Abstract

Abstract. Using the pigeon-hole principle, we derive a new bound for the key length in a l-wise almost universal hash function where the multicollision or l-collision probability is bounded above by ɛ ∈ [0, 1]. The important features of this bound are (1) it decreases very slowly as l 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 l ≥ 2. This work arises from the use of l-wise almost universal hash functions in manual authentication protocols. 1

Citations