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

The introduction of zero-knowledge proofs (ZKPs) has had a profound impact on the blockchain and distributed ledger communities. ZKPs require the utilization of Rank-1 Constraint Systems (R1CS), which serve as verifiers for bi-linear equations. However, the flexibility of R1CS representation leads to notable variations in the compiled R1CS forms derived from circuit language programs with identical semantics. To tackle this challenge, this paper proposes a data-flow-based R1CS paradigm algorithm, producing a standardized format for different R1CS instances with the identical semantics. By adopting the normalized R1CS format circuits, the complexity of circuits’ verification can be reduced. Furthermore, this paper presents an R1CS normalization algorithm benchmark, and our experimental evaluation demonstrates the effectiveness and accuracy of our methods.