Bivariate Polynomial Codes for Secure Distributed Matrix Multiplication

Abstract

We consider the problem of secure distributed matrix multiplication. Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against workers and boosting the computation speed by efficiently mitigating stragglers. In this work, we present a non-direct secure extension of the recently introduced bivariate polynomial codes. Bivariate polynomial codes have been shown to be able to further speed up distributed matrix multiplication by exploiting the partial work done by the stragglers rather than completely ignoring them while reducing the upload communication cost and/or the workers' storage's capacity needs. We show that, especially for upload communication or storage constrained settings, the proposed approach reduces the average computation time of secure distributed matrix multiplication compared to its competitors in the literature. I. INTRODUCTIONMatrix multiplication is a fundamental building block of many applications in signal processing and machine learning. For some applications, especially those involving massive matrices and stringent latency requirements, matrix multiplication in a single computer is infeasible, and distributed solutions need to be adopted. In such scenarios, the full multiplication task is first partitioned into smaller sub-tasks, which are then distributed across dedicated workers.