On the Differential Spectrum and the APcN Property of a Class of Power Functions Over Finite Fields

In this paper, we investigate the power function F(x)=x^{d} over the finite field \mathbb {F}_{2^{4n}} , where n is a positive integer and d=2^{3n}+2^{2n}+2^{n}-1 . We prove that this power function is AP c\text{N} with respect to all c\in \mathbb {F}_{2^{4n}}\setminus \{1\} satisfying c^{2^{2n}+1}=1 , and we determine its c -differential spectrum. To the best of our knowledge, this is the second class of AP c\text{N} power functions over finite fields of even characteristic. By the same proof ideas, we completely determine the differential spectrum of this function, and give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski.