Private and Secure Distributed Matrix Multiplication with Flexible Communication Load

TL;DR

This paper introduces secure and private distributed matrix multiplication codes that optimize the trade-off between recovery threshold and communication load while ensuring data secrecy and privacy in cloud computing environments.

Contribution

It proposes the secure generalized PolyDot (SGPD) codes that extend existing codes to include security against collusion and privacy of data identity, with flexible trade-offs.

Findings

SGPD codes achieve perfect secrecy with flexible load-threshold trade-offs.

The codes support collusion resistance up to a specified number of workers.

A variant of generalized PolyDot codes guarantees data secrecy and identity privacy without collusion.

Abstract

Large matrix multiplications are central to large-scale machine learning applications. These operations are often carried out on a distributed computing platform with a master server and multiple workers in the cloud operating in parallel. For such distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay, yielding a trade-off between recovery threshold, i.e., the number of workers required to recover the matrix product, and communication load, i.e., the total amount of data to be downloaded from the workers. In this paper, in addition to exact recovery requirements, we impose security and privacy constraints on the data matrices, and study the recovery threshold as a function of the communication load. We first assume that both matrices contain private information and that workers can collude to eavesdrop on the content of these data matrices. For this problem, we introduce a novel class of secure codes, referred to as secure generalized PolyDot (SGPD) codes, that generalize state-of-the-art non-secure codes for matrix multiplication. SGPD codes allow a flexible trade-off between recovery threshold and communication load for a fixed maximum number of colluding workers while providing perfect secrecy for the two data matrices. We then study a connection between secure matrix multiplication and private information retrieval. We specifically assume that one of the data matrices is taken from a public set known to all the workers. In this setup, the identity of the matrix of interest should be kept private from the workers. For this model, we present a variant of generalized PolyDot codes that can guarantee both secrecy of one matrix and privacy for the identity of the other matrix for the case of no colluding servers.