NIZK Amplification via Leakage-Resilient Secure Computation

Benny Applebaum, Eliran Kachlon

Abstract: Suppose that we are given a weak Non-Interactive Zero-Knowledge (NIZK) proof system for \(\textbf{NP}\) with non-negligible soundness and zero-knowledge errors, denoted by \(\alpha \) and \(\beta \), respectively. Is it possible to reduce these errors to a negligible level? This problem, known as NIZK amplification, was introduced by Goyal, Jain, and Sahai (Crypto’19) and was further studied by Bitansky and Geier (Crypto’24). The latter work provides amplification theorems for proofs and arguments, assuming the existence of one-way functions and public-key encryption, respectively. Unfortunately, their results only apply when the security level, \(1 - (\alpha + \beta )\), is a constant bounded away from zero. Amplifying NIZK with an inverse polynomial security level remains an open problem and was stated as the main open question in both works.

External IDs:dblp:conf/crypto/ApplebaumK25