Paper 2016/1131

On the Construction of the lightest Circulant MDS Matrices

Shiyi ZHANG and Yongjuan WANG and Yang GAO and Tao WANG

Abstract

4x4 MDS matrices with few XORs have a wide range of applications in plenty of mainstream lightweight ciphers. For 4x4 circulant MDS matrices over GL(4; F2), they have at least 12 XOR operations. In this paper, by traversing their structure characteristics, we firstly investigate the utterly construction and the numeration of the lightest circulant MDS matrices. Then the overall structure and the diagrams of these matrices are given. Finally we find the characteristics of permutation group in the lightest circulant MDS matrices above: they possess characteristics of symmetric group S4, and for a kind of particular MDS matrices, they can even form a Klein four-group in some ways.