Non-Uniformly Sound Certificates with Applications to Concurrent Zero-Knowledge

We introduce the notion of non-uniformly sound certificates: succinct single-message (unidirectional) argument systems that satisfy a "best-possible security" against non-uniform polynomial-time attackers. In particular, no polynomial-time attacker with s bits of non-uniform advice can find significantly more than s accepting proofs for false statements. Our first result is a construction of non-uniformly sound certificates for all NP in the random oracle model, where the attacker's advice can depend arbitrarily on the random oracle. We next show that the existence of non-uniformly sound certificates for P (and collision resistant hash functions) yields a public-coin constant-round fully concurrent zero-knowledge argument for NP.