The preservation of good cryptographyic properties of MDS matrix under direct exponent transformation

Tran Thi Luong, Nguyen Ngoc Cuong, Luong The Dung

Abstract


 Maximum Distance Separable (MDS) code has been studied for a long time in the coding theory and has been applied widely in cryptography. The methods for transforming an MDS into other ones have been proposed by many authors in the literature. These methods are called MDS matrix transformations in order to generate different MDS matrices (dynamic MDS matrices) from an existing one. In this paper, some new results on the preservation of many good cryptographic properties of MDS matrices under direct exponent transformation are presented. These good cryptographic properties include MDS, involutory, symmetric, recursive (exponent of a companion matrix), the number of 1's and distinct elements in a matrix, circulant and circulant-like. In addition, these results are shown to have important applications in constructing dynamic diffusion layers for block ciphers. The strength of the ciphers against developing cryptanalytic techniques can be enhanced by the dynamic MDS diffusion layers.


Keywords


MDS matrix, dynamic MDS matrix, direct exponent matrix, cryptographic properties

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