The solution to an open problem on the bentness of Mesnager's functions

Tang，Chunming1; Han，Peng2; Wang，Qi3; Zhang，Jun4; Qi，Yanfeng5

2023-06-01

10.1016/j.ffa.2023.102170

FINITE FIELDS AND THEIR APPLICATIONS   Impact Factor & Quartile

1071-5797

1090-2465

Let n=2m. In the present paper, we study the binomial Boolean functions of the form [Formula presented] where m is an even positive integer, a∈F and b∈F. We show that f is a bent function if the Kloosterman sum [Formula presented] equals 4, thus settling an open problem of Mesnager. The proof employs tools including computing Walsh coefficients of Boolean functions via multiplicative characters, divisibility properties of Gauss sums, and graph theory.

Bent function Boolean function Directed graph Gauss sum Walsh transform

English

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MATHEMATICS

2-s2.0-85148331811

Scopus

1.School of Information Science and Technology,Southwest Jiaotong University,Chengdu,610031,China
2.School of Mathematics and Information,China West Normal University,Nanchong,Sichuan,637002,China
3.Department of Computer Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China
4.School of Mathematical Sciences,Capital Normal University,Beijing,100048,China
5.School of Science,Hangzhou Dianzi University,Hangzhou,Zhejiang,310018,China

Tang，Chunming,Han，Peng,Wang，Qi,et al. The solution to an open problem on the bentness of Mesnager's functions[J]. FINITE FIELDS AND THEIR APPLICATIONS,2023,88.

Tang，Chunming,Han，Peng,Wang，Qi,Zhang，Jun,&Qi，Yanfeng.(2023).The solution to an open problem on the bentness of Mesnager's functions.FINITE FIELDS AND THEIR APPLICATIONS,88.

Tang，Chunming,et al."The solution to an open problem on the bentness of Mesnager's functions".FINITE FIELDS AND THEIR APPLICATIONS 88(2023).