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From: Alexey Melnikov <aamelnikov@fastmail.fm>
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Subject: [Crypto-panel] Fwd: Review of draft-ietf-lwig-curve-representations-00 by crypto review panel
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Hi,
Can one of Crypto Panel members review this document?

Thank you,
Alexey

----- Original message -----
From: Mohit Sethi M <mohit.m.sethi@ericsson.com>
To: "aamelnikov@fastmail.fm" <aamelnikov@fastmail.fm>, Suresh Krishnan <Suresh@kaloom.com>, Zhen Cao <zhencao.ietf@gmail.com>
Subject: Review of draft-ietf-lwig-curve-representations-00 by crypto review panel
Date: Sun, 4 Nov 2018 08:26:08 +0000

Hi Alexey,

We spoke today about the need for getting more reviews on a LWIG 
document titled "Alternative Elliptic Curve Representations": 
https://tools.ietf.org/html/draft-ietf-lwig-curve-representations-00

The draft describes how to implement Ed25519, Curve25519 and NIST P-256 
with the same underlying implementation. Phillip Hallam-Baker also 
recently requested this on the SAAG list: 
https://mailarchive.ietf.org/arch/msg/saag/QM80DmA-3iEBxlh_VU5B5wOQnnA.

It would be great if someone from the crypto review panel could provide 
feedback on this draft. The draft is currently hosted in the LWIG 
working group and Zhen (in CC) is my co-chair, while Suresh (in CC) is 
the responsible area director.

Rene will also present the draft on Wednesday in LWIG in room Meeting 2 
between 11:20-12:20.

--Mohit


From nobody Tue Nov  6 03:45:39 2018
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From: "Stanislav V. Smyshlyaev" <smyshsv@gmail.com>
Date: Tue, 6 Nov 2018 18:45:16 +0700
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To: Alexey Melnikov <aamelnikov@fastmail.fm>
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Subject: Re: [Crypto-panel] Fwd: Review of draft-ietf-lwig-curve-representations-00 by crypto review panel
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--000000000000ba3c5b0579fd8923
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Dear Alexey,

I=E2=80=99ll be happy to do it.

Since there are many numbers to check, and since it=E2=80=99s much better t=
o be
done using independent implementations of elliptics, it will take some
time.

Will it be OK if I do it until the end of November?

Best regards,
Stanislav

=D0=BF=D0=BD, 5 =D0=BD=D0=BE=D1=8F=D0=B1. 2018 =D0=B3. =D0=B2 17:42, Alexey=
 Melnikov <aamelnikov@fastmail.fm>:

> Hi,
> Can one of Crypto Panel members review this document?
>
> Thank you,
> Alexey
>
> ----- Original message -----
> From: Mohit Sethi M <mohit.m.sethi@ericsson.com>
> To: "aamelnikov@fastmail.fm" <aamelnikov@fastmail.fm>, Suresh Krishnan <
> Suresh@kaloom.com>, Zhen Cao <zhencao.ietf@gmail.com>
> Subject: Review of draft-ietf-lwig-curve-representations-00 by crypto
> review panel
> Date: Sun, 4 Nov 2018 08:26:08 +0000
>
> Hi Alexey,
>
> We spoke today about the need for getting more reviews on a LWIG
> document titled "Alternative Elliptic Curve Representations":
> https://tools.ietf.org/html/draft-ietf-lwig-curve-representations-00
>
> The draft describes how to implement Ed25519, Curve25519 and NIST P-256
> with the same underlying implementation. Phillip Hallam-Baker also
> recently requested this on the SAAG list:
> https://mailarchive.ietf.org/arch/msg/saag/QM80DmA-3iEBxlh_VU5B5wOQnnA.
>
> It would be great if someone from the crypto review panel could provide
> feedback on this draft. The draft is currently hosted in the LWIG
> working group and Zhen (in CC) is my co-chair, while Suresh (in CC) is
> the responsible area director.
>
> Rene will also present the draft on Wednesday in LWIG in room Meeting 2
> between 11:20-12:20.
>
> --Mohit
>
> _______________________________________________
> Crypto-panel mailing list
> Crypto-panel@irtf.org
> https://www.irtf.org/mailman/listinfo/crypto-panel
>

--000000000000ba3c5b0579fd8923
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div><div dir=3D"auto">Dear Alexey,</div></div><div dir=3D"auto"><br></div>=
<div dir=3D"auto">I=E2=80=99ll be happy to do it.=C2=A0</div><div dir=3D"au=
to"><br></div><div dir=3D"auto">Since there are many numbers to check, and =
since it=E2=80=99s much better to be done using independent implementations=
 of elliptics, it will take some time.=C2=A0</div><div dir=3D"auto"><br></d=
iv><div dir=3D"auto">Will it be OK if I do it until the end of November?</d=
iv><div dir=3D"auto"><br></div><div dir=3D"auto">Best regards,</div><div di=
r=3D"auto">Stanislav</div><div><br><div class=3D"gmail_quote"><div dir=3D"l=
tr">=D0=BF=D0=BD, 5 =D0=BD=D0=BE=D1=8F=D0=B1. 2018 =D0=B3. =D0=B2 17:42, Al=
exey Melnikov &lt;<a href=3D"mailto:aamelnikov@fastmail.fm">aamelnikov@fast=
mail.fm</a>&gt;:<br></div><blockquote class=3D"gmail_quote" style=3D"margin=
:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Hi,<br>
Can one of Crypto Panel members review this document?<br>
<br>
Thank you,<br>
Alexey<br>
<br>
----- Original message -----<br>
From: Mohit Sethi M &lt;<a href=3D"mailto:mohit.m.sethi@ericsson.com" targe=
t=3D"_blank">mohit.m.sethi@ericsson.com</a>&gt;<br>
To: &quot;<a href=3D"mailto:aamelnikov@fastmail.fm" target=3D"_blank">aamel=
nikov@fastmail.fm</a>&quot; &lt;<a href=3D"mailto:aamelnikov@fastmail.fm" t=
arget=3D"_blank">aamelnikov@fastmail.fm</a>&gt;, Suresh Krishnan &lt;<a hre=
f=3D"mailto:Suresh@kaloom.com" target=3D"_blank">Suresh@kaloom.com</a>&gt;,=
 Zhen Cao &lt;<a href=3D"mailto:zhencao.ietf@gmail.com" target=3D"_blank">z=
hencao.ietf@gmail.com</a>&gt;<br>
Subject: Review of draft-ietf-lwig-curve-representations-00 by crypto revie=
w panel<br>
Date: Sun, 4 Nov 2018 08:26:08 +0000<br>
<br>
Hi Alexey,<br>
<br>
We spoke today about the need for getting more reviews on a LWIG <br>
document titled &quot;Alternative Elliptic Curve Representations&quot;: <br=
>
<a href=3D"https://tools.ietf.org/html/draft-ietf-lwig-curve-representation=
s-00" rel=3D"noreferrer" target=3D"_blank">https://tools.ietf.org/html/draf=
t-ietf-lwig-curve-representations-00</a><br>
<br>
The draft describes how to implement Ed25519, Curve25519 and NIST P-256 <br=
>
with the same underlying implementation. Phillip Hallam-Baker also <br>
recently requested this on the SAAG list: <br>
<a href=3D"https://mailarchive.ietf.org/arch/msg/saag/QM80DmA-3iEBxlh_VU5B5=
wOQnnA" rel=3D"noreferrer" target=3D"_blank">https://mailarchive.ietf.org/a=
rch/msg/saag/QM80DmA-3iEBxlh_VU5B5wOQnnA</a>.<br>
<br>
It would be great if someone from the crypto review panel could provide <br=
>
feedback on this draft. The draft is currently hosted in the LWIG <br>
working group and Zhen (in CC) is my co-chair, while Suresh (in CC) is <br>
the responsible area director.<br>
<br>
Rene will also present the draft on Wednesday in LWIG in room Meeting 2 <br=
>
between 11:20-12:20.<br>
<br>
--Mohit<br>
<br>
_______________________________________________<br>
Crypto-panel mailing list<br>
<a href=3D"mailto:Crypto-panel@irtf.org" target=3D"_blank">Crypto-panel@irt=
f.org</a><br>
<a href=3D"https://www.irtf.org/mailman/listinfo/crypto-panel" rel=3D"noref=
errer" target=3D"_blank">https://www.irtf.org/mailman/listinfo/crypto-panel=
</a><br>
</blockquote></div></div>

--000000000000ba3c5b0579fd8923--


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From: Alexey Melnikov <aamelnikov@fastmail.fm>
To: "Stanislav V. Smyshlyaev" <smyshsv@gmail.com>
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Subject: Re: [Crypto-panel] Fwd: Review of draft-ietf-lwig-curve-representations-00 by crypto review panel
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On Tue, Nov 6, 2018, at 11:45 AM, Stanislav V. Smyshlyaev wrote:
> Dear Alexey,
>=20
> I=E2=80=99ll be happy to do it.=20
>=20
> Since there are many numbers to check, and since it=E2=80=99s much better=
 to
> be done using independent implementations of elliptics, it will take
> some time.>=20
> Will it be OK if I do it until the end of November?
Thank you. I am sure this will not be a problem!

>=20
> Best regards,
> Stanislav
>=20
> =D0=BF=D0=BD, 5 =D0=BD=D0=BE=D1=8F=D0=B1. 2018 =D0=B3. =D0=B2 17:42, Alex=
ey Melnikov <aamelnikov@fastmail.fm>:>> Hi,
>>  Can one of Crypto Panel members review this document?
>>=20
>>  Thank you,
>>  Alexey
>>=20
>>  ----- Original message -----
>>  From: Mohit Sethi M <mohit.m.sethi@ericsson.com>
>>  To: "aamelnikov@fastmail.fm" <aamelnikov@fastmail.fm>, Suresh
>>  Krishnan <Suresh@kaloom.com>, Zhen Cao <zhencao.ietf@gmail.com>>>  Subj=
ect: Review of draft-ietf-lwig-curve-representations-00 by
>>  crypto review panel>>  Date: Sun, 4 Nov 2018 08:26:08 +0000
>>=20
>>  Hi Alexey,
>>=20
>>  We spoke today about the need for getting more reviews on a LWIG=20
>>  document titled "Alternative Elliptic Curve Representations":=20
>> https://tools.ietf.org/html/draft-ietf-lwig-curve-representations-00>>=20
>>  The draft describes how to implement Ed25519, Curve25519 and
>>  NIST P-256>>  with the same underlying implementation. Phillip Hallam-B=
aker also>>  recently requested this on the SAAG list:=20
>> https://mailarchive.ietf.org/arch/msg/saag/QM80DmA-3iEBxlh_VU5B5wOQnnA.>=
>=20
>>  It would be great if someone from the crypto review panel could
>>  provide>>  feedback on this draft. The draft is currently hosted in the=
 LWIG=20
>>  working group and Zhen (in CC) is my co-chair, while Suresh (in
>>  CC) is>>  the responsible area director.
>>=20
>>  Rene will also present the draft on Wednesday in LWIG in room
>>  Meeting 2>>  between 11:20-12:20.
>>=20
>>  --Mohit
>>=20
>>  _______________________________________________
>>  Crypto-panel mailing list
>> Crypto-panel@irtf.org
>> https://www.irtf.org/mailman/listinfo/crypto-panel


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<title></title>
<style type=3D"text/css">p.MsoNormal,p.MsoNoSpacing{margin:0}</style>
</head>
<body><div>On Tue, Nov 6, 2018, at 11:45 AM, Stanislav V. Smyshlyaev wrote:=
<br></div>
<blockquote type=3D"cite"><div><div>Dear Alexey,<br></div>
</div>
<div><br></div>
<div>I=E2=80=99ll be happy to do it.&nbsp;<br></div>
<div><br></div>
<div>Since there are many numbers to check, and since it=E2=80=99s much bet=
ter to be done using independent implementations of elliptics, it will take=
 some time.&nbsp;<br></div>
<div><br></div>
<div>Will it be OK if I do it until the end of November?<br></div>
</blockquote><div>Thank you. I am sure this will not be a problem!<br></div>
<div><br></div>
<blockquote type=3D"cite"><div><br></div>
<div>Best regards,<br></div>
<div>Stanislav<br></div>
<div><div><br></div>
<div defang_data-gmailquote=3D"yes"><div dir=3D"ltr">=D0=BF=D0=BD, 5 =D0=BD=
=D0=BE=D1=8F=D0=B1. 2018 =D0=B3. =D0=B2 17:42, Alexey Melnikov &lt;<a href=
=3D"mailto:aamelnikov@fastmail.fm">aamelnikov@fastmail.fm</a>&gt;:<br></div>
<blockquote defang_data-gmailquote=3D"yes" style=3D"margin-top:0px;margin-r=
ight:0px;margin-bottom:0px;margin-left:0.8ex;border-left-width:1px;border-l=
eft-style:solid;border-left-color:rgb(204, 204, 204);padding-left:1ex;"><di=
v>Hi,<br></div>
<div> Can one of Crypto Panel members review this document?<br></div>
<div> <br></div>
<div> Thank you,<br></div>
<div> Alexey<br></div>
<div> <br></div>
<div> ----- Original message -----<br></div>
<div> From: Mohit Sethi M &lt;<a href=3D"mailto:mohit.m.sethi@ericsson.com"=
>mohit.m.sethi@ericsson.com</a>&gt;<br></div>
<div> To: "<a href=3D"mailto:aamelnikov@fastmail.fm">aamelnikov@fastmail.fm=
</a>" &lt;<a href=3D"mailto:aamelnikov@fastmail.fm">aamelnikov@fastmail.fm<=
/a>&gt;, Suresh Krishnan &lt;<a href=3D"mailto:Suresh@kaloom.com">Suresh@ka=
loom.com</a>&gt;, Zhen Cao &lt;<a href=3D"mailto:zhencao.ietf@gmail.com">zh=
encao.ietf@gmail.com</a>&gt;<br></div>
<div> Subject: Review of draft-ietf-lwig-curve-representations-00 by crypto=
 review panel<br></div>
<div> Date: Sun, 4 Nov 2018 08:26:08 +0000<br></div>
<div> <br></div>
<div> Hi Alexey,<br></div>
<div> <br></div>
<div> We spoke today about the need for getting more reviews on a LWIG <br>=
</div>
<div> document titled "Alternative Elliptic Curve Representations": <br></d=
iv>
<div> <a href=3D"https://tools.ietf.org/html/draft-ietf-lwig-curve-represen=
tations-00">https://tools.ietf.org/html/draft-ietf-lwig-curve-representatio=
ns-00</a><br></div>
<div> <br></div>
<div> The draft describes how to implement Ed25519, Curve25519 and NIST P-2=
56 <br></div>
<div> with the same underlying implementation. Phillip Hallam-Baker also <b=
r></div>
<div> recently requested this on the SAAG list: <br></div>
<div> <a href=3D"https://mailarchive.ietf.org/arch/msg/saag/QM80DmA-3iEBxlh=
_VU5B5wOQnnA">https://mailarchive.ietf.org/arch/msg/saag/QM80DmA-3iEBxlh_VU=
5B5wOQnnA</a>.<br></div>
<div> <br></div>
<div> It would be great if someone from the crypto review panel could provi=
de <br></div>
<div> feedback on this draft. The draft is currently hosted in the LWIG <br=
></div>
<div> working group and Zhen (in CC) is my co-chair, while Suresh (in CC) i=
s <br></div>
<div> the responsible area director.<br></div>
<div> <br></div>
<div> Rene will also present the draft on Wednesday in LWIG in room Meeting=
 2 <br></div>
<div> between 11:20-12:20.<br></div>
<div> <br></div>
<div> --Mohit<br></div>
<div> <br></div>
<div> _______________________________________________<br></div>
<div> Crypto-panel mailing list<br></div>
<div> <a href=3D"mailto:Crypto-panel@irtf.org">Crypto-panel@irtf.org</a><br=
></div>
<div> <a href=3D"https://www.irtf.org/mailman/listinfo/crypto-panel">https:=
//www.irtf.org/mailman/listinfo/crypto-panel</a><br></div>
</blockquote></div>
</div>
</blockquote><div><br></div>
</body>
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Subject: Re: [Crypto-panel] Fwd: Review of draft-ietf-lwig-curve-representations-00 by crypto review panel
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Good afternoon,

Please find below the review of the document.

Of course, I'll be happy to discuss all questions raised in the review
directly via e-mail: smyshsv@gmail.com


Document: draft-ietf-lwig-curve-representations-00
Reviewer: Stanislav Smyshlyaev
Review Date: 2018-11-26
Summary: Revision needed

The document =E2=80=9CAlternative Elliptic Curve Representations=E2=80=9D c=
ontains
procedures and formulae of representing Montgomery curves and (twisted)
Edwards curves in short Weierstrass form.
The reviewer believes that the document is very helpful and can be used by
developers implementing ECC operations in real-world applications.
The reviewer has verified all decimal numbers (and hexadecimal numbers,
where they are provided in the draft) and does not have any concerns
besides the following ones.

Since some of the concerns seem to be important enough for the overall
document, the reviewer recommends to send an updated version of the draft
to Crypto Review Panel for a new review.

The review was made for draft-ietf-lwig-curve-representations-00. During
the review process an updated version
draft-ietf-lwig-curve-representations-01 was published =E2=80=93 some comme=
nts
about the -01 version can be found in the end of the current review.

Comments:
1) Section C.2: The mapping from Weierstrass curves to Montgomery curves is
not defined in the current version. The mapping from Weierstrass to
Montgomery cannot usually be described as shortly as others, but maybe it
could still be useful here. For example, the root of x^3+ax+b in Fp could
be provided explicitly.
2) It would be better to stress in Appendix C.1 that formulae provided
there do not allow to get parameter a of the twisted Edwards curve equal to
1 or -1. In Appendix D.2 additional constant c is used that helps to obtain
the curve with a equal to -1 (this fact by the way implies that the phrase
=E2=80=9CHere, we used the mapping of Appendix C.1=E2=80=9D is inaccurate).
2a) Section D.2: The formulae (u,v) -> (c*u/v, (u-1)/(u+1)) lead to an
error. It is not clear why it is needed to multiply by the constant c.
2b) Section D.3: The Montgomery curve Curve25519 doesn=E2=80=99t correspond=
 to
Twisted Edwards curve Edwards25519 because of (A+2)/B =3D (486662+2)/1 !=3D=
 -1.
2c) If one uses the formula from C.1 for Montgomery to Edwards mapping
(a:=3D(A+2)/B and d:=3D(A-2)/B), she obtains that d for Edwards25519 is equ=
al
to 486660 but not the value of d which is provided in D.3.
3) Section E.1: The isomorphic mapping between W_{a,b} and W_{a',b'} should
be defined as a=E2=80=99:=3Da*s^4 and b=E2=80=99:=3Db*s^6, instead of a:=3D=
a'*s^4 and b:=3Db'*s^6.
Otherwise the mapping is defined incorrectly and the test vectors from F.3
are incorrect.
4) It seems that the formula for lambda in case Q:=3D2P for Montgomery curv=
e
is wrong. According to http://hyperelliptic.org/EFD/g1p/auto-montgom.html
and to https://eprint.iacr.org/2017/212.pdf (page 4) it should be: lambda =
=3D
(3*x1^2 + 2*A*x1 + 1)/(2*B*y1). So you need to add =E2=80=9CB=E2=80=9D as a=
 factor in the
denominator.
5) in Appendix D.2 it would be better to stress explicitly that we work
with projective coordinates, otherwise the formulae do not have to be
correct.

Editorial comments:
a) It seems that the text will be easier to read if the formulae for group
law are provided in the following form (for example, for Weierstrass):
   x =3D lambda^2 =E2=80=93 x1 =E2=80=93 x2
   y =3D lambda * ... (at a new line, but with =E2=80=9Cand=E2=80=9D)
   lambda =3D ... (again at a new line)
b) In reviewer=E2=80=99s opinion, the text will be easier to read if differ=
ent
symbols for coordinates of different forms of a curve are used. For
example, (x,y) for Weierstrass, (X,Y) for Montgomery and (u,v) for Edwards.
And it would be better to use the same symbols in different parts of the
document (now (u,v) is used for Montgomery in A.2 and (x,y) for Montgomery
in B.2).
c) The term =E2=80=9Cshort Weierstrass form=E2=80=9D is widely used in publ=
ications as is.
The draft, however, has two variants of it =E2=80=93 =E2=80=9Cshort=E2=80=
=9D Weierstrass form and
short-Weierstrass form. It seems that one (commonly used) variant would be
better to use.
d) The reviewer recommends to use only =E2=80=9CGF(p)=E2=80=9D everywhere i=
n document
instead of =E2=80=9CGF(q)=E2=80=9D together with =E2=80=9CGF(p)=E2=80=9D. F=
or example, now in C.1 =E2=80=93 GF(q)
and GF(p) in D.1.

Additional clarifications might be useful:
Also the reviewer believes that it will be useful to write additional
clarifications in D.2 on =E2=80=9Ccan be implemented via integer-only arith=
metic as
a shift of (p+A)/3 for the isomorphic mapping and a shift of -(p+A)/3 for
its inverse=E2=80=9D regarding the need of using the mod operation for
transformation.

###### draft-ietf-lwig-curve-representations-01:

The concerns 1, 2, 2a, 2b, 2c, 4 and 5 for 00 version are still valid for
version -01. The concern 3 has been addressed.
Additional question for draft-ietf-lwig-curve-representations-01:
appendices C.1 and C.2 contain information about properties that help to
recover y-coordinates of a multiple point if one uses Montgomery ladder.
This information may not be needed in the draft, since the ladder itself is
not described there.





Best regards,
Stanislav Smyshlyaev


=D1=87=D1=82, 8 =D0=BD=D0=BE=D1=8F=D0=B1. 2018 =D0=B3. =D0=B2 07:53, Alexey=
 Melnikov <aamelnikov@fastmail.fm>:

> On Tue, Nov 6, 2018, at 11:45 AM, Stanislav V. Smyshlyaev wrote:
>
> Dear Alexey,
>
> I=E2=80=99ll be happy to do it.
>
> Since there are many numbers to check, and since it=E2=80=99s much better=
 to be
> done using independent implementations of elliptics, it will take some
> time.
>
> Will it be OK if I do it until the end of November?
>
> Thank you. I am sure this will not be a problem!
>
>
> Best regards,
> Stanislav
>
> =D0=BF=D0=BD, 5 =D0=BD=D0=BE=D1=8F=D0=B1. 2018 =D0=B3. =D0=B2 17:42, Alex=
ey Melnikov <aamelnikov@fastmail.fm>:
>
> Hi,
> Can one of Crypto Panel members review this document?
>
> Thank you,
> Alexey
>
> ----- Original message -----
> From: Mohit Sethi M <mohit.m.sethi@ericsson.com>
> To: "aamelnikov@fastmail.fm" <aamelnikov@fastmail.fm>, Suresh Krishnan <
> Suresh@kaloom.com>, Zhen Cao <zhencao.ietf@gmail.com>
> Subject: Review of draft-ietf-lwig-curve-representations-00 by crypto
> review panel
> Date: Sun, 4 Nov 2018 08:26:08 +0000
>
> Hi Alexey,
>
> We spoke today about the need for getting more reviews on a LWIG
> document titled "Alternative Elliptic Curve Representations":
> https://tools.ietf.org/html/draft-ietf-lwig-curve-representations-00
>
> The draft describes how to implement Ed25519, Curve25519 and NIST P-256
> with the same underlying implementation. Phillip Hallam-Baker also
> recently requested this on the SAAG list:
> https://mailarchive.ietf.org/arch/msg/saag/QM80DmA-3iEBxlh_VU5B5wOQnnA.
>
> It would be great if someone from the crypto review panel could provide
> feedback on this draft. The draft is currently hosted in the LWIG
> working group and Zhen (in CC) is my co-chair, while Suresh (in CC) is
> the responsible area director.
>
> Rene will also present the draft on Wednesday in LWIG in room Meeting 2
> between 11:20-12:20.
>
> --Mohit
>
> _______________________________________________
> Crypto-panel mailing list
> Crypto-panel@irtf.org
> https://www.irtf.org/mailman/listinfo/crypto-panel
>
>
>

--0000000000001a6d68057b8fe3ac
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div dir=3D"ltr"><div>Good afternoon,</div><div><br></div>=
<div>Please find below the review of the document.</div><div><br></div><div=
>Of course, I&#39;ll be happy to discuss all questions raised in the review=
 directly via e-mail:=C2=A0<a href=3D"mailto:smyshsv@gmail.com" target=3D"_=
blank">smyshsv@gmail.com</a>=C2=A0</div><div>=C2=A0<br></div><div><br></div=
><div>Document: draft-ietf-lwig-curve-representations-00</div><div>Reviewer=
: Stanislav Smyshlyaev</div><div>Review Date: 2018-11-26</div><div>Summary:=
 Revision needed</div><div><br></div><div>The document =E2=80=9CAlternative=
 Elliptic Curve Representations=E2=80=9D contains procedures and formulae o=
f representing Montgomery curves and (twisted) Edwards curves in short Weie=
rstrass form.</div><div>The reviewer believes that the document is very hel=
pful and can be used by developers implementing ECC operations in real-worl=
d applications.=C2=A0</div><div>The reviewer has verified all decimal numbe=
rs (and hexadecimal numbers, where they are provided in the draft) and does=
 not have any concerns besides the following ones.</div><div><br></div><div=
>Since some of the concerns seem to be important enough for the overall doc=
ument, the reviewer recommends to send an updated version of the draft to C=
rypto Review Panel for a new review.</div><div><br></div><div>The review wa=
s made for draft-ietf-lwig-curve-representations-00. During the review proc=
ess an updated version draft-ietf-lwig-curve-representations-01 was publish=
ed =E2=80=93 some comments about the -01 version can be found in the end of=
 the current review.</div><div><br></div><div>Comments:</div><div>1) Sectio=
n C.2: The mapping from Weierstrass curves to Montgomery curves is not defi=
ned in the current version. The mapping from Weierstrass to Montgomery cann=
ot usually be described as shortly as others, but maybe it could still be u=
seful here. For example, the root of x^3+ax+b in Fp could be provided expli=
citly.</div><div>2) It would be better to stress in Appendix C.1 that formu=
lae provided there do not allow to get parameter a of the twisted Edwards c=
urve equal to 1 or -1. In Appendix D.2 additional constant c is used that h=
elps to obtain the curve with a equal to -1 (this fact by the way implies t=
hat the phrase =E2=80=9CHere, we used the mapping of Appendix C.1=E2=80=9D =
is inaccurate).</div><div>2a) Section D.2: The formulae (u,v) -&gt; (c*u/v,=
 (u-1)/(u+1)) lead to an error. It is not clear why it is needed to multipl=
y by the constant c.</div><div>2b) Section D.3: The Montgomery curve Curve2=
5519 doesn=E2=80=99t correspond to Twisted Edwards curve Edwards25519 becau=
se of (A+2)/B =3D (486662+2)/1 !=3D -1.</div><div>2c) If one uses the formu=
la from C.1 for Montgomery to Edwards mapping (a:=3D(A+2)/B and d:=3D(A-2)/=
B), she obtains that d for Edwards25519 is equal to 486660 but not the valu=
e of d which is provided in D.3.</div><div>3) Section E.1: The isomorphic m=
apping between W_{a,b} and W_{a&#39;,b&#39;} should be defined as a=E2=80=
=99:=3Da*s^4 and b=E2=80=99:=3Db*s^6, instead of a:=3Da&#39;*s^4 and b:=3Db=
&#39;*s^6. Otherwise the mapping is defined incorrectly and the test vector=
s from F.3 are incorrect.</div><div>4) It seems that the formula for lambda=
 in case Q:=3D2P for Montgomery curve is wrong. According to <a href=3D"htt=
p://hyperelliptic.org/EFD/g1p/auto-montgom.html" target=3D"_blank">http://h=
yperelliptic.org/EFD/g1p/auto-montgom.html</a> and to <a href=3D"https://ep=
rint.iacr.org/2017/212.pdf" target=3D"_blank">https://eprint.iacr.org/2017/=
212.pdf</a> (page 4) it should be: lambda =3D (3*x1^2 + 2*A*x1 + 1)/(2*B*y1=
). So you need to add =E2=80=9CB=E2=80=9D as a factor in the denominator.</=
div><div>5) in Appendix D.2 it would be better to stress explicitly that we=
 work with projective coordinates, otherwise the formulae do not have to be=
 correct.</div><div><br></div><div>Editorial comments:</div><div>a) It seem=
s that the text will be easier to read if the formulae for group law are pr=
ovided in the following form (for example, for Weierstrass):</div><div>=C2=
=A0 =C2=A0x =3D lambda^2 =E2=80=93 x1 =E2=80=93 x2</div><div>=C2=A0 =C2=A0y=
 =3D lambda * ... (at a new line, but with =E2=80=9Cand=E2=80=9D)</div><div=
>=C2=A0 =C2=A0lambda =3D ... (again at a new line)</div><div>b) In reviewer=
=E2=80=99s opinion, the text will be easier to read if different symbols fo=
r coordinates of different forms of a curve are used. For example, (x,y) fo=
r Weierstrass, (X,Y) for Montgomery and (u,v) for Edwards. And it would be =
better to use the same symbols in different parts of the document (now (u,v=
) is used for Montgomery in A.2 and (x,y) for Montgomery in B.2).</div><div=
>c) The term =E2=80=9Cshort Weierstrass form=E2=80=9D is widely used in pub=
lications as is. The draft, however, has two variants of it =E2=80=93 =E2=
=80=9Cshort=E2=80=9D Weierstrass form and short-Weierstrass form. It seems =
that one (commonly used) variant would be better to use.</div><div>d) The r=
eviewer recommends to use only =E2=80=9CGF(p)=E2=80=9D everywhere in docume=
nt instead of =E2=80=9CGF(q)=E2=80=9D together with =E2=80=9CGF(p)=E2=80=9D=
. For example, now in C.1 =E2=80=93 GF(q) and GF(p) in D.1.</div><div><br><=
/div><div>Additional clarifications might be useful:=C2=A0</div><div>Also t=
he reviewer believes that it will be useful to write additional clarificati=
ons in D.2 on =E2=80=9Ccan be implemented via integer-only arithmetic as a =
shift of (p+A)/3 for the isomorphic mapping and a shift of -(p+A)/3 for its=
 inverse=E2=80=9D regarding the need of using the mod operation for transfo=
rmation.=C2=A0</div><div><br></div><div>###### draft-ietf-lwig-curve-repres=
entations-01:</div><div><br></div><div>The concerns 1, 2, 2a, 2b, 2c, 4 and=
 5 for 00 version are still valid for version -01. The concern 3 has been a=
ddressed.</div><div>Additional question for draft-ietf-lwig-curve-represent=
ations-01: appendices C.1 and C.2 contain information about properties that=
 help to recover y-coordinates of a multiple point if one uses Montgomery l=
adder. This information may not be needed in the draft, since the ladder it=
self is not described there.</div><div><br></div><div><br></div><div><br></=
div><div><br></div><div><br></div><div>Best regards,</div><div>Stanislav Sm=
yshlyaev</div><div><br></div><br><div class=3D"gmail_quote"><div dir=3D"ltr=
">=D1=87=D1=82, 8 =D0=BD=D0=BE=D1=8F=D0=B1. 2018 =D0=B3. =D0=B2 07:53, Alex=
ey Melnikov &lt;<a href=3D"mailto:aamelnikov@fastmail.fm" target=3D"_blank"=
>aamelnikov@fastmail.fm</a>&gt;:<br></div><blockquote class=3D"gmail_quote"=
 style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);p=
adding-left:1ex"><u></u>





<div><div>On Tue, Nov 6, 2018, at 11:45 AM, Stanislav V. Smyshlyaev wrote:<=
br></div>
<blockquote type=3D"cite"><div><div>Dear Alexey,<br></div>
</div>
<div><br></div>
<div>I=E2=80=99ll be happy to do it.=C2=A0<br></div>
<div><br></div>
<div>Since there are many numbers to check, and since it=E2=80=99s much bet=
ter to be done using independent implementations of elliptics, it will take=
 some time.=C2=A0<br></div>
<div><br></div>
<div>Will it be OK if I do it until the end of November?<br></div>
</blockquote><div>Thank you. I am sure this will not be a problem!<br></div=
>
<div><br></div>
<blockquote type=3D"cite"><div><br></div>
<div>Best regards,<br></div>
<div>Stanislav<br></div>
<div><div><br></div>
<div><div dir=3D"ltr">=D0=BF=D0=BD, 5 =D0=BD=D0=BE=D1=8F=D0=B1. 2018 =D0=B3=
. =D0=B2 17:42, Alexey Melnikov &lt;<a href=3D"mailto:aamelnikov@fastmail.f=
m" target=3D"_blank">aamelnikov@fastmail.fm</a>&gt;:<br></div>
<blockquote style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204=
,204,204);padding-left:1ex"><div>Hi,<br></div>
<div> Can one of Crypto Panel members review this document?<br></div>
<div> <br></div>
<div> Thank you,<br></div>
<div> Alexey<br></div>
<div> <br></div>
<div> ----- Original message -----<br></div>
<div> From: Mohit Sethi M &lt;<a href=3D"mailto:mohit.m.sethi@ericsson.com"=
 target=3D"_blank">mohit.m.sethi@ericsson.com</a>&gt;<br></div>
<div> To: &quot;<a href=3D"mailto:aamelnikov@fastmail.fm" target=3D"_blank"=
>aamelnikov@fastmail.fm</a>&quot; &lt;<a href=3D"mailto:aamelnikov@fastmail=
.fm" target=3D"_blank">aamelnikov@fastmail.fm</a>&gt;, Suresh Krishnan &lt;=
<a href=3D"mailto:Suresh@kaloom.com" target=3D"_blank">Suresh@kaloom.com</a=
>&gt;, Zhen Cao &lt;<a href=3D"mailto:zhencao.ietf@gmail.com" target=3D"_bl=
ank">zhencao.ietf@gmail.com</a>&gt;<br></div>
<div> Subject: Review of draft-ietf-lwig-curve-representations-00 by crypto=
 review panel<br></div>
<div> Date: Sun, 4 Nov 2018 08:26:08 +0000<br></div>
<div> <br></div>
<div> Hi Alexey,<br></div>
<div> <br></div>
<div> We spoke today about the need for getting more reviews on a LWIG <br>=
</div>
<div> document titled &quot;Alternative Elliptic Curve Representations&quot=
;: <br></div>
<div> <a href=3D"https://tools.ietf.org/html/draft-ietf-lwig-curve-represen=
tations-00" target=3D"_blank">https://tools.ietf.org/html/draft-ietf-lwig-c=
urve-representations-00</a><br></div>
<div> <br></div>
<div> The draft describes how to implement Ed25519, Curve25519 and NIST P-2=
56 <br></div>
<div> with the same underlying implementation. Phillip Hallam-Baker also <b=
r></div>
<div> recently requested this on the SAAG list: <br></div>
<div> <a href=3D"https://mailarchive.ietf.org/arch/msg/saag/QM80DmA-3iEBxlh=
_VU5B5wOQnnA" target=3D"_blank">https://mailarchive.ietf.org/arch/msg/saag/=
QM80DmA-3iEBxlh_VU5B5wOQnnA</a>.<br></div>
<div> <br></div>
<div> It would be great if someone from the crypto review panel could provi=
de <br></div>
<div> feedback on this draft. The draft is currently hosted in the LWIG <br=
></div>
<div> working group and Zhen (in CC) is my co-chair, while Suresh (in CC) i=
s <br></div>
<div> the responsible area director.<br></div>
<div> <br></div>
<div> Rene will also present the draft on Wednesday in LWIG in room Meeting=
 2 <br></div>
<div> between 11:20-12:20.<br></div>
<div> <br></div>
<div> --Mohit<br></div>
<div> <br></div>
<div> _______________________________________________<br></div>
<div> Crypto-panel mailing list<br></div>
<div> <a href=3D"mailto:Crypto-panel@irtf.org" target=3D"_blank">Crypto-pan=
el@irtf.org</a><br></div>
<div> <a href=3D"https://www.irtf.org/mailman/listinfo/crypto-panel" target=
=3D"_blank">https://www.irtf.org/mailman/listinfo/crypto-panel</a><br></div=
>
</blockquote></div>
</div>
</blockquote><div><br></div>
</div>

</blockquote></div></div></div>

--0000000000001a6d68057b8fe3ac--

