zkMatrix: Batched Short Proof for Committed Matrix Multiplication

Mingshu Cong, Tsz Hon Yuen, Siu-Ming Yiu

Abstract: Matrix multiplication is a common operation in applications like machine learning and data analytics. To demonstrate the correctness of such an operation in a privacy-preserving manner, we propose zkMatrix, a zero-knowledge proof for the multiplication of committed matrices. Among the succinct non-interactive zero-knowledge protocols that have an O(log n) transcript size and O(log n) verifier time, zkMatrix stands out as the first to achieve O(n2) prover time and O(n2) RAM usage for multiplying two n X n matrices. Significantly, zkMatrix distinguishes itself as the first zk-SNARK protocol specifically designed for matrix multiplication. By batching multiple proofs together, each additional matrix multiplication only necessitates O(n) group operations in prover time.