New Non-Interactive Zero-Knowledge Subset Sum, Decision Knapsack And Range Arguments

We propose several new efficient non-interactive zero knowledge (NIZK) arguments in the common reference string model. The final arguments are based on two building blocks, a more efficient version of Lipmaa’s Hadamard product argument from TCC 2012, and a novel shift argument. Based on these two arguments, we speed up the recent range argument by Chaabouni, Lipmaa and Zhang (FC 2012). We also propose efficient arguments for two NP-complete problems, subset sum and decision knapsack, with constant communication, quasilinear prover’s computation and linear verifier’s computation.