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) = xd over the finite field F 24n, where n is a positive integer and d = 23n +22n +2n -1. We prove that this power function is APcN with respect to all c ϵ F 24n /{1} satisfying c22n+1 = 1, and we determine its c-differential spectrum. To the best of our knowledge, this is the second class of APcN 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.