On the concurrent composition of zero-knowledge proofs

We examine the concurrent composition of zero-knowledge proofs. By concurrent composition, we indicate a single prover that is involved in multiple, simultaneous zero-knowledge proofs with one or multiple verifiers. Under this type of composition it is believed that standard zero-knowledge protocols are no longer zero-knowledge. We show that, module certain complexity assumptions, any statement in NP has k(epsilon)-round proofs and arguments in which one can efficiently simulate any k(O(1)) concurrent executions of the protocol.