Further properties of several classes of Boolean functions with optimum algebraic immunity

doi:10.1007/s10623-009-9284-0

CSpace

	Further properties of several classes of Boolean functions with optimum algebraic immunity
	Carlet, Claude 2,3,4; Zeng, Xiangyong 1,5; Li, Chunlei 1; Hu, Lei 6
	2009-09-01
发表期刊	DESIGNS CODES AND CRYPTOGRAPHY
ISSN	0925-1022
卷号	52 期号:3 页码:303-338
摘要	Based on a method proposed by the first author, several classes of balanced Boolean functions with optimum algebraic immunity are constructed, and they have nonlinearities significantly larger than the previously best known nonlinearity of functions with optimal algebraic immunity. By choosing suitable parameters, the constructed n-variable functions have nonlinearity 2(n-1) - (n-1 n/2 -1) + 2(n - 2 n/2 -2) / (n - 2) for even n >= 8 and 2(n-1) - (n - 1 n - 1/2) + Delta(n) for odd n, where Delta(n) is a function increasing rapidly with n. The algebraic degrees of some constructed functions are also discussed.
关键词	Boolean function Algebraic immunity Nonlinearity Balancedness Krawtchouk polynomial
DOI	10.1007/s10623-009-9284-0
语种	英语
资助项目	National Science Foundation of China (NSFC)[60603012] ; National Science Foundation of China (NSFC)[60773134] ; State Key Laboratory of Information Security ; National 863 Project of China[2006AA01Z416] ; National Basic Research (973) Program of China[2007CB311201]
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000266007400005
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/8323
专题	中国科学院数学与系统科学研究院
通讯作者	Zeng, Xiangyong
作者单位	1.Hubei Univ, Fac Math & Comp Sci, Wuhan 430062, Peoples R China 2.Univ Paris 08, Dept Math, LAGA, F-93526 St Denis, France 3.Univ Paris 13, Dept Math, LAGA, F-93526 St Denis, France 4.CNRS, F-93526 St Denis, France 5.Chinese Acad Sci, State Key Lab Informat Secur, Grad Sch, Beijing 100049, Peoples R China 6.Chinese Acad Sci, Key Lab Math Mechanizat, Inst Syst Sci, AMSS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Carlet, Claude,Zeng, Xiangyong,Li, Chunlei,et al. Further properties of several classes of Boolean functions with optimum algebraic immunity[J]. DESIGNS CODES AND CRYPTOGRAPHY,2009,52(3):303-338.
APA	Carlet, Claude,Zeng, Xiangyong,Li, Chunlei,&Hu, Lei.(2009).Further properties of several classes of Boolean functions with optimum algebraic immunity.DESIGNS CODES AND CRYPTOGRAPHY,52(3),303-338.
MLA	Carlet, Claude,et al."Further properties of several classes of Boolean functions with optimum algebraic immunity".DESIGNS CODES AND CRYPTOGRAPHY 52.3(2009):303-338.