On the complexity of constant round ZKIP of possession of knowledge

Abstract

In this paper, we 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 on input x ∈ {0,1}*, outputs y such that (x, y) ∈ R with overwhelming probability if x ∈ dom R, and outputs “⊥” with probability 1 if x ∉ dom R. In the present paper, we also show that without any unproven assumption, there exists a four move blackbox simulation perfect zero-knowledge interactive proof system of possession of the prime factorization, which is optimal in the light of the round complexity.