Re: [Cfrg] A draft merging rpgecc and thecurve25519function.
David Rufino <david.rufino@gmail.com> Mon, 05 January 2015 18:34 UTC
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Date: Mon, 05 Jan 2015 18:34:50 +0000
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From: David Rufino <david.rufino@gmail.com>
To: Tanja Lange <tanja@hyperelliptic.org>
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Subject: Re: [Cfrg] A draft merging rpgecc and thecurve25519function.
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Ok, thank you (and Watson) for pointing that out. So presumably modifying one of draft-black/draft-turner/draft-cfrgcurve to use the montgomery-style NUMS procedure, which will generate curve25519 at WF128, should satisfy everyone's requirements ? Cheers, David On 2 January 2015 at 19:38, Tanja Lange <tanja@hyperelliptic.org> wrote: >> Perhaps it's worth making an explicit decision on whether or not >> 'rigidity' is actually a required feature. The very rough consensus >> appears to be 'no', because it's regarded as improbable ('alien >> technology') that anyone would be able to 'backdoor' the elliptic curve. >> In either case it appears to me that deciding this question ought to fix >> the curve on purely technical grounds (no -> curve25519, yes -> rpgecc) >> > This would be quite a mischaracterization of X25519. The 2006 paper > contains full justifications about every single choice made and > X25519 is historically the first fully rigid curve (unless one includes > Koblitz curves or other curves with very special properties which > coincidentally limit the choice down to just one curve). Its coefficient > A is the smallest one achieving all required properties. The reason > that this draft finds a different (isogenous) curve is that it searches > for the smallest coefficient d for a curve in _Edwards_ form rather > than for the smallest coefficient A for a curve in _Montgomery_ form. > > This 'wiggle room' of choosing a curve shape cannot be eliminated > but it's quite small. (Note that the paper introducing the NUMS curves > had 26 curves spread over 3 levels of security, because of this and > a similar decision of how to optimize the prime choice.) > > I don't understand why the procedure should be part of the draft > anyways. A description of how to rigidly choose curves already > appears in ACM-CSS 2013 [1]. This could be cited along with the > NUMS paper as informative references in the security considerations. > The generation method does not matter for the implementor > > Regards > Tanja > > [1] "Elligator: Elliptic-curve points indistinguishable from uniform > random strings", Bernstein, Hamburg, Krasnova, Lange, ACM-CCS 2013, > http://dx.doi.org/10.1145/2508859.2516734 (Open Access) >
- [Cfrg] A draft merging rpgecc and thecurve25519fu… Adam Langley
- Re: [Cfrg] A draft merging rpgecc and thecurve255… Adam Langley
- Re: [Cfrg] A draft merging rpgecc and thecurve255… Watson Ladd
- Re: [Cfrg] A draft merging rpgecc and thecurve255… Adam Langley
- Re: [Cfrg] A draft merging rpgecc and thecurve255… Adam Langley
- [Cfrg] Wanting a signature scheme, not needing it… Paul Hoffman
- Re: [Cfrg] A draft merging rpgecc and thecurve255… Mike Hamburg
- Re: [Cfrg] A draft merging rpgecc and thecurve255… Brian Smith
- Re: [Cfrg] A draft merging rpgecc and thecurve255… David Rufino
- Re: [Cfrg] A draft merging rpgecc and thecurve255… Stephen Farrell
- Re: [Cfrg] A draft merging rpgecc and thecurve255… Tanja Lange
- Re: [Cfrg] A draft merging rpgecc and thecurve255… David Rufino
- Re: [Cfrg] A draft merging rpgecc and thecurve255… Alexey Melnikov