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 [1], [2]. Provably secure hash functions (in the sense that their security relates to the hardness of some mathematical problems [3]-[6]) 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 Zémor and Tillich proposed in 1994 [6]. 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 "provably secure" hash functions to this day. Finally, we show that our hash function successfully passes most pseudo-randomness tests in the Dieharder suite [7].