A systematic construction approach for all 4×4 involutory MDS matrices

Article Type

Research Article

Publication Title

Journal of Applied Mathematics and Computing

Abstract

Maximum distance separable (MDS) matrices play a crucial role not only in coding theory but also in the design of block ciphers and hash functions. Of particular interest are involutory MDS matrices, which facilitate the use of a single circuit for both encryption and decryption in hardware implementations. In this article, we present several characterizations of involutory MDS matrices of even order. Additionally, we introduce a new matrix form for obtaining all involutory MDS matrices of even order and compare it with other matrix forms available in the literature. We then propose a technique to systematically construct all 4×4 involutory MDS matrices over a finite field F2m. This method significantly reduces the search space by focusing on involutory MDS class representative matrices, leading to the generation of all such matrices within a substantially smaller set compared to considering all 4×4 involutory matrices. Specifically, our approach involves searching for these representative matrices within a set of cardinality (2m-1)5. Through this method, we provide an explicit enumeration of the total number of 4×4 involutory MDS matrices over F2m for m=3,4,…,8.

First Page

4677

Last Page

4697

DOI

10.1007/s12190-024-02142-z

Publication Date

10-1-2024

Comments

Open Access; Green Open Access

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