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On Quadratic Vectorial bent functions in Trace Forms

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Chinese Journal of Electronics 2020年第5期29卷 865-872页

作者： ZHOU Junchao XU Yunge ZHANG Wanshan Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied Mathematics Hubei University School of Computer and Information Engineering Hubei University

By permutation behavior of certain linearized polynomials,the bentness of quadratic vectorial bent functions of the form ■ is investigated,where n=2 kt and m kt with k,t being positive *** numerical results show that... 详细信息

关键词： bent function Linearized permutation polynomial Extended affine equivalence

Three new infinite families of bent functions

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Science China(Information Sciences) 2018年第3期61卷 43-56页

作者： Libo WANG Baofeng WU Zhuojun LIU Dongdai LIN State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of Sciences Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of Sciences

bent functions are maximally nonlinear Boolean functions with an even number of *** 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.

关键词： bent function Hadamard matrix Kasami function Gold-like function Niho exponent

Cascaded Construction of Semi-bent and bent functions

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Journal of Southwest Jiaotong University(English Edition) 2009年第1期17卷 86-89页

作者：王健鹏吴晓雄余新华 School of Mathematics Southwest Jiaotong University Office of Admission and Career Southwest Jiaotong University No.30 Research Institute of China Electronics

Based on the theory of quadratic forms over finite fields, a new construction of semi-bent and bent functions is presented. The proposed construction has a cascaded characteristic. Some previously known constructions ... 详细信息

关键词： bent function Semi-bent function Quadratic form

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Boolean functions with Multiple-Valued Walsh Spectra

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Chinese Journal of Electronics 2019年第6期28卷 1165-1169页

作者： SUN Tianfeng HU Bin Information Engineering University

Compared with the method by Zhang in 2017, an extended one for constructing Boolean functions with multiple-valued Walsh spectra is given, which is derived from a bent function by complementing the values at some points. Based on which, new classes of Boolean functions with four-valued and five-valued Walsh spectra are presented, and some of their cryptographic properties are studied.

关键词： Boolean function bent function Multiple-valued Walsh spectra Algebraic degree