Brute force attacks on hash functions

Abstract We examine preimage, second preimage and collision resistance of cryptoghraphic hash functions for a particular class of brute force attacks. We give exact mathematical expressions for such resistance indices, expressing them as success probabilities of suitable randomized algorithms, and obtaining their functional behaviour in relation to the amount of uniformity in the hash function outcomes. Our work provides a mathematical framework for the study of cryptographic hash functions, and our results can be used as a starting point to derive useful numerical estimates of how much resistance a real hash function has with respect to a class of attacks of practical relevance.

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