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arXiv · 2010.05420

MMH* with arbitrary modulus is always almost-universal

Khodakhast Bibak·Bruce M. Kapron·Venkatesh Srinivasan
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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 $\triangle$-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 $\frac{1}{p}$-almost-$\triangle$-universal, where $p$ is the smallest prime divisor of $n$. This bound is tight.

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Khodakhast Bibak, Bruce M. Kapron, Venkatesh Srinivasan. 2020-10-12. MMH* with arbitrary modulus is always almost-universal. https://doi.org/10.1016/j.ipl.2016.03.009

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