Re: [Cfrg] Chopping out curves
Robert Ransom <rransom.8774@gmail.com> Fri, 17 January 2014 14:33 UTC
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Date: Fri, 17 Jan 2014 06:33:24 -0800
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From: Robert Ransom <rransom.8774@gmail.com>
To: Alyssa Rowan <akr@akr.io>
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Subject: Re: [Cfrg] Chopping out curves
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On 1/17/14, Alyssa Rowan <akr@akr.io> wrote: > There are arguments in favour of both the existing or a new basepoint for > t25519 (which is what I'll call the twisted Edwards representation of > Curve25519 used in Ed25519, as I'm not sure it actually has a name of its > own?). The curve specified as ‘T25519’ (a=121666, d=121665) in draft-ladd-safecurves-03 is something that Watson Ladd made up. The Ed25519 signature scheme paper (<http://ed25519.cr.yp.to/ed25519-20110926.pdf>) specifies the a=-1 form (a=-1, d=-121665/121666). > Generating a new basepoint for t25519: > • Elegant; we can select minimum y that satisfies SafeCurves criteria > - What advantage, really, would that give in implementation? > - Is it worth any perceived benefit? > - Absolute rigidity would be critical to avoid potential manipulation > concerns Watson Ladd actually chose a point with small Edwards-form x, not small Edwards-form y. There is no benefit to choosing a new basepoint, but there's also no benefit to using ‘T25519’ instead of the (more efficient) form specified for Ed25519. As you point out, using a different basepoint does prevent use of keys in different protocols, even when the protocols are designed to be safe to use with the same key material, so that's a real (and unnecessary) cost. > • Reverification necessary, I think. > - New basepoint → new prime order → new primality tests for SafeCurve > script? (Damn. They're the expensive part.) ‘T25519’ is isomorphic to Curve25519, so any non-identity group element of odd order on T25519 generates the same group as the standard basepoint of Curve25519 (and has the same order). > On balance I have to say, I think I prefer keeping the basepoint Ed25519 > already uses for t25519, but it's not a strong preference. If we do change > it, we do need to dot the i's and cross the t's, so to speak. I have a strong preference for throwing out T25519 and using Ed25519 with its standard basepoint. Robert Ransom
- [Cfrg] Chopping out curves Watson Ladd
- Re: [Cfrg] Chopping out curves Trevor Perrin
- Re: [Cfrg] Chopping out curves Michael Hamburg
- Re: [Cfrg] Chopping out curves Dan Harkins
- Re: [Cfrg] Chopping out curves Watson Ladd
- Re: [Cfrg] Chopping out curves Michael Hamburg
- Re: [Cfrg] Chopping out curves Adam Back
- Re: [Cfrg] Chopping out curves Adam Back
- Re: [Cfrg] Chopping out curves Watson Ladd
- Re: [Cfrg] Chopping out curves Alyssa Rowan
- Re: [Cfrg] Chopping out curves David McGrew
- Re: [Cfrg] Chopping out curves Adam Back
- Re: [Cfrg] Chopping out curves Alyssa Rowan
- Re: [Cfrg] Chopping out curves Robert Ransom
- Re: [Cfrg] Chopping out curves Watson Ladd
- Re: [Cfrg] Chopping out curves Manuel Pégourié-Gonnard
- Re: [Cfrg] Chopping out curves Alyssa Rowan
- Re: [Cfrg] Chopping out curves Watson Ladd
- Re: [Cfrg] Chopping out curves Igoe, Kevin M.
- Re: [Cfrg] Chopping out curves Manuel Pégourié-Gonnard
- Re: [Cfrg] Chopping out curves Watson Ladd
- Re: [Cfrg] Chopping out curves Mike Hamburg
- Re: [Cfrg] Chopping out curves Manuel Pégourié-Gonnard
- Re: [Cfrg] Chopping out curves Jon Callas