On Lightweight 4x4 MDS Matrices over Binary Field Extensions

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International Journal of Information Security Science
Volume:9 Issue:2
On Lightweight 4x4 MDS Matrices over Binary Field Extensions

On Lightweight 4x4 MDS Matrices over Binary Field Extensions

Authors : Fatma BUYUKSARACOGLU SAKALLİ, Ozlem AYDİN, Gokhan TUNCAY, Meltem Kurt PEHLİVANOGLU, Gulsum Gozde GUZEL, Muharrem Tolga SAKALLİ

Pages : 94-103

View : 51 | Download : 8

Publication Date : 2020-06-01

Article Type : Research Paper

Abstract :Maximum Distance Separable MDS matrices are used as the main part of diffusion layers in block ciphers and hash functions. MDS matrices derived from MDS codes have the maximum differential and linear branch number, which provide resistance against some well-known attacks like differential and linear cryptanalysis together with the use of a nonlinear layer e.g. S-boxes in a round function of a block cipher. In this paper, we introduce generic methods to generate lightweight $k \times k$ involutory/non-involutory MDS matrices over $\F_{2^m}$ and present the lightest involutory/non-involutory $4 \times 4$ MDS matrices over $\F_{2^4}$ to the best of our knowledge by considering XOR count metric, which is defined to estimate hardware implementation cost. Also, the results are obtained by using a global optimization technique, namely Boyar-Peralta algorithm.
Keywords : MDS matrices, diffusion layer, symmetric key cryptography

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