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A new bound for t−wise almost universal hash functions

L.H. Nguyen and A.W. Roscoe

Abstract

Using the pigeon-hole principle, we derive a new bound for the key length in a t-wise almost universal hash function where the multicollision or t-collision probability is bounded above by epsilon in the range [0,1]. The important features of this bound are (1) it decreases very slowly as t increases, and (2) the key length grows at least linearly with the logarithm of the message length. To our knowledge, this is the first almost universal hash bound for any integer t > 1. This work arises from the use of t-wise almost universal hash functions in manual authentication protocols.

Institution
OUCL
Month
November
Number
RR−10−24
Pages
4
Year
2010