Root of Unity for Secure Distributed Matrix Multiplication: Grid Partition Case

TL;DR

This paper introduces a new secure distributed matrix multiplication scheme using grid partitioning, significantly reducing upload costs while maintaining optimal communication load in extreme cases.

Contribution

It proposes a novel grid partition-based scheme for SDMM that improves upload efficiency and generalizes existing partition strategies.

Findings

Achieves lower upload cost than previous methods

Matches best-known communication load in extreme partition cases

Provides a flexible grid partition approach for SDMM

Abstract

We consider the problem of secure distributed matrix multiplication (SDMM), where a user has two matrices and wishes to compute their product with the help of $N$ honest but curious servers under the security constraint that any information about either $A$ or $B$ is not leaked to any server. This paper presents a \emph{new scheme} that considers a grid product partition for matrices $A$ and $B$, which achieves an upload cost significantly lower than the existing results in the literature. Since the grid partition is a general partition that incorporates the inner and outer ones, it turns out that the communication load of the proposed scheme matches the best-known protocols for those extreme cases.