# An Analysis of the Blockcipher-Based Hash Functions from PGV

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DOI: 10.1007/s00145-010-9071-0

- Cite this article as:
- Black, J., Rogaway, P., Shrimpton, T. et al. J Cryptol (2010) 23: 519. doi:10.1007/s00145-010-9071-0

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## Abstract

Preneel, Govaerts, and Vandewalle (1993) considered the 64 most basic ways to construct a hash function \(H{:\;\:}\{0,1\}^{*}\rightarrow \{0,1\}^{n}\) from a blockcipher \(E{:\;\:}\{0,1\}^{n}\times \{0,1\}^{n}\rightarrow \{0,1\}^{n}\). They regarded 12 of these 64 schemes as secure, though no proofs or formal claims were given. Here we provide a proof-based treatment of the PGV schemes. We show that, in the ideal-cipher model, the 12 schemes considered secure by PGV really *are* secure: we give tight upper and lower bounds on their collision resistance. Furthermore, by stepping outside of the Merkle–Damgård approach to analysis, we show that an additional 8 of the PGV schemes are just as collision resistant (up to a constant). Nonetheless, we are able to differentiate among the 20 collision-resistant schemes by considering their preimage resistance: only the 12 initial schemes enjoy optimal preimage resistance. Our work demonstrates that proving ideal-cipher-model bounds is a feasible and useful step for understanding the security of blockcipher-based hash-function constructions.