有限域F_(2^(n))上一类幂函数的差分谱及应用  

Differential spectrum of a class of power functions over finite field F_(2^(n)) and its application

作　　者：满玉莹 夏永波[1] MAN Yuying;XIA Yongbo(College of Mathematics and Statistics, South-Central University for Nationalities, 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）》2021年第5期519-524,共6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(61771021);中央高校基本科研业务费专项基金资助项目(CZT20023);中南民族大学研究生学术创新基金资助项目(3212021sycxjj315)。

摘　　要：刻画了有限域F_(2^(n))上一类幂函数F(x)=x^(2^(2k)+2^(k)+1)的差分性质,其中n=4k.基于BRACKEN和LEANDER给出的F(x)的Walsh谱,利用差分谱和Walsh变换之间的关系,提出了一种确定F(x)差分谱的新方法,并计算了F(x)的与差分谱相关的两个密码学指标ambiguity和deficiency.The differential properties of a class of power functions F(x)=x^(2^(2k)+2^(k)+1) over finite field F_(2^(n)) are described where n=4k.Based on the Walsh spectrum of F(x)given by BRACKEN and LEANDER,utilizing the relationship between the differential spectrum and the Walsh transform,a new method of computing the differential spectrum of F(x)is given.In addition,the ambiguity and deficiency of F(x)related to its differential spectrum are also calculated.

关 键 词：有限域 差分一致性 差分谱 

分 类 号：O157[理学—数学]