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

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	The lightest 4×4 MDS matrices over GL(4,F2)
Alternative Title	The lightest 4×4 MDS matrices over GL（4, F2）
	Bai Jian 1; Li Ting 2; Sun Yao 2; Wang Dingkang 1; Lin Dongdai 2
	2018
Source Publication	中国科学:信息科学(英文版)
ISSN	1674-733X
Volume	61.0 Issue:011 Pages:119102-1
Abstract	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.
Other Abstract	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 these 3 types matrices for being MDS matrices. Using these conditions, we directly construct more 4×4 MDS matrices over GL(m, F_2) with 10 XORcounts for m > 4.
Keyword	MDS Toeplitz editor
Indexed By	CSCD
Language	中文
CSCD ID	CSCD:6380481
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/55554
Collection	中国科学院数学与系统科学研究院
Affiliation	1.中国科学院数学与系统科学研究院 2.中国科学院信息工程研究所
Recommended Citation GB/T 7714	Bai Jian,Li Ting,Sun Yao,et al. The lightest 4×4 MDS matrices over GL(4,F2)[J]. 中国科学:信息科学(英文版),2018,61.0(011):119102-1.
APA	Bai Jian,Li Ting,Sun Yao,Wang Dingkang,&Lin Dongdai.(2018).The lightest 4×4 MDS matrices over GL(4,F2).中国科学:信息科学(英文版),61.0(011),119102-1.
MLA	Bai Jian,et al."The lightest 4×4 MDS matrices over GL(4,F2)".中国科学:信息科学(英文版) 61.0.011(2018):119102-1.

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