A Fast R1CS Normalization Method Based on Parameter Vectors
摘要
In recent years, the development of blockchain has been flourishing.Blockchain provides decentralization, improved security, and increased transparency compared to conventional centralized transaction systems, which lowers costs and increases transaction efficiency. One frequently used tool in blockchain is the Rank-1 Constraint System (R1CS).By providing a more condensed method of achieving zero-knowledge proofs, R1CS improves the blockchain’s scalability and security even further. The goal of this work is the standardization of R1CS so that any combination of constraints can be transformed into one and uniform format. Additionally, it makes it possible to combine seemingly different but fundamentally similar sets of R1CS constraints into a single new R1CS set, which eliminates duplicate R1CS sets in the process and increases the efficiency of later steps of the creation of zero-knowledge proofs. This study proposes a concise method for standardizing R1CS constraint sets. Given any R1CS constraint set (comprising three matrices A, B, C, the solution vector and their corresponding parameter vector), regardless of whether the original problem is represented by a single variable or multiple variables, it can be converted into a unique standard representation. The study utilized symbolic and equation operations to determine the actual problem to be solved and merges various potentially equivalent R1CS constraint sets into one. Additionally, we use a flow chart to illustrate our process of standardizing R1CS constraint sets. In the experiment section, each experimental group engaged in nine different equivalent transformations. The results showed that all could be successfully converted into a unique R1CS constraint set representation. Compared to previous related research, the time required for R1CS standardization was significantly reduced.