Efficiency and pseudo-randomness of a variant of Zémor-Tillich hash function

Recent breakthroughs concerning the current standard SHA-1 prompted NIST to launch a competition for a new secure hash algorithm by X.Wang et al (2005). Provably secure hash functions (in the sense that their security relates to the hardness of some mathematical problems by V. Lyubashevsky et al (2006) are particularly interesting from a theoretical point of view but are often much slower than heuristic functions like SHA. In this paper, we consider a variant of ZT hash, a provably secure hash function designed by Zemor and Tillich proposed by J.P Tilich and G.Zemor (1994). Despite some attack proposals, its security has not been fundamentally challenged to this day. Our function is twice as fast as ZT hash and has enhanced security properties. We propose optimized parameters and algorithms to increase the speed of both hash functions. This makes our function one of the most efficient ldquoprovably securerdquo hash functions to this day. Finally, we show that our hash function successfully passes most pseudo-randomness tests in the Dieharder suite.