# Distributed and Private Coded Matrix Computation with Flexible Communication Load

## TL;DR

This paper introduces secure generalized PolyDot codes for distributed matrix multiplication that balance recovery threshold, communication load, and security against colluding workers, enhancing privacy in large-scale machine learning tasks.

## Contribution

It proposes a novel class of secure coding schemes extending previous non-secure codes, enabling flexible trade-offs between recovery, communication, and security constraints.

## Key findings

- Achieves secure matrix multiplication with collusion resistance.
- Balances communication load and recovery threshold.
- Extends state-of-the-art secure coding techniques.

## Abstract

Tensor operations, such as matrix multiplication, are central to large-scale machine learning applications. For user-driven tasks these operations can be carried out on a distributed computing platform with a master server at the user side and multiple workers in the cloud operating in parallel. For 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 and communication load. In this paper we impose an additional security constraint on the data matrices and assume that workers can collude to eavesdrop on the content of these data matrices. Specifically, we introduce a novel class of secure codes, referred to as secure generalized PolyDot codes, that generalizes previously published non-secure versions of these codes for matrix multiplication. These codes extend the state-of-the-art by allowing a flexible trade-off between recovery threshold and communication load for a fixed maximum number of colluding workers.