Re: [Cfrg] Mishandling twist attacks
Samuel Neves <sneves@dei.uc.pt> Sat, 29 November 2014 01:20 UTC
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Date: Sat, 29 Nov 2014 01:19:45 +0000
From: Samuel Neves <sneves@dei.uc.pt>
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Subject: Re: [Cfrg] Mishandling twist attacks
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On 28-11-2014 17:22, Watson Ladd wrote: > What exactly is wrong with telling everyone to multiply by 8, not 4, > even if the cofactor is 4? If your protocol is tightly coupled with an elliptic curve, nothing wrong with that, I suppose. But schemes and protocols are often specified in terms of generic groups, where order and cofactor always exist, but the notion of twist security may not. > So if we add this requirement to have the curve have larger cofactor > then the twist, then we still get E-521, and we will get Curve25519 at > the low end. It seems to me like we should make this change to the > generation method, and run it on 2^389-21 to get the intermediate size > curve. All this bickering further convinces me that complete Edwards curves over 3 (mod 4) primes are the way to go: - Square root computations are the simplest. 1 (mod 4) is too lenient, by the way: I don't think anybody is interested in computing square roots over 1 (mod 8) primes. - Edwards curves over 3 (mod 4) primes can have both order and twist with cofactor 4. - For users obsessed with speed, Mike Hamburg has described how to use an isogeny to get twisted Edwards-speed out of these curves [1]. We already have an excellent candidate in this space, namely Curve1174 over 2^251-9. E-521 is also such a curve. Since 2^389-21---which appears to be one of the nicest primes in that range (the other one being 2^379-19)---is also congruent to 3 (mod 4), it seems logical to keep things consistent and choose 3 (mod 4) primes for every work factor. [1] https://eprint.iacr.org/2014/027
- Re: [Cfrg] Mishandling twist attacks Watson Ladd
- [Cfrg] Mishandling twist attacks D. J. Bernstein
- Re: [Cfrg] Mishandling twist attacks Michael Hamburg
- Re: [Cfrg] Mishandling twist attacks Alyssa Rowan
- Re: [Cfrg] Mishandling twist attacks Samuel Neves
- Re: [Cfrg] Mishandling twist attacks David Leon Gil
- Re: [Cfrg] Mishandling twist attacks D. J. Bernstein
- Re: [Cfrg] Mishandling twist attacks Ilari Liusvaara
- Re: [Cfrg] Mishandling twist attacks Lochter, Manfred
- Re: [Cfrg] Mishandling twist attacks D. J. Bernstein
- Re: [Cfrg] Mishandling twist attacks Lochter, Manfred
- Re: [Cfrg] Mishandling twist attacks Watson Ladd
- Re: [Cfrg] Mishandling twist attacks Lochter, Manfred
- Re: [Cfrg] Mishandling twist attacks Watson Ladd