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The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude

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Abstract

Recently, a class of binary sequences with optimal autocorrelation magnitude has been presented by Su et al. based on Ding-Helleseth-Lam sequences and interleaving technique (Designs, Codes and Cryptography 86, 1329–1338, 2018). The linear complexity of this class of sequences has been proved to be large enough to resist the B-M Algorithm by Fan (Designs, Codes and Cryptography 86, 2441–2450, 2018). In this paper, we study the 2-adic complexities of these sequences with period 4p and show they are no less than 2p, i.e., its 2-adic complexity is large enough to resist the Rational Approximation Algorithm.

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Acknowledgments

Parts of this work were suggested by Prof. Qiang Wang who works in School of Mathematics and Statistics, Carleton University. The authors wish to thank his good suggestions.

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Authors and Affiliations

  1. College of Sciences, China University of Petroleum, Qingdao, 266555, Shandong, China

    Yuhua Sun & Tongjiang Yan

  2. Provincial Key Laboratory of Applied Mathematics, Putian University, Putian, Fujian, 351100, China

    Yuhua Sun & Zhixiong Chen

  3. Shandong Computer Science Center (National Supercomputer Center in Jinan), Shandong Provincial Key Laboratory of Computer Networks, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China

    Yuhua Sun & Lianhai Wang

Authors
  1. Yuhua Sun
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  2. Tongjiang Yan
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  3. Zhixiong Chen
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  4. Lianhai Wang
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Corresponding author

Correspondence to Tongjiang Yan.

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The work is financially supported by National Natural Science Foundation of China (No. 61902429, No.11775306), Shandong Provincial Natural Science Foundation of China (No. ZR2017MA001, ZR2019MF070), Fundamental Research Funds for the Central Universities (No. 19CX02058A, No. 17CX02030A), the Open Research Fund from Shandong provincial Key Laboratory of Computer Networks, Grant No. SDKLCN-2017-03, No. SDKLCN-2018-02, Key Laboratory of Applied Mathematics of Fujian Province University (Putian University) (No. SX201702, No.SX201806), the Projects of International Cooperation and Exchanges NSFC-RFBR (No. 61911530130), and International Cooperation Exchange Fund of China University of Petroleum (UPCIEF2019020).

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Sun, Y., Yan, T., Chen, Z. et al. The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude. Cryptogr. Commun. 12, 675–683 (2020). https://doi.org/10.1007/s12095-019-00411-4

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  • DOI: https://doi.org/10.1007/s12095-019-00411-4

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