Security of permutation-based compression function Ip231

In this paper, we study security of a certain class of permutation-based compression functions. Denoted lp231 in [10], they are 2n-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 query complexity and collision resistant up to 2 n 2 /n query complexity for any > 0. Based on a single permutation, lp231 provides both efficiency and almost optimal collision security.