Lattice-Based Zero-Knowledge Proofs for Blockchain Confidential Transactions

We propose new zero-knowledge proofs for efficient and postquantum ring confidential transaction (RingCT) protocols based on lattice assumptions in Blockchain systems. First, we introduce an inner-product based linear equation satisfiability approach for balance proofs with a wide range (e.g., 64-bit precision). Unlike existing bal-ance proofs (MatRiCT and MatRiCT+) that require additional proofs for some “corrector values”, our approach avoids the corrector values for better efficiency. Furthermore, we design a ring signature scheme to efficiently hide a user’s identity in large anonymity sets. Different from existing approaches that adopt a one-out-of-many proof (MatRiCT and MatRiCT+), we show that a linear sum proof suffices in ring signa-tures, which could avoid the costly binary proof part. We further use the idea of “unbalanced” relations to build a logarithmic-size ring signa-ture scheme. Finally, we show how to adopt these techniques in RingCT protocols and implement a prototype to compare the performance with existing approaches. The results show our solutions can reduce up to 50% 50% and 20% 20% proof size, 30% 30% and 20% 20% proving time, 20% 20% and 20% 20% veri-fication time of MatRiCT and MatRiCT+, respectively. We also believe our techniques are of independent interest for other applications and are applicable in a generic setting.