On the complexity of constant round ZKIP of possession of knowledge

In this paper, we investigate the round complexity of zero-knowledge interactive proof systems of possession of knowledge, and mainly show that if a relation R has a three move blackbox simulation zero-knowledge interactive proof system of possession of knowledge, then there exists a probabilistic polynomial time algorithm that can be satisfied under certain conditions. The result can be generalized to zero-knowledge interactive proof systems of possession of knowledge with more than four moves, because it s known that there exist a 'four' move blackbox simulation perfect zero-knowledge interactive proof system of possession of knowledge for a nontrivial relation R.