Experimental methods for constructing MDS matrices of a special form

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 units 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 ($8 \times 8$)-matrices of a special form with many units 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. Tab. 7, bibliogr. 15.