Secure Distributed Matrix Multiplication with Precomputation

TL;DR

This paper introduces a secure distributed matrix multiplication method leveraging precomputation, reducing complexity and increasing collusion tolerance compared to existing schemes.

Contribution

It presents polynomial schemes for outer product partitioning that utilize precomputation to enhance security and efficiency in distributed matrix multiplication.

Findings

Precomputation reduces time complexity for fixed collusion percentages.

The scheme tolerates any collusion percentage below 100%.

Precomputation increases collusion tolerance from 50% to nearly 100%.

Abstract

We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show how to construct polynomial schemes for the outer product partitioning which take advantage of the user's ability to precompute, and provide bounds for our technique. We show that precomputation allows for a reduction in the order of the time complexity for the cases where the number of colluding servers is a fixed percentage of the number of servers. Furthermore, with precomputation, any percentage (less than 100%) of collusions can be tolerated, compared to the upper limit of 50% for the case without precomputation.