On Existence of Robust Combiners for Cryptographic Hash Functions

A (k, l)-robust combiner for collision resistant hash functions is a construction, which takes l hash functions and combines them so that if at least k of the components are collision resistant, then so is the resulting combination. A black-box (k, l)-robust combiner is robust combiner, which takes its components as black-boxes. A trivial black-box combiner is concatenation of any (l−k+1) of the hash functions. Boneh and Boyen [1] followed by Pietrzak [3] proved, that for collision resistance we cannot do much better that concatenation, i.e. there does not exist black box (k, l)-robust combiner for collision resistance, whose output is significantly shorter that the output of the trivial combiner. In this paper we analyze whether robust combiners for other hash function properties (e.g. preimage resistance and second preimage resistance) exist.