Affiliations: [a] LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China. rabbitting@126.com | [b] School of Mathematics and Information, China West Normal University, Sichuan Nanchong, 637002, China | [c] LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China | [d] LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China. mzxu@pku.edu.cn
Correspondence:
[†]
Address for correspondence: LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China.
Note: [*] This work is supported by National Natural Science Foundation of China under Grants No. 61272499, No. 61472016.
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 introduce 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 efficiently. Furthermore, we present some 4 × 4 and 8 × 8 efficient MDS matrices of this class which are suitable for MDS diffusion layer. Compared with previous results, our construction provides better efficiency for the implementation of both the matrix and the its inverse matrix.
