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Computationally efficient matrix multiplication is a fundamental requirementin various fields, including and particularly in data analytics. To do so, thecomputation task of a large-scale matrix multiplication is typically outsourcedto multiple servers. However, due to data misusage at the servers, security istypically of concern. In this paper, we study the two-sided secure matrixmultiplication problem, where a user is interested in the matrix product$\boldsymbol{AB}$ of two finite field private matrices $\boldsymbol{A}$ and$\boldsymbol{B}$ from an information-theoretic perspective. In this problem,the user exploits the computational resources of $N$ servers to compute thematrix product, but simultaneously tries to conceal the private matrices fromthe servers. Our goal is twofold: (i) to maximize the communication rate, and,(ii) to minimize the effective number of server observations needed todetermine $\boldsymbol{AB}$, while preserving security, where we allow for upto $\ell\leq N$ servers to collude. To this end, we propose a general alignedsecret sharing scheme for which we optimize the matrix partition of matrices$\boldsymbol{A}$ and $\boldsymbol{B}$ in order to either optimize objective (i)or (ii) as a function of the system parameters (e.g., $N$ and $\ell$). Aproposed inductive approach gives us analytical, close-to-optimal solutions forboth (i) and (ii). With respect to (i), our scheme significantly outperformsthe existing scheme of Chang and Tandon in terms of (a) communication rate, (b)maximum tolerable number of colluding servers and (c) computational complexity.

Rate-Efficiency and Straggler-Robustness through Partition in Distributed Two-Sided Secure Matrix Computation