A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity

doi:10.1007/s10623-010-9413-9

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	A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity
	Tu, Ziran 1,2; Deng, Yingpu1,3
	2011-07-01
发表期刊	DESIGNS CODES AND CRYPTOGRAPHY
ISSN	0925-1022
卷号	60 期号:1 页码:1-14
摘要	In this paper, a combinatorial conjecture about binary strings is proposed. Under the assumption that the proposed conjecture is correct, two classes of Boolean functions with optimal algebraic immunity can be obtained. The functions in first class are bent, and then it can be concluded that the algebraic immunity of bent functions can take all possible values except one. The functions in the second class are balanced, and they have optimal algebraic degree and the best nonlinearity up to now.
关键词	Boolean function Algebraic immunity Bent function Balancedness Nonlinearity Algebraic degree
DOI	10.1007/s10623-010-9413-9
语种	英语
资助项目	NNSF of China[60821002] ; NNSF of China[10971250]
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000290172100001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12185
专题	系统科学研究所
通讯作者	Deng, Yingpu
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Henan Univ Sci & Technol, Fac Sci, Luoyang 471003, Peoples R China 3.Chinese Acad Sci, Grad Univ, State Key Lab Informat Secur, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Tu, Ziran,Deng, Yingpu. A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity[J]. DESIGNS CODES AND CRYPTOGRAPHY,2011,60(1):1-14.
APA	Tu, Ziran,&Deng, Yingpu.(2011).A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity.DESIGNS CODES AND CRYPTOGRAPHY,60(1),1-14.
MLA	Tu, Ziran,et al."A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity".DESIGNS CODES AND CRYPTOGRAPHY 60.1(2011):1-14.