Re: [Cfrg] New names for draft-ladd-safecurves
Watson Ladd <watsonbladd@gmail.com> Tue, 21 January 2014 16:33 UTC
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From: Watson Ladd <watsonbladd@gmail.com>
To: Bodo Moeller <bmoeller@acm.org>
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Cc: "cfrg@irtf.org" <cfrg@irtf.org>, Jon Callas <jon@callas.org>
Subject: Re: [Cfrg] New names for draft-ladd-safecurves
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On Tue, Jan 21, 2014 at 7:28 AM, Bodo Moeller <bmoeller@acm.org> wrote: > Jon Callas <jon@callas.org>: > >> I spent time talking to Dan and Tanja this weekend at ShmooCon about this >> sort of thing and I think that our agreement was that names like "Curve >> 255-19" (which covers both Curve25519 and Ed25519) or "Curve 414-17" (for >> the curve formerly known as Curve3617) made sense. My one concern which I've stated before is that we would then need a single wire format for Curve25519 and Ed25519. Robert Ransom's idea (sorry for the hijack) is the following: Suppose Bv^2=u^3+Au^2+u is isogenous to ax^2+y^2=1+dx^2y^2, with the isogenies u=(1+y)/(1-y), v=(1+y)/(1-y)x=ux. Then we represent points as u and the sign of x. A=2(a+d)/(a-d) B=4/(a-d). An implementation using the Montgomery ladder to multiply proceeds as usual, using the fact that A is the reciprocal of a small integer to rewrite the equations. It then reconstructs v (there is a fast formula), and uses that to compute the sign of x. One using the Edwards curves proceeds as usual, then inverts the isogeny to get u, and uses x to get the sign bit. The argument for this is we can specify all our curves in twisted Edwards form with d small, a=+/-1, and life is nice for everyone. Unfortunately Curve25519 doesn't fit this nice pattern, and people want to use that exact curve. This form also involves a bit of extra field math for everyone, even if they are all going to do ECDH or Edwards addition afterwards, and so will want that form anyway. There is also a problem of exceptional cases if a and d are nonsquares modulo p for example. Have I rendered correctly the arguments for and against? > > > Yes, it does. This would fix the single major flaw of Curve25519 -- > concatenating base-10 numbers to spell out a tuple just doesn't make sense > (except as a trap, so that if anyone reads it out as "twenty-five thousand > ..." you'll know they don't know what they're saying). I also don't really > like having whitespace in those names, so I'd prefer "Curve-255-19" over > "Curve 255-19". > > ("Curve" isn't very descriptive, but I've yet to see a more descriptive name > for this curve that is actually helpful.) NIST isn't useful either as a prefix, but we live with it. Anyway, my view is whatever people want to call these they can call them, bobo and kiki aside. > > Bodo > > > _______________________________________________ > 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
- Re: [Cfrg] New names for draft-ladd-safecurves Watson Ladd
- Re: [Cfrg] New names for draft-ladd-safecurves Mike Hamburg
- [Cfrg] New names for draft-ladd-safecurves Watson Ladd
- Re: [Cfrg] New names for draft-ladd-safecurves Jon Callas
- Re: [Cfrg] New names for draft-ladd-safecurves Watson Ladd
- Re: [Cfrg] New names for draft-ladd-safecurves Jon Callas
- Re: [Cfrg] New names for draft-ladd-safecurves Mike Hamburg
- Re: [Cfrg] New names for draft-ladd-safecurves Robert Ransom
- Re: [Cfrg] New names for draft-ladd-safecurves Robert Ransom
- Re: [Cfrg] New names for draft-ladd-safecurves Robert Ransom
- Re: [Cfrg] New names for draft-ladd-safecurves Robert Ransom
- Re: [Cfrg] New names for draft-ladd-safecurves Mike Hamburg
- Re: [Cfrg] New names for draft-ladd-safecurves Robert Ransom
- Re: [Cfrg] New names for draft-ladd-safecurves Mike Hamburg
- Re: [Cfrg] New names for draft-ladd-safecurves Bodo Moeller
- Re: [Cfrg] New names for draft-ladd-safecurves Watson Ladd
- Re: [Cfrg] New names for draft-ladd-safecurves Paul Lambert
- Re: [Cfrg] New names for draft-ladd-safecurves Watson Ladd
- Re: [Cfrg] New names for draft-ladd-safecurves Paul Lambert
- Re: [Cfrg] New names for draft-ladd-safecurves Manuel Pégourié-Gonnard
- Re: [Cfrg] New names for draft-ladd-safecurves Jon Callas
- Re: [Cfrg] New names for draft-ladd-safecurves Watson Ladd
- Re: [Cfrg] New names for draft-ladd-safecurves Bodo Moeller
- Re: [Cfrg] New names for draft-ladd-safecurves Watson Ladd
- Re: [Cfrg] New names for draft-ladd-safecurves Bodo Moeller
- Re: [Cfrg] New names for draft-ladd-safecurves Paul Lambert