Building 8×8 Effective Block Circulant MDS Matrices by Utilizing Hadamard Matrices and Circulant Matrices

The MDS matrix is widely used to design the linear layer of modern block ciphers. A selected MDS matrix needs to meet the safety and efficient installation criteria. In this paper, we propose a type of effective block circulant MDS matrices by utilizing Hadamard matrices and circulant matrices. Based on the special structure of this matrix form, we have stated and proven some theoretical results. Then, we select a number of 8×8 effective block circulant MDS matrices. In addition, we also estimate the installation resources required for these recommendations and make comparisons with previous publications. As a result, we can efficiently implement these MDS matrices for encryption and their inverse matrices.