On the Differential Uniformity and Nonlinearity of a Class of Permutation Quadrinomials Over $\mathbb{F}_{2^{2m}}$

Abstract

Permutation polynomials with low differential uniformity and high nonlinearity are preferred in cryptographic systems. In 2018, Tu, Zeng and Helleseth constructed a new class of permutation quadrinomials over the finite field $\mathbb{F}_{2^{2m}}$ for an odd integer $m$. In this paper, we aim to investigate the differential uniformity and nonlinearity of this class of permutation polynomials so as to find 4-uniform permutation polynomials with high nonlinearity.