Experimental Methods for Constructing MDS Matrices of a Special Form

Abstract

MDS matrices are widely used as a diffusion primitive in the construction of block type encryption algorithms and hash functions (such as AES and GOST 34.12-2015). The matrices with the maximum number of 1s and minimum number of different elements are important for more efficient realizations of the matrix-vector multiplication. The article presents a new method for the MDS testing of matrices over finite fields and shows its application to the (8 × 8)-matrices of a special form with many 1s and few different elements; these matrices were introduced by Junod and Vaudenay. For the proposed method we obtain some theoretical and experimental estimates of effectiveness. Moreover, the article comprises a list of some MDS matrices of the above-indicated type.