NIZK from SNARG

Abstract

We give a construction of a non-interactive zero-knowledge (NIZK) argument for all \(\mathsf {NP}\) languages based on a succinct non-interactive argument (SNARG) for all \(\mathsf {NP}\) languages and a one-way function. The succinctness requirement for the SNARG is rather mild: We only require that the proof size be \(|\pi |=\mathsf {poly}(\lambda )(|x|+|w|)^c\) for some constant \(c<1/2\), where |x| is the statement length, |w| is the witness length, and \(\lambda \) is the security parameter. Especially, we do not require anything about the efficiency of the verification.