يبقيياب

MDS matrices are one of the most important components in designing block ciphers. Based on the hardware terminologies, the acceptable speed of the implementation of MDS matrix and its inverse is one of the main features of MDS matrix for SPN structures. In this paper, a new type of binary block matrices called semi involutory is used such that the cost of implementation of these matrices and their inverses are equal. At first, by using binary linear functions over binary sparse matrices, a 44 semi involutory MDS matrix is proposed so that the cost of implementation of the proposed matrix is 68 bitwise XOR for 8 bit input. The structure of proposed 44 MDSmatrix and its inverse are based on the DSI structures, so they have suitable implementation from hardware point of view. Next, a 88 semi involutory MDS matrix is proposed by applying DSI structures such that the proposed 88 matrix is implemented with the 320 bitwise XOR for 8 bit input. The proposed 88 semi involutoryMDS matrix is the major result, since the best known result in the implementation of a 88 semi involutoryMDS matrix for 8 bit input, based on the heuristic algorithm, is 392 bitwise XOR while 320 bitwise XORwas obtained in this research. Moreover, the proposed 44 MDS matrix is implemented with 8m 4 XOR for m  4 bit input by applying suitable binary sparse matrices.