OHSS: Optimizing Homomorphic Secret Sharing to Support Fast Matrix Multiplication

Homomorphic Secret Sharing (HSS) has evolved as a state-of-the-art methodology for achieving secure two-party computation, synthesizing the advantages of secret sharing and homomorphic encryption. This amalgamation ensures minimal computational and communicational overhead, making it particularly adept at arithmetic operations. However, HSS faces challenges in scalability and efficiency when confronted with extensive matrix operations, including both matrix-vector and matrix-matrix multiplications, which are fundamental in numerous privacy-preserving computations, notably within the realm of privacy-preserving machine learning. In this research, we introduce Optimized Homomorphic Secret Sharing (OHSS), a refined version of HSS, crafted to address these limitations. Our contributions include enhancements to the key generation phase alongside the development of efficient algorithms for matrix-vector multiplication and matrix-matrix multiplication. Comprehensive security evaluations and performance benchmarks demonstrate that OHSS not only fulfills stringent security criteria but also boasts superior efficiency.