A class of APcN power functions over finite fields of even characteristic

Abstract

In this paper, we investigate the power functions $F(x)=x^d$ over the finite field ${\mathbb{F}}_{2^{4n}}$, where $n$ is a positive integer and $d=2^{3n}+2^{2n}+2^n-1$. It is proved that $F(x)=x^d$ is APcN at certain $c$'s in ${\mathbb{F}}_{2^{4n}}$, and it is the second class of APcN power functions over finite fields of even characteristic. Further, the $c$-differential spectrum of these power functions is also determined.

References in corpus (1)

• Power Functions over Finite Fields with Low $c$-Differential Uniformity