Data-Flow-Based Normalization Generation Algorithm of R1CS for Zero-Knowledge Proof

TL;DR

This paper introduces a data-flow-based normalization algorithm for R1CS in zero-knowledge proofs, standardizing different representations of equivalent circuits to improve verification efficiency.

Contribution

It proposes a novel normalization algorithm for R1CS based on data flow, enabling consistent representation of equivalent circuits and reducing verification complexity.

Findings

The normalization algorithm produces standardized R1CS formats.

Experimental results confirm the effectiveness and correctness of the method.

Reduces complexity in circuit verification processes.

Abstract

The communities of blockchains and distributed ledgers have been stirred up by the introduction of zero-knowledge proofs (ZKPs). Originally designed to solve privacy issues, ZKPs have now evolved into an effective remedy for scalability concerns and are applied in Zcash (internet money like Bitcoin). To enable ZKPs, Rank-1 Constraint Systems (R1CS) offer a verifier for bi-linear equations. To accurately and efficiently represent R1CS, several language tools like Circom, Noir, and Snarky have been proposed to automate the compilation of advanced programs into R1CS. However, due to the flexible nature of R1CS representation, there can be significant differences in the compiled R1CS forms generated from circuit language programs with the same underlying semantics. To address this issue, this paper uses a data-flow-based R1CS paradigm algorithm, which produces a standardized format for different R1CS instances with identical semantics. By using the normalized R1CS format circuits, the complexity of circuits' verification can be reduced. In addition, this paper presents an R1CS normalization algorithm benchmark, and our experimental evaluation demonstrates the effectiveness and correctness of our methods.