MMH⁎ with arbitrary modulus is always almost-universal

Abstract

Universal hash functions, discovered by Carter and Wegman in 1979, are of great importance in computer science with many applications. MMH⁎ is a well-known △-universal hash function family, based on the evaluation of a dot product modulo a prime. In this paper, we introduce a generalization of MMH⁎, that we call GMMH⁎, using the same construction as MMH⁎ but with an arbitrary integer modulus n>1, and show that GMMH⁎ is 1p-almost-△-universal, where p is the smallest prime divisor of n. This bound is tight.