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

^*Corresponding author for this work

Software Engineering Institute

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

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	2119-2132
Number of pages	14
Journal	Designs, Codes, and Cryptography
Volume	88
Issue number	10
DOIs	https://doi.org/10.1007/s10623-020-00768-1
State	Published - 1 Oct 2020

Keywords

Block cipher
Finite field
Permutation polynomial
Triple-cycle permutation

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10.1007/s10623-020-00768-1

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title = "Characterizations and constructions of triple-cycle permutations of the form xrh(xs)",

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",

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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

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M3 - 文章

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IS - 10

ER -

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

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Keywords

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