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Volume 38, Issue 2
On the Differential Uniformity and Nonlinearity of a Class of Permutation Quadrinomials Over $\mathbb{F}_{2^{2m}}$

Mengyu Hu, Nian Li & Xiangyong Zeng

DOI: 10.4208/cmr.2020-0532

Commun. Math. Res., 38 (2022), pp. 223-245.

Published online: 2022-02

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  • 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.

  • Keywords

Differential uniformity, finite field, nonlinearity, permutation polynomial.

  • AMS Subject Headings

05A05, 11T06, 11T23, 11T55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-38-223, author = {Hu , MengyuLi , Nian and Zeng , Xiangyong}, title = {On the Differential Uniformity and Nonlinearity of a Class of Permutation Quadrinomials Over $\mathbb{F}_{2^{2m}}$}, journal = {Communications in Mathematical Research }, year = {2022}, volume = {38}, number = {2}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0532}, url = {http://global-sci.org/intro/article_detail/cmr/20272.html} }
TY - JOUR T1 - On the Differential Uniformity and Nonlinearity of a Class of Permutation Quadrinomials Over $\mathbb{F}_{2^{2m}}$ AU - Hu , Mengyu AU - Li , Nian AU - Zeng , Xiangyong JO - Communications in Mathematical Research VL - 2 SP - 223 EP - 245 PY - 2022 DA - 2022/02 SN - 38 DO - http://doi.org/10.4208/cmr.2020-0532 UR - https://global-sci.org/intro/article_detail/cmr/20272.html KW - Differential uniformity, finite field, nonlinearity, permutation polynomial. AB -

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.

Hu , MengyuLi , Nian and Zeng , Xiangyong. (2022). On the Differential Uniformity and Nonlinearity of a Class of Permutation Quadrinomials Over $\mathbb{F}_{2^{2m}}$. Communications in Mathematical Research . 38 (2). 223-245. doi:10.4208/cmr.2020-0532
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