一类低差分均匀度幂函数的差分谱  

Differential spectra of a class of power functions with low differential uniformity

作　　者：夏永波[1] 包福荣 彭丽娜 XIA Yongbo;BAO Furong;PENG Lina(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）》2024年第1期126-132,共7页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(62171479);中南民族大学研究生学术创新基金资助项目(3212023sycxjj004)。

摘　　要：刻画了有限域Fpn上一类低差分均匀度幂函数f(x)=x 2的差分谱,其中p和n满足pn≡3(mod 4)和pn≠27.通过研究函数f(x)的差分方程,找到了使得差分方程f(x+1)-f(x)=b有两个解的充要条件并计算了Fpn中满足条件的b的个数,从而计算出了该函数的差分谱.The differential spectra of a class of power functions-3 f(x)=x 2 over finite field Fpn with low differential uniformity are described,where p and n satisfy pn≡3(mod 4)and pn≠27.By studying the differential equation of f(x),the necessary and sufficient conditions for which the differential equation f(x+1)-f(x)=b has exactly two solutions are given.Furthermore the number of elements b∈Fpn that satisfies the condition is calculated.Based on the obtained results,the differential spectra of these power functions are determined.

关 键 词：有限域 差分均匀度 差分谱 差分方程 

分 类 号：O157[理学—数学]