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

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.