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Volume 9
Issue 18
10.3390/math9182285
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Article

Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two

by
Jiang Ma
,
Wei Zhao
,
Yanguo Jia
*,
Xiumin Shen
and
Haiyang Jiang
School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(18), 2285; https://doi.org/10.3390/math9182285
Submission received: 9 August 2021 / Revised: 4 September 2021 / Accepted: 14 September 2021 / Published: 16 September 2021
Versions Notes

Abstract

Linear complexity is an important property to measure the unpredictability of pseudo-random sequences. Trace representation is helpful for analyzing cryptography properties of pseudo-random sequences. In this paper, a class of new Ding generalized cyclotomic binary sequences of order two with period pq is constructed based on the new segmentation of Ding Helleseth generalized cyclotomy. Firstly, the linear complexity and minimal polynomial of the sequences are investigated. Then, their trace representation is given. It is proved that the sequences have larger linear complexity and can resist the attack of the Berlekamp–Massey algorithm. This paper also confirms that generalized cyclotomic sequences with good randomness may be obtained by modifying the characteristic set of generalized cyclotomy.
Keywords: pseudo-random sequences; stream cipher; Linear complexity; trace representation; generalized cyclotomic sequence pseudo-random sequences; stream cipher; Linear complexity; trace representation; generalized cyclotomic sequence

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MDPI and ACS Style

Ma, J.; Zhao, W.; Jia, Y.; Shen, X.; Jiang, H. Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two. Mathematics 2021, 9, 2285. https://doi.org/10.3390/math9182285

AMA Style

Ma J, Zhao W, Jia Y, Shen X, Jiang H. Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two. Mathematics. 2021; 9(18):2285. https://doi.org/10.3390/math9182285

Chicago/Turabian Style

Ma, Jiang, Wei Zhao, Yanguo Jia, Xiumin Shen, and Haiyang Jiang. 2021. "Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two" Mathematics 9, no. 18: 2285. https://doi.org/10.3390/math9182285

APA Style

Ma, J., Zhao, W., Jia, Y., Shen, X., & Jiang, H. (2021). Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two. Mathematics, 9(18), 2285. https://doi.org/10.3390/math9182285

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