GAPN多项式函数的构造  

Constructions of GAPN Polynomial Functions

作　　者：庞婷婷 徐运阁 陈智军 PANG Tingting;XU Yunge;CHEN Zhijun(Faculty of Mathematics&Statistics,Hubei Key Laboratory of Applied Mathematics,Hubei University,Wuhan 430062;School of Computer Science and Information Engineering,Hubei University,Wuhan 430062)

机构地区：[1]湖北大学数学与统计学学院,应用数学湖北省重点实验室,武汉430062 [2]湖北大学计算机与信息工程学院,武汉430062

出　　处：《系统科学与数学》2019年第9期1500-1512,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61761166010)资助课题

摘　　要：提出了一类GAPN单项式和一类GAPN二项式,推广了以前的两类构造;还提出了一种由已知GAPN函数构造大量GAPN多项式函数的方法.文章的构造能生成扩展仿射不等价于所有已知GAPN函数的GAPN函数,此外还对GAPN函数的差分性质进行了初步探讨.In this paper,we propose a class of GAPN monomials and a class of GAPN binomials,generalizing two previous constructions.A new method is proposed to construct a large number of GAPN polynomials from known GAPN functions.The constructions proposed in this paper can generate new GAPN functions extended affine inequivalent to all known GAPN functions.In addition,the differential properties of GAPN functions are also discussed.

关 键 词：APN函数 GAPN函数 扩展仿射等价 差分均匀度 

分 类 号：G63[文化科学—教育学]