provided for convenience, in case someone chooses to re-use softwar=
e (or hardware). It is not suggesting that the fastest way to compute POLYV=
AL is through GHASH.=C2=A0</div><div dir=3D"ltr"><br></div><div dir=3D"ltr"=
>The reason is (again) the order of bits inside the bytes. The definition o=
f AES-GCM which has this order reversed with respect to the order of bits i=
n the bytes of AES input/output.=C2=A0</div><div dir=3D"ltr"><br></div><div=
 dir=3D"ltr">In fact, although many would think that AES-GCM operates nativ=
ely in GF(2^128) with the reduction polynomial is x^128 + x^7 + x^2 + x + 1=
, this is not the case (unless you are reversing the bits in the bytes of e=
ach block). AES-GCM is operating in the field represented by the reduction =
polynomial x^128 + x^127 + x^126 + x^121 + 1.=C2=A0</div><div dir=3D"ltr"><=
br></div><div dir=3D"ltr">There will be explained in detail in a paper that=
 I will post soon. But perhaps the slides in my RWC talk could explain this=
 for now (<a href=3D"https://crypto.stanford.edu/RealWorldCrypto/slides/gue=
ron.pdf" target=3D"_blank">https://crypto.stanford.edu/<wbr>RealWorldCrypto=
/slides/gueron.<wbr>pdf</a>)</div><div dir=3D"ltr"><br></div><div dir=3D"lt=
r">Regards, Shay =C2=A0</div><div><div class=3D"gmail-h5"><div dir=3D"ltr">=
<br></div><div class=3D"gmail_extra"><br><div class=3D"gmail_quote"><div di=
r=3D"ltr">2017-01-30 23:58 GMT+02:00 Alex Cope <span dir=3D"ltr">&lt;<a hre=
f=3D"mailto:alexcope@google.com" target=3D"_blank">alexcope@google.com</a>&=
gt;</span>:</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>I&#39;m also unconvinced that defining POLYVAL as modulo x^12=
8 + x^127 + x^126 + x^121 + 1 is better than defining it modulo x^128 + x^7=
 + x^2 + x + 1.=C2=A0<br></div><div><br></div><div>My reasons for thinking =
that =C2=A0x^128 + x^7 + x^2 + x + 1 is a better reducing polynomial are:</=
div><div>1) On X86, no performant implementation of POLYVAL will reduce to =
GHASH, as that would result in unnecessarily byte swapping twice then calli=
ng PCLMULQDQ. The same seems true for any implementation in a little-endian=
 machine.</div><div>2) If the concern is making a less performance sensitiv=
e implantation of GCM-SIV easier to write given a GCM implantation, the rel=
ationship between POLYVAL as currently defined and GHASH does help slightly=
. However, implementing finite field multiplication with POLYVAL&#39;S byte=
 ordering modulo x^128 + x^7 + x^2 + x + 1 given a reference GHASH implemen=
tation is quite easy*, and most accidental errors in such implementation wi=
ll be detected by test vectors.=C2=A0 Thus I don&#39;t think the current de=
sign choice makes GCM-SIV substantially easier to implement correctly.</div=
><div>3) x^128 + x^7 + x^2 + x + 1 is more &#39;natural&#39; as as the lexi=
cography first irreducible polynomial.=C2=A0 It seems likely that future wo=
rk that relies on finite field multiplication will opt to use the byte orde=
ring of POLYVAL because it makes the most sense on little endian machines, =
and will also reduce modulo =C2=A0x^128 + x^7 + x^2 + x + 1.=C2=A0 I doubt =
anyone else will want to use GHASH as currently defined, but if it were def=
ined modulo x^128 + x^7 + x^2 + x + 1, the implementation could be nicely r=
eused. I think that in the long term this will lead to more code reuse than=
 having POLYVAL as a one off finite field representation.</div><div><br></d=
iv><div>If you are strongly concerned reusing dedicated hardware or big-end=
ian implementations of GHASH then the current design makes some sense as a =
compromise, but I&#39;m unaware of such requirements.</div><div><br></div><=
div>Regards</div><div>-Alex</div><div><font color=3D"#000000"><span style=
=3D"font-size:13.3333px"><br></span></font></div><div><font color=3D"#00000=
0"><span style=3D"font-size:13.3333px">*I did it recently for a table-based=
 implementation. You can look at the patch here:=C2=A0<a href=3D"https://pa=
tchwork.kernel.org/patch/9428397/" target=3D"_blank">https://patchwork.kern=
el<wbr>.org/patch/9428397/</a></span></font></div></div><div class=3D"gmail=
-m_114949061650247928gmail-HOEnZb"><div class=3D"gmail-m_114949061650247928=
gmail-h5"><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">On Fri,=
 Jan 27, 2017 at 12:21 PM, Adam Langley <span dir=3D"ltr">&lt;<a href=3D"ma=
ilto:agl@imperialviolet.org" target=3D"_blank">agl@imperialviolet.org</a>&g=
t;</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0px 0=
px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><span=
>On Thu, Jan 26, 2017 at 6:26 PM, Dan Harkins &lt;<a href=3D"mailto:dharkin=
s@lounge.org" target=3D"_blank">dharkins@lounge.org</a>&gt; wrote:<br>
&gt;=C2=A0 =C2=A0But that is the definition used in the seminal work on the=
 matter, [1].<br>
&gt; If you want to have a different notion concerning a lesser restriction=
 on<br>
&gt; nonce reuse then you should use a different term.<br>
<br>
</span>That paper formalises an advantage that an attacker might have over =
an<br>
ideal scheme. In the same way that block ciphers aren&#39;t ideal PRFs,<br>
nonce-misuse-resistant schemes aren&#39;t hitting that ideal either. RFC<br=
>
5297 doesn&#39;t hit it, at minimum because it&#39;ll run out of counter-sp=
ace<br>
after enough messages. AES-GCM-SIV isn&#39;t hitting it either.<br>
<br>
But that doesn&#39;t mean that they aren&#39;t practically useful.<br>
<br>
I&#39;m not sure what an ideal NMR AEAD would look like, but it&#39;s proba=
bly<br>
quite different to both RFC 5297 and AES-GCM-SIV and probably looks<br>
like a wide-block construction. If someone can point at something they<br>
think does hit it, that would be interesting to me at least. (Although<br>
perhaps it&#39;s well trodden ground for those who are more familiar with<b=
r>
the literature than I.)<br>
<span><br>
&gt;=C2=A0 =C2=A0Which brings up a question I&#39;ve resisted asking: Why a=
re you doing this?<br>
&gt;<br>
&gt;=C2=A0 =C2=A0If you want to have an AEAD scheme that is nonce-misuse re=
sistant that<br>
&gt; can use a fast(er) authentication scheme then why not just do RFC 5297=
<br>
&gt; with GHASH instead of AES-CMAC?<br>
<br>
</span>AES-GCM has lead to a state of the world where our large machines,<b=
r>
which need to encrypt and decrypt lots of data, end up having hardware<br>
support for AES and GF(128) operations. We would like to take<br>
advantage of that because it&#39;s hard to beat the speed and power<br>
efficiency of dedicated hardware, but sometimes we want not to have to<br>
worry about nonces.<br>
<span><br>
&gt; You&#39;re defining a new irreducible<br>
&gt; polynomial that, to my knowledge, is not in existing hardware the way<=
br>
&gt; that PCLMULQDQ using x^128 + x^7 + x^2 + x + 1, is in Intel chips.<br>
<br>
</span>PCLMULQDQ (and other hardware implementations, to my knowledge) is n=
ot<br>
specific to that polynomial. Also, the polynomial in AES-GCM-SIV is<br>
that polynomial, just with some ordering oddities addressed. See<br>
<a href=3D"https://tools.ietf.org/html/draft-irtf-cfrg-gcmsiv-03#appendix-A=
" rel=3D"noreferrer" target=3D"_blank">https://tools.ietf.org/html/dr<wbr>a=
ft-irtf-cfrg-gcmsiv-03#append<wbr>ix-A</a>.<br>
<span><br>
&gt; You&#39;re defining a(nother) KDF /inside/ the cipher mode itself inst=
ead of<br>
&gt; just letting a KDF, which all users of AES-GCM-SIV will use, generate =
a<br>
&gt; double-wide key. And I don&#39;t see the reason for either.<br>
<br>
</span>Our KDF is per-nonce; it&#39;s not the same as having a double-width=
 key<br>
and partitioning it internally. We do this in order to get better<br>
bounds when encrypting very large numbers of messages.<br>
<div class=3D"gmail-m_114949061650247928gmail-m_-5268966438158733069HOEnZb"=
><div class=3D"gmail-m_114949061650247928gmail-m_-5268966438158733069h5"><b=
r>
<br>
Cheers<br>
<br>
AGL<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>
</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></div>
</blockquote></div><br></div></div>

--001a113c06d477de1e05475a1778--


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To: Adam Langley <agl@imperialviolet.org>
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Subject: Re: [Cfrg] AES GCM SIV analysis
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On Fri, Jan 27, 2017 at 12:21 PM, Adam Langley <agl@imperialviolet.org> wrote:
> On Thu, Jan 26, 2017 at 6:26 PM, Dan Harkins <dharkins@lounge.org> wrote:
>>   But that is the definition used in the seminal work on the matter, [1].
>> If you want to have a different notion concerning a lesser restriction on
>> nonce reuse then you should use a different term.
>
> That paper formalises an advantage that an attacker might have over an
> ideal scheme. In the same way that block ciphers aren't ideal PRFs,
> nonce-misuse-resistant schemes aren't hitting that ideal either. RFC
> 5297 doesn't hit it, at minimum because it'll run out of counter-space
> after enough messages. AES-GCM-SIV isn't hitting it either.
>
> But that doesn't mean that they aren't practically useful.
>
> I'm not sure what an ideal NMR AEAD would look like, but it's probably
> quite different to both RFC 5297 and AES-GCM-SIV and probably looks
> like a wide-block construction. If someone can point at something they
> think does hit it, that would be interesting to me at least. (Although
> perhaps it's well trodden ground for those who are more familiar with
> the literature than I.)

AEZ looks promising to me:

http://web.cs.ucdavis.edu/~rogaway/aez/

--Andy


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Date: Tue, 31 Jan 2017 12:13:10 +0100
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Subject: [Cfrg] [IEEE ATC 2017] Call for Workshop and Special Session Proposal Extended
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Dear colleague,
   

  Apologies for multiple postings.

  In conjunction with the 14th IEEE International Conference on  
Advanced and Trusted Computing (ATC 2017), we will organize some  
workshops.

  The workshop proposals should be submitted to ieee-atc2017@googlegroups.com

  Further information are provided in the ATC Call for Workshop page[1] .

  All accepted papers will be included in the ATC 2017 proceedings  
published by IEEE.

   

  Workshop/Special Session proposals should contain following information:

  ·  The title of the workshop/special session, including both full  
name and abbreviation (for workshop)

  ·  The objectives, scope, and contributions to the main conference  
(up to 1 page)

  ·  The short bios of the key organizers and their related experience

  ·  The procedure for selecting papers, plans for dissemination  
(e.g., how to advertise and special issues of journals), and the  
expected number of participants

  ·  A tentative list of program committee members

  ·  The (tentative) website/URL of the proposed workshop/special session

   

  Important Schedule for ATC Workshops and Special Sessions:

  ·  Proposal Due: extended to Feb 15, 2017

  ·  Proposal Notification: extended to Feb 20, 2017

  ·  Paper Submission, Notification: TBD by individual workshops

  ·  Final Camera-ready Paper Due: June 10, 2017

   

  Best regards,

   

  Riccardo Lazzeretti

  riccardo.lazzeretti@math.unipd.it

  Workshop Chair

  IEEE Advanced and Trusted Computing (ATC 2017)

 


Links:
------
[1] http://cse.stfx.ca/~smartworld/2017/atc/cfw.php

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<p><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34); font-size: 9.5pt; white-space: pre-wrap;">Dear colleague,</span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;">&nbsp;</p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:12pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">Apologies for multiple postings.</span></span></p>
<p><br></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:12pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">In conjunction with the 14th IEEE International Conference on Advanced and Trusted Computing (ATC 2017), we will organize some workshops.</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:12pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">The workshop proposals should be submitted to</span> <span style="font-size: 9.5pt; background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">ieee-atc2017@googlegroups.com</span></span></p>
<p><br></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:12pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">Further information are provided in the</span> <a href="http://cse.stfx.ca/~smartworld/2017/atc/cfw.php" style="text-decoration:none;"><span style="font-size: 9.5pt; color: rgb(17, 85, 204); background-color: rgb(255, 255, 255); text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">ATC Call for Workshop page</span></a> <span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">.</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:12pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">All accepted papers will be included in the ATC 2017 proceedings published by IEEE.</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;">&nbsp;</p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">Workshop/Special Session proposals should contain following information:</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-left: 47pt;text-indent: -18pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 10pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">&middot;</span> <span style='font-size: 7pt; font-family: "Times New Roman"; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;'>&nbsp;</span><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">The title of the workshop/special session, including both full name and abbreviation (for workshop)</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-left: 47pt;text-indent: -18pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 10pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">&middot;</span> <span style='font-size: 7pt; font-family: "Times New Roman"; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;'>&nbsp;</span><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">The objectives, scope, and contributions to the main conference (up to 1 page)</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-left: 47pt;text-indent: -18pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 10pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">&middot;</span> <span style='font-size: 7pt; font-family: "Times New Roman"; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;'>&nbsp;</span><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">The short bios of the key organizers and their related experience</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-left: 47pt;text-indent: -18pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 10pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">&middot;</span> <span style='font-size: 7pt; font-family: "Times New Roman"; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;'>&nbsp;</span><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">The procedure for selecting papers, plans for dissemination (e.g., how to advertise and special issues of journals), and the expected number of participants</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-left: 47pt;text-indent: -18pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 10pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">&middot;</span> <span style='font-size: 7pt; font-family: "Times New Roman"; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;'>&nbsp;</span><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">A tentative list of program committee members</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-left: 47pt;text-indent: -18pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 10pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">&middot;</span> <span style='font-size: 7pt; font-family: "Times New Roman"; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;'>&nbsp;</span><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">The (tentative) website/URL of the proposed workshop/special session</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:12pt;">&nbsp;</p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Important Schedule for ATC Workshops and Special Sessions:</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-left: 47pt;text-indent: -18pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 10pt; color: rgb(255, 0, 0); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">&middot;</span> <span style='font-size: 7pt; font-family: "Times New Roman"; color: rgb(255, 0, 0); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;'>&nbsp;</span><span style="font-size: 9.5pt; color: rgb(255, 0, 0); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">Proposal Due: extended to Feb 15, 2017</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-left: 47pt;text-indent: -18pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 10pt; color: rgb(255, 0, 0); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">&middot;</span> <span style='font-size: 7pt; font-family: "Times New Roman"; color: rgb(255, 0, 0); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;'>&nbsp;</span><span style="font-size: 9.5pt; color: rgb(255, 0, 0); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">Proposal Notification: extended to Feb 20, 2017</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-left: 47pt;text-indent: -18pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 10pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">&middot;</span> <span style='font-size: 7pt; font-family: "Times New Roman"; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;'>&nbsp;</span><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">Paper Submission, Notification: TBD by individual workshops</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;margin-left: 47pt;text-indent: -18pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 10pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">&middot;</span> <span style='font-size: 7pt; font-family: "Times New Roman"; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;'>&nbsp;</span><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">Final Camera-ready Paper Due: June 10, 2017</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;">&nbsp;</p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">Best regards,</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;">&nbsp;</p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">Riccardo Lazzeretti</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">riccardo.lazzeretti@math.unipd.it</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">Workshop Chair</span></span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt;"><span id="docs-internal-guid-891000a9-f439-4e3f-d185-0ff97905cd72"><span style="font-size: 9.5pt; color: rgb(34, 34, 34); background-color: rgb(255, 255, 255); vertical-align: baseline; white-space: pre-wrap;">IEEE Advanced and Trusted Computing (ATC 2017)</span></span></p>
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From: Michael Richardson <mcr+ietf@sandelman.ca>
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Date: Tue, 31 Jan 2017 12:11:39 -0500
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Cc: draft-irtf-cfrg-eddsa@ietf.org
Subject: [Cfrg] readability suggestion about rfc8032 section 5.2, table 2
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Should we do a bis, this is a readability suggestion.  Maybe there
was a flame war over this already, if so, I appologize :-)

{And, I can't tell you how happy I am to have 8032 out. Thank you thank you
thank you!!!!!}


It says:

   |   PH(x)   | x (i.e., the identity function)                       |
   +-----------+-------------------------------------------------------+

                       Table 2: Parameters of Ed448

   Ed448ph is the same but with PH being SHAKE256(x, 64) and phflag
   being 1, i.e., the input is hashed before signing with Ed448 with a
   hash constant modified.

It really took me awhile to tweak into the "ph" in the "Ed448ph" in that
sentence.  It sure looked like an errata in the table.  As if there
was a copy and paste error from Ed25519, and that 448 and 25519 should
differ by PH(x) as well.

I think that the presentation would work better if the B and L value were
removed from the table and presented inline. (It would also be easier to
copy and paste into code, or be extracted via xmlpath).  With those
values removed from the table, it would be much more readable, and I
would suggest that it have three columns, one for Ed448 and one for Ed448ph.

Similarily for the Ed25519/Ed25519ph/Ed22519ctx table, which could then
have four columns.


I also suggest that the point addition examples in 5.1.4 not repeat any
of the variables used in the tables, specifically, "B" :-)

Please let me know if this is sufficiently important to enter an errata.


--
Michael Richardson <mcr+IETF@sandelman.ca>, Sandelman Software Works
 -= IPv6 IoT consulting =-




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