Characterizations and constructions of triple-cycle permutations of the form xrh(xs)

Mengna Wu; Chengju Li; Zilong Wang

doi:10.1007/s10623-020-00768-1

Characterizations and constructions of triple-cycle permutations of the form x^rh(x^s)

Mengna Wu
, Chengju Li^*
, Zilong Wang

^*此作品的通讯作者

软件工程学院

East China Normal University
Xidian University
School of Cyber Engineering, Xidian University

科研成果: 期刊稿件 › 文章 › 同行评审

9 引用（Scopus）

摘要

Let F_q be the finite field with q elements and let f be a permutation polynomial over F_q. Let S_q denote the symmetric group on F_q. In this paper, we mainly investigate some characterizations on the elements f∈ S_q of order 3, i.e., f∘ f∘ f= I, where f is also called a triple-cycle permutation in the literature. Some explicit triple-cycle permutations are constructed.

源语言	英语
页（从-至）	2119-2132
页数	14
期刊	Designs, Codes, and Cryptography
卷	88
期	10
DOI	https://doi.org/10.1007/s10623-020-00768-1
出版状态	已出版 - 1 10月 2020

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10.1007/s10623-020-00768-1

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abstract = "Let Fq be the finite field with q elements and let f be a permutation polynomial over Fq. Let Sq denote the symmetric group on Fq. In this paper, we mainly investigate some characterizations on the elements f∈ Sq of order 3, i.e., f∘ f∘ f= I, where f is also called a triple-cycle permutation in the literature. Some explicit triple-cycle permutations are constructed.",

keywords = "Block cipher, Finite field, Permutation polynomial, Triple-cycle permutation",

author = "Mengna Wu and Chengju Li and Zilong Wang",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Wu, Mengna

AU - Li, Chengju

AU - Wang, Zilong

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Y1 - 2020/10/1

N2 - Let Fq be the finite field with q elements and let f be a permutation polynomial over Fq. Let Sq denote the symmetric group on Fq. In this paper, we mainly investigate some characterizations on the elements f∈ Sq of order 3, i.e., f∘ f∘ f= I, where f is also called a triple-cycle permutation in the literature. Some explicit triple-cycle permutations are constructed.

AB - Let Fq be the finite field with q elements and let f be a permutation polynomial over Fq. Let Sq denote the symmetric group on Fq. In this paper, we mainly investigate some characterizations on the elements f∈ Sq of order 3, i.e., f∘ f∘ f= I, where f is also called a triple-cycle permutation in the literature. Some explicit triple-cycle permutations are constructed.

KW - Block cipher

KW - Finite field

KW - Permutation polynomial

KW - Triple-cycle permutation

UR - https://www.scopus.com/pages/publications/85086790511

U2 - 10.1007/s10623-020-00768-1

DO - 10.1007/s10623-020-00768-1

M3 - 文章

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SN - 0925-1022

VL - 88

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EP - 2132

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

IS - 10

ER -

Characterizations and constructions of triple-cycle permutations of the form xrh(xs)

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Characterizations and constructions of triple-cycle permutations of the form x^rh(x^s)