两类面向算术化幂函数的差分性质  

Differential properties of two classes of arithmetization-oriented power mappings

作　　者：胡志泽 夏永波[1] HU Zhize;XIA Yongbo(College of Mathematics and Statistics,South-Central Minzu University,Wuhan 430074,China)

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报(自然科学版)》2025年第3期426-432,共7页Journal of South-Central Minzu University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(62171479);中央高校基本科研业务费专项资金资助项目(CZZ23004)。

摘　　要：设p为素数,n为正整数.主要研究有限域Fpn上低阶非线性幂函数x5以及x7的差分性质.通过研究函数x5和x7的差分方程,刻画了差分方程有特定解数的条件,利用二次特征和确定了这两类幂函数差分谱.在面向算术的密码原语中,这两类低阶非线性幂函数可用于构造S盒或轮函数,其差分性质可为评估他们抗差分攻击的性能提供参考.Let p be a prime number and n be a positive integer.The differential properties of two classes of low-degree nonlinear power mappings x5 and x7 over finite field Fpn are investigated.By investigating the derivative equations of the functions x5 and x7,the conditions under which the differential equations have a specific number of solutions are characterized.Utilizing quadratic character sums,the differential spectrum of these two classes of power mappings are determined.These two classes of low-degree nonlinear power mappings can be used to design S-boxes or round functions in arithmetizationoriented cryptographic primitives,and their differential properties can provide a reference for evaluating their performance against differential attack.

关 键 词：有限域 幂函数 差分方程 差分谱 特征和 

分 类 号：O157[理学—数学]