, Volume 8, Issue 2, pp 87-99

Necessary and sufficient conditions for collision-free hashing

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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 pseudopermutations. We also give a simple construction of collision-free hash functions from everywhere-defined claw-free (pseudo-) permutations.

Communicated by Oded Goldreich
Supported by an NSF Graduate Fellowship, NSF Grant 92-12184, AFOSR F49620-92-J-0125, and DARPA N00014-92-J-1799.