Secure Distributed Gram Matrix Multiplication

TL;DR

This paper introduces SDGMM, a novel scheme for securely computing Gram matrices in distributed settings, reducing communication overhead compared to traditional SDMM methods, with applications in linear regression.

Contribution

The paper proposes SDGMM, a new method that efficiently computes Gram matrices securely in distributed environments, avoiding redundant encoding and reducing communication costs.

Findings

SDGMM reduces communication overhead in secure Gram matrix computation.

The scheme enables efficient privacy-preserving linear regression.

Experimental results demonstrate improved performance over existing methods.

Abstract

The Gram matrix of a matrix $A$ is defined as $AA^T$ (or $A^T\!A$). Computing the Gram matrix is an important operation in many applications, such as linear regression with the least squares method, where the explicit solution formula includes the Gram matrix of the data matrix. Secure distributed matrix multiplication (SDMM) can be used to compute the product of two matrices using the help of worker servers. If a Gram matrix were computed using SDMM, the data matrix would need to be encoded twice, which causes an unnecessary overhead in the communication cost. We propose a new scheme for this purpose called secure distributed Gram matrix multiplication (SDGMM). It can leverage the advantages of computing a Gram matrix instead of a regular matrix product.