We prove the existence of an oracle relative to which there exist seveial well-known cryptographic primitives, including one-way permutations, but excluding (for a suitably strong definition) collision-intractible hash functions. Thus any proof that such functions can be derived from these weaker primitives is necessarily non-relativizing; in particular, no provable construction of a collision-intractable hash function can exist based solely on a "black box" one-way permutation. This result can be viewed as a partial justification for the common practice of treating the collision-intractable hash function as a cryptographic primitive, rather than attempting to derive it from a weaker primitive (such as a one-way permutation).
Simon REF shows that collision-resistant hash-functions cannot be constructed form one-way functions via a black-box reduction.
Finding Collisions on a One-Way Street: Can Secure Hash Functions be Based on General Assumptions
EUROCRYPT
Computer Science