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

Jiang Ma, Wei Zhao, Yanguo Jia, Xiumin Shen and Haiyang Jiang
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Jiang Ma: School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
Wei Zhao: School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
Yanguo Jia: School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
Xiumin Shen: School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
Haiyang Jiang: School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China

Mathematics, 2021, vol. 9, issue 18, 1-13

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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