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Three new infinite families of bent functions
Wang, Libo1,2; Wu, Baofeng1; Liu, Zhuojun2; Lin, Dongdai1
AbstractBent functions are maximally nonlinear Boolean functions with an even number of variables. They are closely related to some interesting combinatorial objects and also have important applications in coding, cryptography and sequence design. In this paper, we firstly give a necessary and sufficient condition for a type of Boolean functions, which obtained by adding the product of finitely many linear functions to given bent functions, to be bent. In the case that these known bent functions are chosen to be Kasami functions, Gold- like functions and functions with Niho exponents, respectively, three new explicit infinite families of bent functions are obtained. Computer experiments show that the proposed familes also contain such bent functions attaining optimal algebraic degree.
Keywordbent function Hadamard matrix Kasami function Gold-like function Niho exponent
Funding ProjectNational Natural Science Foundation of China[61502482] ; National Natural Science Foundation of China[61379139] ; National Natural Science Foundation of China[11526215] ; National Key Research Program of China[2016YFB0800401] ; "Strategic Priority Research Program" of Chinese Academy of Sciences[XDA06010701]
WOS Research AreaComputer Science
WOS SubjectComputer Science, Information Systems
WOS IDWOS:000417486900003
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Document Type期刊论文
Corresponding AuthorWu, Baofeng
Affiliation1.Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mech, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Wang, Libo,Wu, Baofeng,Liu, Zhuojun,et al. Three new infinite families of bent functions[J]. SCIENCE CHINA-INFORMATION SCIENCES,2018,61(3):14.
APA Wang, Libo,Wu, Baofeng,Liu, Zhuojun,&Lin, Dongdai.(2018).Three new infinite families of bent functions.SCIENCE CHINA-INFORMATION SCIENCES,61(3),14.
MLA Wang, Libo,et al."Three new infinite families of bent functions".SCIENCE CHINA-INFORMATION SCIENCES 61.3(2018):14.
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