Non-interactive Zero-Knowledge Proofs to Multiple Verifiers

Abstract

In this paper, we study zero-knowledge (ZK) proofs for circuit satisfiability that can prove to n verifiers at a time efficiently. The proofs are secure against the collusion of a prover and a subset of t verifiers. We refer to such ZK proofs as multi-verifier zero-knowledge (MVZK) proofs and focus on the case that a majority of verifiers are honest (i.e., $$t<n/2$$ ). We construct efficient MVZK protocols in the random oracle model where the prover sends one message to each verifier, while the verifiers only exchange one round of messages. When the threshold of corrupted verifiers $$t<n/2$$ , the prover sends $$1/2+o(1)$$ field elements per multiplication gate to every verifier; when $$t<n(1/2-\epsilon )$$ for some constant $$0<\epsilon <1/2$$ , we can further reduce the communication to O(1/n) field elements per multiplication gate per verifier. Our MVZK protocols demonstrate particularly high scalability: the proofs are streamable and only require a memory proportional to what is needed to evaluate the circuit in the clear.