Abstract

This paper determines an exact relationship between collision-free hash functions and other cryptographic primitives. Namely, it introduces a new concept, the pseudopermutation, and shows that the existence of collision-free hash functions is equivalent to the existence of claw-free pairs of pseudo-permutations. We also give a simple construction of collision-free hash functions from everywhere-defined claw-free (pseudo-) permutations. 1 Introduction Hash functions with various cryptographic properties have been studied extensively, especially with respect to signing algorithms (see [2, 3, 4, 10, 12, 14, 15]). We focus on the most natural of these functions, the collision-free hash functions. A function h is a collision-free hash function if jh(x)j jxj \Gamma 1 and it is infeasible, given h and 1 k , to find a pair (x; y) so that jxj = jyj = k and h(x) = h(y). These functions were first carefully studied by Damgard [2] and have found several applications. In particular, they have b...

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