Construction of a set of circulant matrix submatrices for faster MDS matrix verification

TL;DR

This paper introduces an efficient algorithm to verify if a circulant matrix is MDS by constructing a smaller subset of submatrices, significantly reducing computational complexity compared to traditional methods.

Contribution

It presents a novel algorithm that constructs a reduced set of submatrices for MDS verification specifically tailored to circulant matrices, improving efficiency.

Findings

Reduces the size of the testing set by approximately two matrix orders.

Provides a faster verification method for circulant MDS matrices.

Demonstrates the algorithm's effectiveness in reducing computational complexity.

Abstract

The present paper focuses on the construction of a set of submatrices of a circulant matrix such that it is a smaller set to verify that the circulant matrix is an MDS (maximum distance separable) one, comparing to the complete set of square submatrices needed in general case. The general MDS verification method requires to test for singular submatrices: if at least one square submatrix is singular the matrix is not MDS. However, the complexity of the general method dramatically increases for matrices of a greater dimension. We develop an algorithm that constructs a smaller subset of submatrices thanks to a simple structure of circulant matrices. The algorithm proposed in the paper reduces the size of the testing set by approximately two matrix orders.