Secure and Efficient Distributed Matrix Multiplication Based on Polynomial Coding

Matrix multiplication is a fundamental computational operation widely used in various engineering applications. To accelerate large-scale matrix multiplication, computing tasks are commonly outsourced to distributed servers or cloud platforms. However, the involvement of untrusted nodes brings significant security risks. To address these challenges, this paper proposes a distributed computing framework based on polynomial coding theory. Specifically, input matrices are divided into multiple sub-blocks and encoded using carefully designed polynomials evaluated at distinct points, enabling reliable reconstruction of the final result with responses from a minimal number of servers. We first present the PEP protocol, which efficiently supports distributed computation of high-dimensional matrices. Building on PEP, we further propose the SDMC protocol by introducing random perturbation matrices, achieving stronger information-theoretic security and enhanced resistance to colluding servers. Experimental results show that the proposed framework achieves an order-of-magnitude enhancement in scalability and performance relative to conventional methods, and consistently maintains an optimal trade-off among computational, communication, and security overheads.