A complete characterization of the APN property of a class of quadrinomials

Abstract

In this paper, by the Hasse-Weil bound, we determine the necessary and sufficient condition on coefficients $a_1,a_2,a_3\in {\mathbb{F}}_{2^n}$ with $n=2m$ such that $f(x)=x^{3\cdot 2^m}+a_1{x}^{2^{m+1}+1}+a_2{x}^{2^m+2}+a_3{x}^3$ is an APN function over ${\mathbb{F}}_{2^n}$. Our result resolves the first half of an open problem by Carlet in International Workshop on the Arithmetic of Finite Fields, 83-107, 2014.

References in corpus (1)

• $4$-uniform BCT permutations from generalized butterfly structure

Cited by in corpus (1)

• Two new infinite classes of APN functions