有限域F_(2^(n))上两类三项式的密码学性质  

Cryptographic properties of two classes of trinomials over finite field F2n

作　　者：余仁杰 夏永波[1] YU Renjie;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2期277-282,共6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);中南民族大学中央高校基本科研业务费专项资金资助项目(CZZ23004)。

摘　　要：刻画了有限域F_(2^(n))上两类三项式的差分谱,第一类是f(x)=x+x^(2^(m+1)-1)+x^((2^(n))-2^(m+1)+1),其中n=2m+1;第二类是g(x)=x^(2^(2k)+2^(k))+x^(2^(2^(k))+1)+x^(2^(k)+1),其中gcd(n,k)=1.对于第一类三项式采用的方法是通过计算f(x)的Walsh谱,再根据差分谱和Walsh谱之间的关系来确定它的差分谱;对于第二类则是直接通过研究g(x)的差分方程有确定解数的条件,从而计算出差分谱,此外根据二次型理论,还确定了它的Walsh谱.The differential spectra of two classes of trinomials over finite field F2n are described.The first class is f(x)=x+x^(2^(m+1)-1)+x^((2^(n))-2^(m+1)+1) with n=2m+1,and the second one is g(x)=x^(2^(2k)+2^(k))+x^(2^(2^(k))+1)+x^(2^(k)+1),where gcd(n,k)=1.For the first class,the differential spectrum is determined by calculating the Walsh spectrum of f(x).For the second one,the differential spectrum is calculated directly by determining the conditions for which the differential equation has specific number of solutions.Moreover,the Walsh spectrum of g(x)is also determined based on the theory of quadratic forms.

关 键 词：有限域 差分均匀度 差分谱 WALSH谱 

分 类 号：O157[理学—数学]