Re: [Cfrg] Fwd: Re: Safecurves draft
Robert Ransom <rransom.8774@gmail.com> Thu, 09 January 2014 09:50 UTC
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Date: Thu, 09 Jan 2014 01:50:48 -0800
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From: Robert Ransom <rransom.8774@gmail.com>
To: Manuel Pégourié-Gonnard <mpg@elzevir.fr>
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Subject: Re: [Cfrg] Fwd: Re: Safecurves draft
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On 1/9/14, Manuel Pégourié-Gonnard <mpg@elzevir.fr> wrote: > On 09/01/2014 09:12, Alyssa Rowan wrote: >> On 08/01/2014 23:50, Watson Ladd wrote: >> >>> I don't want to rename curves because that induces consistency >>> issues. >> >> Entirely accepted: I raised it merely as a question. People are >> already beginning to adopt these curves of their own volition, so >> changing the names of them could be confusing, yes. >> > About names, I'd really like the names to reflect the type of the curve > (Montgomery or Edwards). This is already the case for other curve families, > by > the way. So, Mxxx and Exxx seem great to me. I'd even go so far as to rename > Curve25519 as M255, but I'm sure there are good reasons to disagree on this > point. Remember that Curve25519's parameter is *not* minimal subject to the constraint of twist security with minimal cofactors -- Dr. Bernstein considered a slightly more subtle criterion regarding the group orders too. Keep that in mind if you try to establish a systematic name for Curve25519. > While at it, I also think the document should define the curves for each > type in > distinct sections. Overall, the goal is that it should be easy for other > document to define the of just the Montgomery (or just the Edwards) curves > for > use in a protocol, and refer to the appropriate section of this draft. I don't see the benefit of defining both a ‘safe’ Montgomery curve (for the present definition of “safe”) and a ‘safe’ Edwards curve over the same coordinate field -- every Edwards curve with minimal parameter can be used efficiently with Montgomery's formulas. (The Montgomery-form parameter becomes the reciprocal of a small integer, which can be handled as efficiently as a small integer itself.) (For that matter, I would suggest replacing Curve25519 with the twisted Edwards curve a=-1, d=121665 over the same field in any new application or standard.) I would also recommend highlighting the most efficient curves -- Curve25519 and Curve3617 have especially nice coordinate fields; even 2^521 - 1 is less convenient (the limb arrangement is less regular). > Take the points list on the frontpage of the safecurves site, for instance > (numbered by me for convenience). > > 1. Your implementation produces incorrect results for some rare curve > points. > 2. Your implementation leaks secret data when the input isn't a curve point. > 3. Your implementation leaks secret data through branch timing. > 4. Your implementation leaks secret data through cache timing. > Overall, of course it's nice that issues 1 and 2 are completely annihilated > by > Montgomery and Edwards curves, Issue 2 is obviated by twist security for single-scalar multiplication of a Montgomery-form x coordinate. It remains relevant for any application which operates on full points (whether transmitted uncompressed or compressed). > and to be fair point 4 is a bit easier to > address > with these curves too. Why 4? The benefit of complete addition formulas is that implementations don't need to switch to a doubling routine when two points are equal. Nothing about SafeCurves makes constant-time table lookups any easier. Robert Ransom
- [Cfrg] Safecurves draft Watson Ladd
- Re: [Cfrg] Safecurves draft Stephen Farrell
- Re: [Cfrg] Safecurves draft Watson Ladd
- Re: [Cfrg] Safecurves draft Manuel Pégourié-Gonnard
- Re: [Cfrg] Safecurves draft Watson Ladd
- Re: [Cfrg] Safecurves draft Manuel Pégourié-Gonnard
- Re: [Cfrg] Safecurves draft Dan Harkins
- Re: [Cfrg] Safecurves draft Manuel Pégourié-Gonnard
- Re: [Cfrg] Safecurves draft Paul Lambert
- Re: [Cfrg] Safecurves draft Watson Ladd
- Re: [Cfrg] Safecurves draft Alyssa Rowan
- Re: [Cfrg] Safecurves draft Stephen Farrell
- Re: [Cfrg] Safecurves draft Alyssa Rowan
- Re: [Cfrg] Safecurves draft Stephen Farrell
- Re: [Cfrg] Safecurves draft Watson Ladd
- Re: [Cfrg] Safecurves draft Paul Lambert
- Re: [Cfrg] Safecurves draft Watson Ladd
- Re: [Cfrg] Safecurves draft Paul Lambert
- Re: [Cfrg] Safecurves draft Isaac Chua
- Re: [Cfrg] Safecurves draft Dan Brown
- Re: [Cfrg] Safecurves draft Manuel Pégourié-Gonnard
- [Cfrg] Fwd: Re: Safecurves draft Alyssa Rowan
- Re: [Cfrg] Fwd: Re: Safecurves draft Manuel Pégourié-Gonnard
- Re: [Cfrg] Safecurves draft Adam Back
- Re: [Cfrg] Fwd: Re: Safecurves draft Robert Ransom
- Re: [Cfrg] Fwd: Re: Safecurves draft Manuel Pégourié-Gonnard
- Re: [Cfrg] Safecurves draft Johannes Merkle
- Re: [Cfrg] Safecurves draft Bodo Moeller
- Re: [Cfrg] Safecurves draft Robert Ransom
- Re: [Cfrg] Safecurves draft Bodo Moeller
- Re: [Cfrg] Safecurves draft Robert Ransom
- Re: [Cfrg] Safecurves draft Bodo Moeller
- Re: [Cfrg] Fwd: Re: Safecurves draft Robert Ransom
- Re: [Cfrg] Safecurves draft Mike Hamburg
- Re: [Cfrg] Safecurves draft Watson Ladd
- Re: [Cfrg] Safecurves draft Jon Callas
- Re: [Cfrg] Safecurves draft Paul Lambert
- Re: [Cfrg] Safecurves draft Paul Lambert
- Re: [Cfrg] Safecurves draft Watson Ladd
- Re: [Cfrg] Safecurves draft Bodo Moeller
- Re: [Cfrg] Fwd: Re: Safecurves draft Manuel Pégourié-Gonnard
- Re: [Cfrg] Safecurves draft Robert Ransom
- Re: [Cfrg] Fwd: Re: Safecurves draft Robert Ransom