The Need for Alignment in Rate-Efficient Distributed Two-Sided Secure Matrix Computation

Computationally efficient matrix multiplication is a fundamental requirement in various fields, including and particularly in data analytics. To do so, the computation task of a large-scale matrix multiplication is typically outsourced to multiple servers. However, due to data misusage at the servers, security is typically of concern. In this paper, we study the two-sided secure matrix multiplication problem, where a user is interested in the matrix product AB of two finite field private matrices A and B. In this problem, the user exploits the computational resources of N servers to compute the matrix product, but simultaneously tries to conceal the private matrices from the servers. Our goal is to maximize the communication rate while preserving security, where we allow for up to l <= N servers to collude. To this end, we propose a general aligned secret sharing and matrix partition scheme for which we optimize the partition of matrices A and B as a function of N and. in order to maximize the achievable rate. A proposed inductive approach gives us an analytical close-to-optimal solution which significantly outperforms the existing scheme of Chang and Tandon in terms of (i) communication rate, (ii) maximum tolerable number of colluding servers and (iii) computational complexity.