Round-Optimal Zero-Knowledge Proofs of Knowledge for NP.
Hongda Li, Dengguo Feng, Bao Li, Haixia Xue · IACR Cryptology ePrint Archive · 2008
It is well known that all the known black-box zero-knowledge proofs of knowledge for NP are nonconstant-round. Whether there exit constant-round black-box zero-knowledge proofs of knowledge for all NP languages under certain standard assumptions is a open problem. This paper focuses on the problem and give a positive answer by presenting two constructions of constant-round (black-box) zero-knowledge proofs of knowledge for the HC (Hamiltonian Cycle) problem. By the recent result of Katz, our second construction which relies on the existence of claw-free functions has optimal round complexity (5-round) assuming the polynomial hierarchy does not collapse.