Bivariate Polynomial Codes for Secure Distributed Matrix Multiplication

TL;DR

This paper introduces a secure extension of bivariate polynomial codes for distributed matrix multiplication, improving efficiency and reducing computation time in constrained settings by leveraging partial work from stragglers.

Contribution

It presents a novel secure bivariate polynomial coding scheme that enhances speed and efficiency in distributed matrix multiplication under communication and storage constraints.

Findings

Reduces average computation time compared to existing methods.

Effectively exploits partial work from stragglers.

Improves efficiency in communication and storage-constrained environments.

Abstract

We consider the problem of secure distributed matrix multiplication (SDMM). 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 SDMM compared to its competitors in the literature.