# Necessary and sufficient conditions for collision-free hashing

## 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.

### Key words

Cryptography Hash functions## Copyright information

© International Association for Cryptologic Research 1995