On The Number of Different Entries in Involutory MDS Matrices over Finite Fields of Characteristic Two

TL;DR

This paper studies involutory MDS matrices over finite fields of characteristic two, focusing on the minimum number of distinct entries for matrices of small order, revealing lower bounds on diversity of elements.

Contribution

It provides new bounds on the number of different entries in involutory MDS matrices of orders 3 and 4 over characteristic two fields.

Findings

At least three different elements in order 3 matrices

At least four different elements in order 4 matrices

Lower bounds on element diversity in involutory MDS matrices

Abstract

Two of many criteria of a good MDS matrix are being involutory and having few different elements. This paper investigates the number of different entries in an involutory MDS matrices of order 1, 2, 3, and 4 over finite fields of characteristic two. There are at least three and four different elements in an involutory MDS matrices with, respectively, order three and four, over finite fields of characteristic two.