On the calculation of input and output for dynamic MDS matrices in diffusion layer of SPN block ciphers

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 to create dynamic MDS matrix for use have been proposed by many authors in the literature. In this paper, dynamic MDS matrices generated from direct exponent and scalar multiplication transformations are studied in the term of calculating effectively the outputs of the dynamic MDS matrices based on original MDS matrices when the inputs are known, as well as the calculating effectively the inputs of the dynamic MDS matrices based on original MDS matrices when the outputs are known. The process of encryption and decryption by dynamic MDS matrices is proven to be calculated more quickly by salvaging the original MDS matrices. In addition, a way for calculating quickly the direct exponent of MDS matrices based on a lookup table is presented.