中南民族大学学报（自然科学版）2025，Vol.44Issue(3)：426-432,7.DOI:10.20056/j.cnki.ZNMDZK.20250317
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
摘要
Abstract
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 arithmetization-oriented 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Key words
finite field/power mapping/derivative equation/differential spectrum/character sums分类
数理科学引用本文复制引用
胡志泽,夏永波..两类面向算术化幂函数的差分性质[J].中南民族大学学报（自然科学版）,2025,44(3):426-432,7.基金项目
国家自然科学基金资助项目(62171479) （62171479）
中央高校基本科研业务费专项资金资助项目(CZZ23004) （CZZ23004）
