Perfectly Hiding Commitment Scheme with Two-Round from Any One-Way Permutation

Commitment schemes are arguably among the most important and useful primitives in cryptography. According to the computational power of receivers, commitments can be classified into three possible types: computational hiding commitments, statistically hiding commitments and perfect computational commitments. The fist commitment with constant rounds had been constructed from any one-way functions in last centuries, and the second with non-constant rounds were constructed from any one-way functions in FOCS2006, STOC2006 and STOC2007 respectively, furthermore, the lower bound of round complexity of statistically hiding commitments has been proven to be n logn rounds under the existence of one-way function. Perfectly hiding commitments implies statistically hiding, hence, it is also infeasible to construct a practically perfectly hiding commitments with constant rounds under the existence of one-way function. In order to construct a perfectly hiding commitments with constant rounds, we have to relax the assumption that one-way functions exist. In this paper, we will construct a practically perfectly hiding commitment with two-round from any one-way permutation. To the best of our knowledge, these are the best results so far.