Post-quantum security of the sponge construction

We investigate the post-quantum security of hash functions based on the sponge construction. A crucial property for hash functions in the post-quantum setting is the collapsing property (a strengthening of collision-resistance). We show that the sponge construction is collapsing (and in consequence quantum collision-resistant) under suitable assumptions about the underlying block function. In particular, if the block function is a random function or a (non-invertible) random permutation, the sponge construction is collapsing. We also give a quantum algorithm for finding collisions in an arbitrary function. For the sponge construction, the algorithm complexity asymptotically matches the complexity implied by collision resistance.