On the construction of universal families of hash functions via geometric codes and concatenation

In this paper we use coding theory to give simple explanations of some recent results on universal hashing. We first apply our approach to give a precise and elegant analysis of the Wegman-Carter construction for authentication codes. Using Reed-Solomon codes and the well known concept of concatenated codes we can then give some new constructions, which require much less key size than previously known constructions. The relation to coding theory allows the use of codes from algebraic curves for the construction of hash functions. Particularly, we show how codes derived from Artin-Schreier curves, Hermitian curves and Suzuki curves yield good classes of universal hash functions.