基于迹函数的negabent函数构造  

Construction of Negabent Function Based on Trace Function over Finite Field

作　　者：赵海霞 李文宇 韦永壮 ZHAO Haixia;LI Wenyu;WEI Yongzhuang(School of Mathematics and Computing Science,Guangxi University Key Laboratory of Data Analysis and Calculation,Guilin University of Electronic Technology,Guilin 541002,China;Center for Applied Mathematics of Guangxi(GUET),Guilin 541002,China;Guangxi Key Laboratory of Cryptology and Information Security,Guilin 541002,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西高校数据分析与计算重点实验室,桂林541002 [2]广西应用数学中心,桂林541002 [3]广西密码学与信息安全重点实验室,桂林541002

出　　处：《电子与信息学报》2024年第1期335-343,共9页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(62162016);广西自然科学基金(2019GXNSFGA245004)。

摘　　要：Negabent函数是一种具有最优自相关性、较高非线性度的布尔函数,在密码学、编码理论及组合设计中都有着广泛的应用。该文基于有限域上的迹函数,将其与置换多项式相结合,提出两种构造negabent函数的方法。所构造的两类negabent函数均具备Tr_(1)^(k)(λx^(2^(k)+1))+Tr_(1)^(n)(ux)Tr_(1)^(n)(vx)+Tr_(1)^(n)(mx)Tr_(1)^(n)(dx)形式:构造方法1通过调整λ,u,v,m中的3个参数来获得negabent函数,特别地,当λ≠1时,能得到(2^(n-1)-2)(2^(n)-1)(2^(n)-4)个negabent函数;构造方法2通过调整λ,μ,v,m,d中的4个参数来获得negabent函数,特别地,当λ≠1时,至少能够得到2^(n-1)[(2^(n-1)-2)(2^(n-1)-3)+2^(n-1)-4]个negabent函数。Negabent function is a Boolean function with optimal autocorrelation and high nonlinearity,which has been widely used in cryptography,coding theory and combination design.In this paper,by combining trace function on a finite field with permutation polynomials,two methods for constructing negabent functions are proposed.Both the two kinds of constructed negabent functions take on such form:Tr_(1)^(k)(λx^(2^(k)+1))+Tr_(1)^(n)(ux)Tr_(1)^(n)(vx)+Tr_(1)^(n)(mx)Tr_(1)^(n)(dx).In the first construction method,negabent functions can be obtained by adjusting the three parameters inλ,u,v,m.In particular,whenλ≠1,(2^(n-1)-2)(2^(n)-1)(2^(n)-4) negabent functions can be obtained.In the second construction method,negabent functions can be obtained by adjusting the four parameters inλ,u,v,m,d.In particular,whenλ≠1,at least 2^(n-1)[(2^(n-1)-2)(2^(n-1)-3)+2^(n-1)-4] negabent functions can be obtained.

关 键 词：Negabent函数 迹函数 置换多项式 

分 类 号：TN918.2[电子电信—通信与信息系统]