On the Existence of Three Round Zero Knowledge Proofs


We study the round complexity of zero-knowledge (ZK) proof systems. While five round ZK proofs for $\mathsf{NP}$ are known from standard assumptions [Goldreich-Kahan, J. Cryptology’96], Katz [TCC’08] proved that four rounds are insufficient for this task w.r.t. black-box simulation.
In this work, we study the feasibility of ZK proofs using non-black-box simulation.Our main result is that three round private-coin ZK proofs for $\mathsf{NP}$ do not exist (even w.r.t. non-black-box simulation), under certain assumptions on program obfuscation. We closely follow recent work by Kalai et al. [Crypto’17] who ruled out constant round public-coin ZK proofs under the same assumptions.

37th Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2018)