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Finding Collisions on a OneWay Street: Can Secure Hash Functions be Based on General Assumptions
, 1998
"... We prove the existence of an oracle relative to which there exist seveial wellknown cryptographic primitives, including oneway permutations, but excluding (for a suitably strong definition) collisionintractible hash functions. Thus any proof that such functions can be derived from these weaker ..."
Abstract

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We prove the existence of an oracle relative to which there exist seveial wellknown cryptographic primitives, including oneway permutations, but excluding (for a suitably strong definition) collisionintractible hash functions. Thus any proof that such functions can be derived from these weaker primitives is necessarily nonrelativizing; in particular, no provable construction of a collisionintractable hash function can exist based solely on a “black box ” oneway permutation. This result can be viewed as a partial justification for the common practice of treating the collisionintractable hash function as a cryptographic primitive, rather than attempting to derive it from a weaker primitive (such as a oneway permutation). Key words: Hash functions, oracle, cryptography, complexity theory 1