Efficient Modular NIZK Arguments from Shift and Product

Abstract

We propose a non-interactive product argument, that is more efficient than the one by Groth and Lipmaa, and a novel shift argument. We then use them to design several novel non-interactive zero-knowledge (NIZK) arguments. We obtain the first range proof with constant communication and subquadratic prover\u27s computation. We construct NIZK arguments for $\mathbf{NP}$-complete languages, {\textsc{Set-Partition}}, {\textsc{Subset-Sum}} and {\textsc{Decision-Knapsack}}, with constant communication, subquadratic prover\u27s computation and linear verifier\u27s computation