The lightest 4×4 MDS matrices over GL(4, F2)

作     者：Jian BAI Ting LI Yao SUN Dingkang WANG Dongdai LIN 

作者机构：Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of Sciences School of Cyber Security University of Chinese Academy of Sciences 

出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))

年 卷 期：2018年第61卷第11期

页      面：238-240页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No. 11371356) 

主　　题：MDS matrices over GL F2 The lightest 4 GL 

摘      要：Dear editor,We present an algorithm for searching MDS matrices without any prior structures. We find all the lightest 4×4 MDS matrices over GL(4, F2)that have 10 XOR-counts, including the Toeplitz MDS matrices presented in [1]. We classify all these lightest MDS matrices to 3 types, and give some sufficient and necessary conditions for these3 types matrices for being MDS matrices. Using these conditions, we directly construct more4×4 MDS matrices over GL(m, F2) with 10 XORcounts for m4.