Efficient NIZK arguments via parallel verification of Benes networks

Abstract

We work within the recent paradigm, started by Groth (ASIACRYPT 2010), of constructing short non-interactive zero knowledge arguments from a small number basic arguments in a modular fashion. The main technical result of this paper is a new permutation argument, by using product and shift arguments of Lipmaa (2014) and a parallelizable variant of the Beneš network. We use it to design a short non-interactive zero knowledge argument for the NP-complete language CircuitSAT with Θ(n log2 n) prover’s computational complexity, where n is the size of the circuit. The permutation argument can be naturally used to design direct NIZK arguments for many other NP-complete languages.