Re: [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS] Additional Elliptic Curves (Curve25519 etc) for TLS ECDH key agreement)
Watson Ladd <watsonbladd@gmail.com> Sun, 12 January 2014 22:39 UTC
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Date: Sun, 12 Jan 2014 14:39:42 -0800
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From: Watson Ladd <watsonbladd@gmail.com>
To: Vadym Fedyukovych <vf@unity.net>
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Subject: Re: [Cfrg] EdDSA and > 512 curve & hash (Re: [TLS] Additional Elliptic Curves (Curve25519 etc) for TLS ECDH key agreement)
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On Sun, Jan 12, 2014 at 2:29 PM, Vadym Fedyukovych <vf@unity.net> wrote: > On Sun, Jan 12, 2014 at 07:13:16AM -0800, Robert Ransom wrote: >> On 1/12/14, Adam Back <adam@cypherspace.org> wrote: >> >> > So actually Bernstein went in the opposite direction, not only using >> > sub-group size, but double sub-group size hash, basically because he could >> > without increasing the signature size, and thereby slightly even further >> > reducing the dependency on hash security and hash properties. I do not >> > consider its necessary, just its because he could, slightly more security >> > almost for free. But I think an EdDSA variant that used a 512-bit curve >> > could safely use a 512-bit hash, because even the double width hash is >> > over-engineering. >> >> It can for the hash of the message. >> >> > EdDSA also uses the deterministic DSA k trick (computed from m and x the >> > private key). >> >> Deterministic generation of message keys is the primary reason that >> EdDSA requires a double-length hash function. >> >> EdDSA relies on the hash function having double-length output in two ways: >> >> * Message key generation relies on the output being noticeably longer >> than the group order in order to generate *uniform* exponents. > > Choosing a message key (an initial random in interactive system) > from a large interval is a well-known idea for a group of a hidden order. > For a group of known order, reducing almost anything modulo group order > would likely result in quite a non-uniform distribution. > It is non-trivial to see how/whether hash of roughly twice-bitlength of group order > would be better than hash smaller than group order. Completely wrong for trivial reasons. Let's say we are picking a random number up to k by taking one up to n and reducing. Write n=kq+r, with r the remainder. Then the bias is exactly r/n, which for n the square of k is at most 1/k, and hence negligible if k is big enough. This is clearly better than if the hash length is smaller than the group order, in which case a significant number of group elements will never be picked. Sincerely, Watson Ladd > > Hash bitlength is rather non-critical while choosing a challenge, > that should be just a large enough set. > > Vadym Fedyukovych > > _______________________________________________ > 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
- [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