Field Trace Polynomial Codes for Secure Distributed Matrix Multiplication

TL;DR

This paper introduces field trace polynomial codes that improve communication efficiency in secure distributed matrix multiplication by leveraging field trace techniques, challenging the assumption that more servers always increase communication costs.

Contribution

It presents a novel family of codes that utilize field trace methods, outperforming existing codes in certain regimes for secure distributed matrix multiplication.

Findings

Field trace polynomial codes outperform existing codes in specific regimes.

Using field traces reduces communication costs compared to downloading entire computations.

The approach adapts Reed-Solomon code repair techniques to matrix multiplication.

Abstract

We consider the problem of communication efficient secure distributed matrix multiplication. The previous literature has focused on reducing the number of servers as a proxy for minimizing communication costs. The intuition being, that the more servers used, the higher the communication cost. We show that this is not the case. Our central technique relies on adapting results from the literature on repairing Reed-Solomon codes where instead of downloading the whole of the computing task, a user downloads field traces of these computations. We present field trace polynomial codes, a family of codes, that explore this technique and characterize regimes for which our codes outperform the existing codes in the literature.