Re: [Cfrg] Thoughts on a Next-Generation Elliptic Curve Signature Scheme?
Robert Ransom <rransom.8774@gmail.com> Sat, 11 January 2014 18:44 UTC
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Date: Sat, 11 Jan 2014 10:44:37 -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] Thoughts on a Next-Generation Elliptic Curve Signature
Scheme?
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On 1/11/14, Alyssa Rowan <akr@akr.io> wrote: > -----BEGIN PGP SIGNED MESSAGE----- > Hash: SHA512 > > At some point, clearly we're going to need a signature scheme for > these "Chicago curves" specified in SafeCurves, for later use to > replace ECDSA with something which is a more convenient fit for them > and doesn't want random numbers for each signature, for future use in > certificates, authentication, and the like. > > I feel like now would be a good point, hence this request for ideas. > > On 11/01/2014 17:40, Robert Ransom wrote: >> Dr. Bernstein's EdDSA is even worse: it prohibits every curve that >> Dr. Bernstein himself has specified since Curve25519. > > EdDSA seem like a pretty good start for a new signature scheme to me, > even if as it stands I think it's closely tied to Ed25519 itself > (basically, due to the size and construction?). EdDSA specifies some details that are irrelevant to how the signature scheme works: it specifies that the coordinate field's order must be congruent to 5 mod 8, and it specifies that the curve group must have cofactor 8 (cofactor 4 is possible even mod 2^255 - 19, e.g. a=-1, d=446 if I'm retyping it correctly). > Either the Edwards curves or the Edwards isomorphism of one of the > Montgomery curves would do, although the ones specified as Edwards > curves would likely be cleaner, particularly Curve1174, Curve3617 and > E521: in fact, those would be the three I'd plump for, as I think they > provide three pretty good security/efficiency points. Please, not Curve1174. If you don't like Curve25519's awkward fractional value of Edwards-form d, use the isogenous curve with a=-1,d=121665 over the same field. > We're going to need a hash, too. I suggest that we should use one of > the new hash algorithms that came out of the SHA-3 competition. All > the finalists have something to recommend them (I really like Skein > and BLAKE myself): BLAKE2 is better than BLAKE. > but the least controversial in my eyes, and so the > one I'd on consideration suggest, is Keccak, given it was the winner > and thus has the additional backing of being SHA-3. (I can see ways > its particular attributes might prove helpful, too.) Because NSA wants other people to rely on Keccak? Really? I can see advantages to using a sponge, but “NSA wants us to eat it” has never been a good argument. Robert Ransom
- [Cfrg] Thoughts on a Next-Generation Elliptic Cur… Alyssa Rowan
- Re: [Cfrg] Thoughts on a Next-Generation Elliptic… Robert Ransom
- Re: [Cfrg] [TLS] Additional Elliptic Curves (Curv… Alyssa Rowan
- [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS] Ad… Adam Back
- Re: [Cfrg] [TLS] Additional Elliptic Curves (Curv… Daniel Kahn Gillmor
- Re: [Cfrg] [TLS] Additional Elliptic Curves (Curv… Robert Ransom
- Re: [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS… Robert Ransom
- Re: [Cfrg] [TLS] Additional Elliptic Curves (Curv… Adam Back
- Re: [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS… Adam Back
- Re: [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS… Mike Hamburg
- Re: [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS… Vadym Fedyukovych
- Re: [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS… Watson Ladd
- Re: [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS… Vadym Fedyukovych