Differential spectra of a class of power permutations with characteristic 5

Abstract

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.