Constant-Round Concurrent Zero Knowledge from P-Certificates

We present a constant-round concurrent zero-knowledge protocol for NP. Our protocol relies on the existence of families of collision-resistant hash functions, and a new, but in our eyes, natural complexity-theoretic assumption: the existence of P-certificates-that is, "succinct" non-interactive proofs/arguments for P. As far as we know, our results yield the first constant-round concurrent zero-knowledge protocol for NP with an explicit zero-knowledge simulator based on any assumption.