Binary Sequences Derived from Monomial Permutation Polynomials over GF(2p )

Qun Xiong Zheng; Yupeng Jiang; Dongdai Lin; Wen Feng Qi

doi:10.1007/978-3-030-88323-2_20

Binary Sequences Derived from Monomial Permutation Polynomials over GF(2^p )

Qun Xiong Zheng
, Yupeng Jiang^*
, Dongdai Lin
, Wen Feng Qi

^*Corresponding author for this work

School of Cyber Science and Technology

Information Engineering University
CAS - Institute of Information Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, we propose a class of binary sequences induced by monomial permutation polynomials over GF (2^p) and study the period property and the shift-equivalence of these binary sequences. In particularly, we give a necessary and sufficient condition for such a sequence to have maximal period. Moreover, we also give a necessary and sufficient condition for two such sequences to be shift equivalent.

Original language	English
Title of host publication	Information Security and Cryptology - 17th International Conference, Inscrypt 2021, Revised Selected Papers
Editors	Yu Yu, Moti Yung
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	371-383
Number of pages	13
ISBN (Print)	9783030883225
DOIs	https://doi.org/10.1007/978-3-030-88323-2_20
State	Published - 2021
Event	17th International Conference on Information Security and Cryptology, Inscrypt 2021 - Virtual, Online Duration: 12 Aug 2021 → 14 Aug 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13007 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Conference on Information Security and Cryptology, Inscrypt 2021
City	Virtual, Online
Period	12/08/21 → 14/08/21

Keywords

Mersenne prime
Periodicity
Permutation polynomial
Pseudorandom sequence
Shift equivalence

Access to Document

10.1007/978-3-030-88323-2_20

Cite this

Zheng, Q. X., Jiang, Y., Lin, D., & Qi, W. F. (2021). Binary Sequences Derived from Monomial Permutation Polynomials over GF(2^p ). In Y. Yu, & M. Yung (Eds.), Information Security and Cryptology - 17th International Conference, Inscrypt 2021, Revised Selected Papers (pp. 371-383). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13007 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-88323-2_20

Zheng, Qun Xiong ; Jiang, Yupeng ; Lin, Dongdai et al. / Binary Sequences Derived from Monomial Permutation Polynomials over GF(2^p ). Information Security and Cryptology - 17th International Conference, Inscrypt 2021, Revised Selected Papers. editor / Yu Yu ; Moti Yung. Springer Science and Business Media Deutschland GmbH, 2021. pp. 371-383 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Binary Sequences Derived from Monomial Permutation Polynomials over GF(2p )",

abstract = "In this paper, we propose a class of binary sequences induced by monomial permutation polynomials over GF (2p) and study the period property and the shift-equivalence of these binary sequences. In particularly, we give a necessary and sufficient condition for such a sequence to have maximal period. Moreover, we also give a necessary and sufficient condition for two such sequences to be shift equivalent.",

keywords = "Mersenne prime, Periodicity, Permutation polynomial, Pseudorandom sequence, Shift equivalence",

author = "Zheng, \{Qun Xiong\} and Yupeng Jiang and Dongdai Lin and Qi, \{Wen Feng\}",

note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; 17th International Conference on Information Security and Cryptology, Inscrypt 2021 ; Conference date: 12-08-2021 Through 14-08-2021",

year = "2021",

doi = "10.1007/978-3-030-88323-2\_20",

language = "英语",

isbn = "9783030883225",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "371--383",

editor = "Yu Yu and Moti Yung",

booktitle = "Information Security and Cryptology - 17th International Conference, Inscrypt 2021, Revised Selected Papers",

address = "德国",

}

Zheng, QX, Jiang, Y, Lin, D & Qi, WF 2021, Binary Sequences Derived from Monomial Permutation Polynomials over GF(2^p ). in Y Yu & M Yung (eds), Information Security and Cryptology - 17th International Conference, Inscrypt 2021, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13007 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 371-383, 17th International Conference on Information Security and Cryptology, Inscrypt 2021, Virtual, Online, 12/08/21. https://doi.org/10.1007/978-3-030-88323-2_20

Binary Sequences Derived from Monomial Permutation Polynomials over GF(2^p ). / Zheng, Qun Xiong; Jiang, Yupeng; Lin, Dongdai et al.
Information Security and Cryptology - 17th International Conference, Inscrypt 2021, Revised Selected Papers. ed. / Yu Yu; Moti Yung. Springer Science and Business Media Deutschland GmbH, 2021. p. 371-383 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13007 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - In this paper, we propose a class of binary sequences induced by monomial permutation polynomials over GF (2p) and study the period property and the shift-equivalence of these binary sequences. In particularly, we give a necessary and sufficient condition for such a sequence to have maximal period. Moreover, we also give a necessary and sufficient condition for two such sequences to be shift equivalent.

KW - Mersenne prime

KW - Periodicity

KW - Permutation polynomial

KW - Pseudorandom sequence

KW - Shift equivalence

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PB - Springer Science and Business Media Deutschland GmbH

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Zheng QX, Jiang Y, Lin D, Qi WF. Binary Sequences Derived from Monomial Permutation Polynomials over GF(2^p ). In Yu Y, Yung M, editors, Information Security and Cryptology - 17th International Conference, Inscrypt 2021, Revised Selected Papers. Springer Science and Business Media Deutschland GmbH. 2021. p. 371-383. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-88323-2_20