Three new infinite families of bent functions

Research Paper
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Abstract

Bent 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.

Keywords

bent function Hadamard matrix Kasami function Gold-like function Niho exponent 

Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61502482, 61379139, 11526215), National Key Research Program of China (Grant No. 2016YFB0800401), and “Strategic Priority Research Program” of Chinese Academy of Sciences (Grant No. XDA06010701).

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Libo Wang
    • 1
    • 2
  • Baofeng Wu
    • 1
  • Zhuojun Liu
    • 2
  • Dongdai Lin
    • 1
  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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