# MMH* with arbitrary modulus is always almost-universal

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 1/p-almost--universal, where p is the smallest prime divisor of n. This bound is tight.

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