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

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

Year:    2022

Author:    Mengyu Hu, Nian Li, Xiangyong Zeng

Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 223–245

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cmr.2020-0532

Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 223–245

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Differential uniformity finite field nonlinearity permutation polynomial.

Author Details

Mengyu Hu

Nian Li

Xiangyong Zeng