Black-Box Analysis of the Block-Cipher-Based Hash-Function Constructions from PGV

Preneel, Govaerts, and Vandewalle [6] considered the 64 most basic ways to construct a hash function H: (0, 1)* → (0, 1)n from a block cipher E: (0, 1)n × (0, 10n → (0, 1)n. They regarded 12 of these 64 schemes as secure, though no proofs or formal claims were given. The remaining 52 schemes were shown to be subject to various attacks. Here we provide a formal and quantitative treatment of the 64 constructions considered by PGV. We prove that, in a black-box model, the 12 schemes that PGV singled out as secure really are secure: we give tight upper and lower bounds on their collision resistance. Furthermore, by stepping outside of the Merkle-Damgåard approach to analysis, we show that an additional 8 of the 64 schemes are just as collision resistant (up to a small constant) as the first group of schemes. Nonetheless, we are able to differentiate among the 20 collision-resistant schemes by bounding their security as one-way functions. We suggest that proving black-box bounds, of the style given here, is a feasible and useful step for understanding the security of any block-cipher-based hash-function construction.