# GASP Codes for Secure Distributed Matrix Multiplication

## TL;DR

This paper introduces GASP Codes, a new class of polynomial codes for secure distributed matrix multiplication, which outperform previous codes in download efficiency by leveraging combinatorial structures called degree tables.

## Contribution

The paper develops GASP Codes based on arithmetic progressions and degree tables, providing a novel approach that improves download rate in secure distributed matrix multiplication.

## Key findings

- GASP Codes outperform previous polynomial codes in download rate.
- GASP Codes are based on arithmetic progressions and degree tables.
- The codes enhance efficiency in secure distributed matrix multiplication.

## Abstract

We consider the problem of secure distributed matrix multiplication (SDMM) in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We construct polynomial codes for SDMM by studying a combinatorial problem on a special type of addition table, which we call the degree table. The codes are based on arithmetic progressions, and are thus named GASP (Gap Additive Secure Polynomial) Codes. GASP Codes are shown to outperform all previously known polynomial codes for secure distributed matrix multiplication in terms of download rate.