Let n be a positive integer and \(F(x)=x^d\) over \({\mathbb {F}}_{5^n}\), where \(d=\frac{5^n-3}{2}\). In this paper, we study the differential properties of the power permutation F(x). It is shown that F(x) is differentially 4-uniform when n is even, and differentially 5-uniform when n is odd. Based on some knowledge on elliptic curves over finite fields, the differential spectrum of F(x) is also determined.

中文翻译：

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一类特征为5的功率置换的微分谱

令n为正整数，在\（{\ mathbb {F}} _ {5 ^ n} \）上\\（F（x）= x ^ d \），其中\（d = \ frac {5 ^ n- 3} {2} \）。在本文中，我们研究了功率置换F（x）的微分性质。结果表明，当n为偶数时，F（x）微分为4均匀，而当n为奇数时，微分5是均匀的。基于对有限域上椭圆曲线的一些了解，还可以确定F（x）的微分谱。