On the impossibility of efficiently combining collision resistant hash functions

Abstract

Let H1, H2 be two hash functions. We wish to construct a new hash function H that is collision resistant if at least one of H1 or H2 is collision resistant. Concatenating the output of H1 and H2 clearly works, but at the cost of doubling the hash output size. We ask whether a better construction exists, namely, can we hedge our bets without doubling the size of the output? We take a step towards answering this question in the negative - we show that any secure construction that evaluates each hash function once cannot output fewer bits than simply concatenating the given functions. © International Association for Cryptologic Research 2006.