Concurrent and resettable zero-knowledge in poly-loalgorithm rounds

Abstract

A proof is concurrent zero-knowledge if it remains zero-knowledge when many copies of the proof are run in an asynchronous environment, such as the Internet. Richardson and Kilian have shown that there exists a concurrent zero-knowledge proof for any language in NP, but with round complexity polynomial in the maximum number of concurrent proofs. In this paper, we present a concurrent zero-knowledge proof for all languages in NP with a poly-logarithmic round complexity: specifically, ω(log^2 k) rounds given at most k concurrent proofs. Finally, we show that a simple modification of our proof is a resettable zero-knowledge proof for NP, with ω(log^2 k) rounds; previously known protocols required a polynomial number of rounds.