A Simple Variant of the Merkle-Damgard Scheme with a Permutation

We propose a new composition scheme for hash functions. It is a variant of the Merkle-Damg??ard construction with a permutation applied right before the processing of the last message block. We analyze the security of this scheme using the indifferentiability formalism, which was first adopted by Coron et al. to the analysis of hash functions. And we study the security of simple MAC constructions out of this scheme. Finally, we also discuss the random oracle indifferentiability of this scheme with a double-block-length compression function or the Davies-Meyer compression function composed of a block cipher