DIRECT EXPONENT AND SCALAR MULTIPLICATION TRANSFORMATIONS OF MDS MATRICES: SOME GOOD CRYPTOGRAPHIC RESULTS FOR DYNAMIC DIFFUSION LAYERS OF BLOCK CIPHERS

Abstract

Abstract: MDS (Maximum Distance Separable) matrices have an important role in the design of block ciphers and hash functions. The methods for transforming an MDS matrix into other ones have been proposed by many authors in the literature. In this paper, some new results about direct exponent and scalar multiplication transformations are given including the preservation of good cryptographic properties (the coefficient of fixed points and involutory property) of MDS matrices and other important cryptographic properties obtained from studying equivalence relations based on these transformations. An estimation of the number of MDS matrices over is also presented. In addition, these results are shown to be an important theoretical basis for building efficient dynamic diffusion layer algorithms for block ciphers.