Re: [TLS] [Cfrg] FW: Schnorr Signatures

On Jul 7, 2014 7:53 AM, "Johannes Merkle" <johannes.merkle@secunet.com>
wrote:
>
> Nigel Smart wrote on 26.06.2014 22:56:
> > With Schnorr you dont send the x-coord of R. What you send is
> > half the hash value e
> >     e=Hash(R||Message)
> > So if using SHA-256 you send 128 bits of e over.
>
> Actually, the Schnorr signature is defined as using the full hash value,
but it has been repeatedly proposed (originally
> by Schnorr himself) to use a half-length hash function (and that could be
truncated SHA-256).
>
> However, as you pointed out in [1], the security proofs you mentioned do
not work with reduced hash length h=b AND
> standard group order g = 2^(2b) for security level b. Your proof in the
generic model [1] requires h=2*b and the proof
> of Pointcheval and Stern in the Random oracle model [2] needs g=2^(3b).
Thus, when using half-length hash values you
> sacrifice provable security.

While the Pointcheval and Stern result is not tight, no one has made
attacks that do better.

The most compact and performant variant sends R and S. R is the size of a
group element, S the size of order of the group. This way the length of
what is to be transmitted does not depend on the hash used.
>
>
> [1] Gregory Neven, Nigel P. Smart, and Bogdan Warinschi. Hash function
requirements for schnorr
> signatures. J. Mathematical Cryptology, 3(1):69–87, 2009
>
> [2] David Pointcheval and Jacques Stern. Security arguments for digital
signatures and blind signatures.
> Journal of Cryptology, 13(3):361–396, March 2000.
>
>
> --
> Johannes
>
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