Abstract. We revisit the rate-1 blockcipher based hash functions as first studied by Preneel, Govaerts and Vandewalle (Crypto’93) and later extensively analysed by Black, Rogaway and Shrimpton (Crypto’02). We analyse a further generalization where any pre- and postprocessing is considered. This leads to a clearer understanding of the current classification of rate-1 blockcipher based schemes as introduced by Preneel et al. and refined by Black et al. In addition, we also gain insight in chopped, overloaded and supercharged compression functions. In the latter category we propose two compression functions based on a single call to a blockcipher whose collision resistance exceeds the birthday bound on the cipher’s blocklength. 1

Abstract. In this paper, we study security for a certain class of permutation-based compression functions. Denoted lp231 in [12], they are 2n-bit to n-bit compression functions using three calls to a single n-bit random permutation. We prove that lp231 is asymptotically preimage resistant up to (2 2n 3 /n) queries, adaptive preimage resistant up to (2 n 2 /n) queries/commitments, and collision resistant up to (2 n 2 /n 1+ɛ) queries for ɛ> 0. 1