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, modulo certain complexity assumptions, any statement in NP has k∈-round proofs and arguments in which one can efficiently simulate any kO(1) concurrent executions of the protocol.