Universal hash functions from exponential sums over finite fields and galois rings

Abstract

In this paper new families of strongly universal hash functions, or equivalently, authentication codes, are proposed. Their parameters are derived from bounds on exponential sums over finite fields and Galois rings. This is the first time hash families based upon such exponential sums have been considered. Their performance improves the previously best known constructions and they can be made general in their choice of parameters. Furthermore, the constructions are suitable both for hardware and software implementations. The latter is an aspect that is significant and has been considered in several recent papers.