Construction of Efficient MDS Matrices Based on Block Circulant Matrices for Lightweight Application

Abstract

Maximum distance separable (MDS) codes introduce MDS matrices which not only have applications in coding theory but also are of great importance in the design of block ciphers. It has received a great amount of attention. In this paper, we first i ntroduce a special generalization of circulant matrices called block circulants with circulant blocks, which can be used to construct MDS matrices. Then we investigate some interesting and useful properties of this class of matrices and prove that their inverse matrices can be implemented efficie ntly. Furthermore, we present some 4×4 and8×8 efficient MDS matrices of this class which are suitable for MD S diffusion layer. Compared with previous results, our construction provides better ef ficiency for the implementation of both the matrix and the its inverse matrix.