Paper 2010/602

An Improved Algebraic Attack on Hamsi-256

Itai Dinur and Adi Shamir

Abstract

Hamsi is one of the $14$ second-stage candidates in NIST's SHA-3 competition. The only previous attack on this hash function was a very marginal attack on its 256-bit version published by Thomas Fuhr at Asiacrypt $2010$, which is better than generic attacks only for very short messages of fewer than $100$ 32-bit blocks, and is only $26$ times faster than a straightforward exhaustive search attack. In this paper we describe a different algebraic attack which is less marginal: It is better than the best known generic attack for all practical message sizes (up to $4$ gigabytes), and it outperforms exhaustive search by a factor of at least $512$. The attack is based on the observation that in order to discard a possible second preimage, it suffices to show that one of its hashed output bits is wrong. Since the output bits of the compression function of Hamsi-256 can be described by low degree polynomials, it is actually faster to compute a small number of output bits by a fast polynomial evaluation technique rather than via the official algorithm.

Note: Updated according to comments by anonymous referees