Security of permutation-based compression function lp231lp231

•We study the security of a single permutation based compression function lp231.•lp231 provides 2n/32n/3-bit preimage resistance for the output size n.•lp231 provides n/2n/2-bit collision resistance ignoring log factor.

In this paper, we study security of a certain class of permutation-based compression functions. Denoted by lp231lp231 in [10], they are 2n-to-n-bit compression functions using three calls to a single n  -bit random permutation. We prove that lp231lp231 is asymptotically preimage resistant up to 22n3/n query complexity and collision resistant up to 2n2/n1+ϵ query complexity for any ϵ>0ϵ>0. Based on a single permutation, lp231lp231 provides both efficiency and almost optimal collision security.