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.
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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.