Re: [Cfrg] Suggestions for draft-irtf-cfrg-curves-01.txt
Watson Ladd <watsonbladd@gmail.com> Mon, 02 February 2015 16:36 UTC
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Date: Mon, 02 Feb 2015 08:35:21 -0800
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From: Watson Ladd <watsonbladd@gmail.com>
To: Evgeny Alekseev <eamsucmc@gmail.com>
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Subject: Re: [Cfrg] Suggestions for draft-irtf-cfrg-curves-01.txt
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On Mon, Feb 2, 2015 at 7:07 AM, Evgeny Alekseev <eamsucmc@gmail.com> wrote: > Stanislav V. Smyshlyaev wrote: > >> Dear colleagues, >> >> We would like you to consider several proposals on the latest variant of >> draft (draft-irtf-cfrg-curves-01). >> >> 1) In our opinion, some important clarifications have to be done >> explicitly in the document, though needed references are given. >> a) In Section 3.3 declare explicitly what "r” denotes. >> b) In Section 5 mention explicitly Schoof–Elkies–Atkin algorithm as an >> algorithm used to calculate number of curve points or even fully cite it >> there. >> c) Add explicit description of algorithms used to examine curve on MOV-, >> CM- and twist-security as well as Frobenius trace calculation formula. Add >> “perform checks” step in algorithms proposed in sections 5.1 and 5.2. >> 2) Select and add a higher security curve (512- or 521-bit). >> 3) Add some explanations on parameter d of the selected 255-bit curve >> (the current draft leaves the question whether it is the first d to be >> returned by 5.2 algorithm and the reason of choice if it is not). >> 4) Introduce a rigid base point generation algorithm (either the one >> that was proposed in the previous version of the draft or one using >> cryptographic hash function). We consider that important to ensure the >> generated points > could be safely used in applied protocols like >> password-based key establishment protocols (PAKE, EKE, PACE etc.) and RNGs >> like Dual EC DRBG. >> >> >> Best regards, >> Stanislav V. Smyshlyaev, Ph.D., >> Head of Information Security Department, >> CryptoPro LLC > > > I agree with Stanislav Smyshlyaev’s questions and suggestions about current > draft version. I would like to draw attention to the 3d remark. If the > answer to this question ("... whether it is the first d to be returned by > 5.2 algorithm ...") is “no” then it turns out that extra requirements that > are not mentioned in the draft are implicitly applied to the curve. Also it > seems strange that the recommended curve is not the one with the smallest d, > but the isogeny of this curve. Also I would like to add that it would be > convenient if the recommended Edwards curve is included in the document in > the same way as twisted Edwards curve. The recommended curve is y^2=x^3+486662x^2+x. Were we to use an isomorphic curve, as opposed to a 4-isogenous one, that 486662 would be replaced by a larger number, and thus slow down implementations significantly. Note that 486662 is the smallest value of a that ensures that y^2=x^3+ax^2+x has order 8*prime, twist order 4*prime, and the usual CM restrictions. This is the same as 121665 being the smallest d that ensure that y^2+x^2=1+dx^2y^2 has the same order and CM restrictions. Sincerely, Watson Ladd > > Kind regards, Evgeny Alekseev, Doctor of Philosophy, > Moscow State University, Faculty of Computational Mathematics and > Cybernetics > > > > _______________________________________________ > Cfrg mailing list > Cfrg@irtf.org > http://www.irtf.org/mailman/listinfo/cfrg > -- "Those who would give up Essential Liberty to purchase a little Temporary Safety deserve neither Liberty nor Safety." -- Benjamin Franklin
- [Cfrg] Suggestions for draft-irtf-cfrg-curves-01.… Stanislav V. Smyshlyaev
- Re: [Cfrg] Suggestions for draft-irtf-cfrg-curves… Evgeny Alekseev
- Re: [Cfrg] Suggestions for draft-irtf-cfrg-curves… Watson Ladd
- Re: [Cfrg] Suggestions for draft-irtf-cfrg-curves… Paul Lambert
- Re: [Cfrg] Suggestions for draft-irtf-cfrg-curves… Evgeny Alekseev