一类Bent函数的再证明和新构造  

New Proof of a Class of Bent Functions and New Construction

作　　者：马陵勇 廉玉忠[1] 卓泽朋[2] MA Lingyong;LIAN Yuzhong;ZHUO Zepeng(Department of Computer and Information Sciences,City College of Dongguan University of Technology,Dongguan 523106,China;School of Mathematical Science,Huaibei Nornal University,Huaibei 235000,China)

机构地区：[1]东莞理工学院城市学院计算机与信息学院,广东东莞523106 [2]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《东莞理工学院学报》2021年第1期1-5,共5页Journal of Dongguan University of Technology

基　　金：东莞市社会科技发展计划(一般)项目(2019507151569)。

摘　　要：Bent函数作为非线性最优的布尔函数在对称密码系统的设计中有着诸多应用。利用组合布尔函数方法给出了一类间接构造的Bent函数的新证明,所给方法证明过程较为简便、计算量小。其次,利用新的构造方法得到了具有n+m+2个变元的Bent函数,并在特殊取值下分析了所得构造与已有间接构造之间的关系。As a nonlinear optimal Boolean functions,Bent function has many applications in the design of symmetric cryptography systems.In this paper,a new proof of a class of indirectly constructed Bent functions is presented by using the method of combined Boolean function.The method is simple and the calculation is small.In addition,The Bent function with n+m+2 variables is obtained by using new method,and the relationship between the obtained structure and the existing indirect structure is analyzed under the special value.

关 键 词：组合布尔函数 BENT函数 拉格朗日插值公式 WALSH变换 对偶性 

分 类 号：TP918.1[自动化与计算机技术]