Restricted-Verifier Precise Bounded-Concurrent Zero-Knowledge

We present a stronger notion of precise bounded-concurrent zero-knowledge. Our notion captures the idea that view of any verifier in a bounded-concurrent interaction can be reconstructed in the almost same time. Precise zero-knowledge in stand-alone setting was introduced by Micali and Pass in STOC´06 and they constructed some precise stand-alone zero-knowledge protocols for NP using at least omega(1) rounds. Via providing a precise simulator for the known O(1)-round bounded-concurrent non-black-box zero-knowledge argument, we show the existence of O(1)- round bounded-concurrent zero-knowledge arguments with polynomial precision for NP. Our result assumes that the ratio of running-time of any adversarial verifier on any two different views in bounded-concurrent execution of the protocol is bounded by n^a, where a is any predeterminate constant. Such verifiers are called restricted verifiers.