Construction, Randomness and Security of New Hash Functions Derived from Chaos Mappings

Abstract

We introduce new hash functions SSInhash, n=160, 192, 256, 384, 512, 1024 and 2048, whose algorithm is, differently from many other hash functions, consisting of multiplication and shift of multiple-precision integers. The base of algorithm is a repetition of piecewise linear chaos mappings called SSR computations. We first construct a tiny hash function SSRhash which is derived from SSR algorithm directly, and then translate it into all-integer version SSInhash whose hash value is n bits. After constructing hash functions we verify randomness of hash values generated by SSInhash by applying the NIST statistical test suite and TestU01. We further discuss the security of our hash function by deriving algebraic equation of high degree.