On a Probabilistic Approach to the Security Analysis of Cryptographic Hash Functions

In this paper we focus on the three basic security requirements for a cryptographic hash function, commonly referred as preimage, second preimage and collision resistance. We examine these security requirements in the case of attacks which do not take advantage on how the hash function is computed, expressing them as success probabilities of suitable randomized algorithms. We give exact mathematical expressions for such resistance indices, and obtain 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, which enable us to give proofs for some prevailing beliefs.