An Efficient Zero-Knowledge Range Proof Scheme Based on Multibit Split Square Decomposition

With the continuous development of blockchain technology, an increasing number of scholars have begun to consider the harm of data leakage during on-chain transactions and the requirement for privacy data protection. Zero-knowledge range proof, as a cryptographic technology, can perform legitimacy verification of data while hiding private data, effectively realizing the protection of private data on the blockchain, so it is increasingly used to protect blockchain privacy. The mainstream construction methods for range proofs can be mainly divided into two categories: n-ary decomposition and square decomposition. This paper introduces and analyzes the advantages and disadvantages of these construction methods in detail. Then, based on these two methods, a zero-knowledge range proof scheme based on multibit split square decomposition (ZKRPMSSD) is proposed, which requires no trusted third-party setting and can achieve range proofs for arbitrary ranges. The proposed ZKRPMSSD scheme processes the original data based on the multibit split idea, and the acquisition method of secret value components is optimized so that the acquisition of components does not depend on the scale of the original problem. Additionally, the algorithms for proof generation and verification in the ZKRPMSSD scheme are redesigned based on the \(\Sigma\) protocol and Pedersen commitments, effectively reducing the computational cost of the proof generation and verification process. Finally, typical n-ary decomposition and square decomposition zero-knowledge range proof construction schemes are taken for comparative analysis. Under 256-bit security and the same problem scale, experimental results indicate that ZKRPMSSD has advantages in proof and verification time costs.