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

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.