一类多项式型的超bent函数  

On Hyper-bent Functions in Polynomial Forms

作　　者：周俊超 ZHOU Junchao(Faculty of Mathematics and Statistics,Hubei Engineering University,Xiaogan,Hubei,432000,P.R.China)

机构地区：[1]湖北工程学院数学与统计学院,孝感湖北432000

出　　处：《数学进展》2021年第3期451-470,共20页Advances in Mathematics（China）

基　　金：Supported by Science Research Project of Hubei Provincial Department of Education(No.B2020150);Natural Science Project of Xiaogan City(No.XGKJ2020010045);Technology Creative Project of Excellent Middle and Young Team of Hubei Province(No.T201920)。

摘　　要：Bent函数是一类著名的布尔函数,它们具有偶数个变元和最大的非线性度,并且在密码、编码和序列设计方面有着广泛的应用.超bent函数是bent函数的一个重要的子类,并且具有最大的代数次数.本文提出了一类多项式型的超bent函数,利用与Dickson多项式相关的完全指数和、Kloosterman和以及Weil和刻画了这类函数的超bent性质.Bent functions are famous Boolean functions in an even number of variables with the highest possible nonlinearity.They have wide applications in cryptography,coding theory,and sequence design.Hyper-bent functions are an important subclass of bent functions with optimal algebraic degree.In this paper,a class of hyper-bent functions in polynomial forms is proposed.The hyper-bentness of these functions is characterized by complete exponential sums related to Dickson polynomials,Kloosterman sums and Weil sums.

关 键 词：超bent函数 指数和 KLOOSTERMAN和 Weil和 

分 类 号：O153.4[理学—数学] O157.4[理学—基础数学]