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Trace representation of the binary pq2-periodic sequences derived from Euler quotients

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Abstract

Given a binary sequence, its trace representation allows us to reconstruct itself efficiently and to analyze its properties, such as the linear complexity. In this paper, we study a family of the binary sequences derived from Euler quotients modulo pq, where p and q are two distinct odd primes and p divides q − 1. Our main contribution is to give a trace representation of this family within these assumptions by determining the defining pairs of the corresponding subsequences. As a byproduct, we rediscover some known results of linear complexities by using trace representations of the proposed sequences.

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Acknowledgments

All of the authors wish to thank the associate editor and the two anonymous reviewers for their valuable comments.

The work of Chang-An Zhao is partially supported by National Key R&D Program of China under Grant No. 2017YFB0802500, by NSFC under Grant No. 61972428, by the Major Program of Guangdong Basic and Applied Research under Grant No. 2019B030302008 and by the Open Fund of State Key Laboratory of Information Security (Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093) under grant No. 2020-ZD-02. The work of Jingwei Zhang was partially supported by the National Social Science Fund of China under Grant No.14BXW031 and by Guangdong Basic and Applied Basic Research Foundation under Grant No. 2019A1515011797. The work of Chuangqiang Hu is partially supported by NSFC under Grant No. 11961141005. The research carried out by Xiang Fan is supported by the Natural Science Foundation of Guangdong Province (No. 2018A030310080).

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Authors and Affiliations

  1. School of Information Science, Guangdong University of Finance and Economics, Guangzhou, 510320, People’s Republic of China

    Jingwei Zhang

  2. Guangdong Intelligent Business Engineering Technology Research Center, Guangzhou, People’s Republic of China

    Jingwei Zhang

  3. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China

    Chuangqiang Hu, Xiang Fan & Chang-An Zhao

  4. Guangdong Key Laboratory of Information Security, Guangzhou, 510006, People’s Republic of China

    Chang-An Zhao

  5. State Key Laboratory of Information Security (Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, People’s Republic of China

    Chang-An Zhao

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  1. Jingwei Zhang
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  2. Chuangqiang Hu
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  3. Xiang Fan
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  4. Chang-An Zhao
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Correspondence to Chang-An Zhao.

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Zhang, J., Hu, C., Fan, X. et al. Trace representation of the binary pq2-periodic sequences derived from Euler quotients. Cryptogr. Commun. 13, 343–359 (2021). https://doi.org/10.1007/s12095-021-00475-1

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  • DOI: https://doi.org/10.1007/s12095-021-00475-1

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