Non-interactive Zaps and New Techniques for NIZK

Abstract. In 2000, Dwork and Naor proved a very surprising result: that there exist “Zaps”, two-round witness-indistinguishable proofs in the plain model without a common reference string, where the Verifier asks a single question and the Prover sends back a single answer. This left open the following tantalizing question: does there exist a non-interactive witness indistinguishable proof, where the Prover sends a single mes-sage to the Verifier for some non-trivial NP-language? In 2003, Barak, Ong and Vadhan answered this question affirmatively by derandomizing Dwork and Naor’s construction under a complexity theoretic assumption, namely that Hitting Set Generators against co-nondeterministic circuits exist. In this paper, we construct non-interactive Zaps for all NP-languages. We accomplish this by introducing new techniques for building Non-Interactive Zero Knowledge (NIZK) Proof and Argument systems, which we believe to be of independent interest, and then modifying these t