Efficient and Concurrent Zero-Knowledge from any public coin HVZK protocol

Abstract

We show how to efficiently transform any public coin honest verifier zero knowledge proof system into a proof system that is concurrent zero-knowledge with respect to any (possibly cheating) verifier via black box simulation. By efficient we mean that our transformation incurs only an additive overhead (both in terms of the number of rounds and the computational and communication complexity of each round), and the additive term is close to optimal (for black box simulation): only ω(log n) additional rounds, and ω(log n) additional public key operations for each round of the original protocol, where n is a security parameter, and ω(log n) can be any superlogarithmic function of n independent of the complexity of the original protocol. The transformation preserves (up to negligible additive terms) the soundness and completeness error probabilities, and the new proof system is proved secure based on the Decisional Diffie-Hellman (DDH) assumption, in the standard model of computation, i.e., no random oracles, shared random strings, or public key infrastructure is assumed. We prove our main result...