Near Quadratic Matrix Multiplication Modulo Composites

TL;DR

This paper demonstrates a method for matrix multiplication modulo composite numbers using near-quadratic complexity, expanding the computational techniques beyond prime-power moduli.

Contribution

It introduces a novel approach to matrix multiplication modulo composite numbers with near-quadratic complexity, improving upon previous methods.

Findings

Matrix multiplication modulo composites can be performed with $n^{2+o(1)}$ multiplications.

The method extends the applicability of fast matrix multiplication algorithms to composite moduli.

Potential implications for computational number theory and cryptography.

Abstract

We show how one can use non-prime-power, composite moduli for computing representations of the product of two $n\times n$ matrices using only $n^{2+o(1)}$ multiplications.