Concurrent Zero Knowledge in the Public-Key Model

The concurrent setting for Zero-Knowledge protocols is very challenging as it requires protocols to remain secure even when several parties execute the same protocol concurrently. Indeed, it has been proved that achieving concurrent security for (black-box-simulation) zero-knowledge protocols in standard models requires a non-constant number of rounds, thus severely limiting efficiency. As a result, a few models with additional setup or network assumptions have been introduced to present constant-round concurrently-secure zero-knowledge protocols for all languages in ${\mathcal NP}$. In this paper we consider the bare public-key model, which is known to have very minimal setup assumptions, and we present the first constant round and concurrently secure zero-knowledge argument for any languages in ${\mathcal NP}$, under standard intractability assumptions. In fact, our protocol requires 4 rounds and is therefore round-optimal, is a proof of knowledge, and is time-efficient, in the sense that it is based on a tranformation that does not require any expensive ${\mathcal NP}$ reduction from prover or verifier. One 5-round variant of our protocol can be based on the minimal assumption of the existence of a one-way function.