A Note on "New techniques for noninteractive zero-knowledge"

TL;DR

This paper critiques a 2012 study on noninteractive zero-knowledge systems, revealing a flaw in their basic system that allows cheating, and notes that key open questions remain unresolved.

Contribution

It identifies a critical flaw in a previously proposed NIZK system, highlighting unresolved issues in the field.

Findings

The basic system can be cheated by the prover.

Key open problems in NIZK remain unsolved.

The original claims of perfect NIZK are invalid due to the flaw.

Abstract

In 2012, Groth, et al. [J. ACM, 59 (3), 1-35, 2012] developed some new techniques for noninteractive zero-knowledge (NIZK) and presented: the first perfect NIZK argument system for all NP; the first universally composable NIZK argument for all NP in the presence of an adaptive adversary; the first noninteractive zap for all NP, which is based on a standard cryptographic security assumption. These solved several long-standing open questions. In this note, we remark that their basic system is flawed because the prover can cheat the verifier to accept a false claim. Thus, these problems remain open now.