IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1202-d788311.html

Complex Modified Projective Difference Function Synchronization of Coupled Complex Chaotic Systems for Secure Communication in WSNs

Author

Listed:
  • Fangfang Zhang

    (School of Control Science and Engineering, Shandong University, Jinan 250061, China
    Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Rui Gao

    (School of Control Science and Engineering, Shandong University, Jinan 250061, China)

  • Zhe Huang

    (Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Cuimei Jiang

    (School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Yawen Chen

    (Department of Computer Science, University of Otago, Dunedin 9016, New Zealand)

  • Haibo Zhang

    (Department of Computer Science, University of Otago, Dunedin 9016, New Zealand)

Abstract

Complex-variable chaotic systems (CVCSs) have numerous advantages over real-variable chaotic systems in chaos communication due to their increased unpredictability, confidentiality, and the ease of implementation. Synchronization between the master and slave systems in CVCSs is key to achieving encryption and decryption. However, existing synchronization schemes for CVCSs require the amplitude of the chaotic signal to be much larger than that of the plaintext. Moreover, traditional chaotic masking of complete synchronization (CS) requires uniformity between the transmitter and receiver ends. Therefore, we propose a complex modified projective difference function synchronization (CMPDFS) of CVCSs to address these issues, where the modified projective matrix helps address the issues with the amplitude. The receiver end is reconstructed without uniformity of the transmitter. We design the CMPDFS controller and propose a new secure communication scheme for wireless sensor networks (WSNs). The basic principle is fundamentally different from traditional chaotic masking. Simulation results and security analysis demonstrate that the CMPDFS communication scheme has a large key space, high sensitivity to encryption keys, high security, and an acceptable encryption speed. Hence, the proposed scheme can improve the security of WSNs. Moreover, it also can be applied to similar communication systems.

Suggested Citation

  • Fangfang Zhang & Rui Gao & Zhe Huang & Cuimei Jiang & Yawen Chen & Haibo Zhang, 2022. "Complex Modified Projective Difference Function Synchronization of Coupled Complex Chaotic Systems for Secure Communication in WSNs," Mathematics, MDPI, vol. 10(7), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1202-:d:788311
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1202/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/7/1202/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fangfang Zhang & Zhengfeng Li & Kai Sun & Xue Zhang & Peng Ji, 2021. "A New Hyperchaotic Complex System With Parametric Attractors," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-20, November.
    2. Mahmoud, Emad E. & Abo-Dahab, S.M., 2018. "Dynamical properties and complex anti synchronization with applications to secure communications for a novel chaotic complex nonlinear model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 273-284.
    3. Mahmoud, Emad E., 2013. "Modified projective phase synchronization of chaotic complex nonlinear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 69-85.
    4. Fangfang Zhang & Shutang Liu, 2014. "Self-time-delay synchronization of time-delay coupled complex chaotic system and its applications to communication," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(03), pages 1-13.
    5. Jiaxun Liu & Zuoxun Wang & Minglei Shu & Fangfang Zhang & Sen Leng & Xiaohui Sun, 2019. "Secure Communication of Fractional Complex Chaotic Systems Based on Fractional Difference Function Synchronization," Complexity, Hindawi, vol. 2019, pages 1-10, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Fangfang & Zhang, Shuaihu & Chen, Guanrong & Li, Chunbiao & Li, Zhengfeng & Pan, Changchun, 2022. "Special attractors and dynamic transport of the hybrid-order complex Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Mahmoud, Gamal M. & Mahmoud, Emad E. & Arafa, Ayman A., 2018. "Synchronization of time delay systems with non-diagonal complex scaling functions," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 86-95.
    3. Emad E. Mahmoud & M. Higazy & Turkiah M. Al-Harthi, 2019. "A New Nine-Dimensional Chaotic Lorenz System with Quaternion Variables: Complicated Dynamics, Electronic Circuit Design, Anti-Anticipating Synchronization, and Chaotic Masking Communication Application," Mathematics, MDPI, vol. 7(10), pages 1-26, September.
    4. Mahmoud, Emad E. & AL-Harthi, Bushra H., 2020. "A hyperchaotic detuned laser model with an infinite number of equilibria existing on a plane and its modified complex phase synchronization with time lag," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    5. Xuan-Toa Tran & Hee-Jun Kang, 2017. "Fixed-Time Complex Modified Function Projective Lag Synchronization of Chaotic (Hyperchaotic) Complex Systems," Complexity, Hindawi, vol. 2017, pages 1-9, July.
    6. Chih-Hsueh Lin & Chia-Wei Ho & Guo-Hsin Hu & Baswanth Sreeramaneni & Jun-Juh Yan, 2021. "Secure Data Transmission Based on Adaptive Chattering-Free Sliding Mode Synchronization of Unified Chaotic Systems," Mathematics, MDPI, vol. 9(21), pages 1-11, October.
    7. Mahmoud, Emad E. & Abo-Dahab, S.M., 2018. "Dynamical properties and complex anti synchronization with applications to secure communications for a novel chaotic complex nonlinear model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 273-284.
    8. Cuimei Jiang & Shutang Liu, 2017. "Synchronization and Antisynchronization of -Coupled Complex Permanent Magnet Synchronous Motor Systems with Ring Connection," Complexity, Hindawi, vol. 2017, pages 1-15, January.
    9. Jiang, Cuimei & Ye, Yunxiao & Zhang, Fangfang & Kou, Lei & Bao, Han & Zhang, Jianlin & Liu, Hongjun, 2025. "Hardware implementation and information security application of a novel chaotic system with a cubic memristor and complex parameters," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    10. Xuan-Bing Yang & Yi-Gang He & Chun-Lai Li, 2018. "Dynamics Feature and Synchronization of a Robust Fractional-Order Chaotic System," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    11. Hao, Zhang & Xing-yuan, Wang & Peng-fei, Yan & Yu-jie, Sun, 2020. "Combination synchronization and stability analysis of time-varying complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    12. Gao, Wei & Yan, Li & Saeedi, Mohammadhossein & Saberi Nik, Hassan, 2018. "Ultimate bound estimation set and chaos synchronization for a financial risk system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 154(C), pages 19-33.
    13. repec:plo:pone00:0152099 is not listed on IDEAS
    14. Yanyun Xie, 2022. "A Fractional‐Order Discrete Lorenz Map," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    15. Zuoxun Wang & Wenzhu Zhang & Lei Ma & Guijuan Wang, 2022. "Several Control Problems of a Class of Complex Nonlinear Systems Based on UDE," Mathematics, MDPI, vol. 10(8), pages 1-15, April.
    16. Wu, Xiangjun & Zhu, Changjiang & Kan, Haibin, 2015. "An improved secure communication scheme based passive synchronization of hyperchaotic complex nonlinear system," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 201-214.
    17. Zhai, Junchang & Qin, Yuping, 2026. "Predefined-time adaptive fault tolerant anti-synchronization control for unified chaotic system with unknown actuator faults," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    18. Jiaxun Liu & Zuoxun Wang & Minglei Shu & Fangfang Zhang & Sen Leng & Xiaohui Sun, 2019. "Secure Communication of Fractional Complex Chaotic Systems Based on Fractional Difference Function Synchronization," Complexity, Hindawi, vol. 2019, pages 1-10, August.
    19. Li, Xintong & Zhao, Judi & Zhang, Yinxing, 2025. "Generation of one-dimensional complex discrete hyperchaotic maps with hardware implementation," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    20. Emad E. Mahmoud & Fatimah S. Abood, 2017. "A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization," Complexity, Hindawi, vol. 2017, pages 1-13, August.
    21. Zhang, Zefeng & Huang, Lilian & Liu, Jin & Guo, Qiang & Du, Xiuli, 2022. "A new method of constructing cyclic symmetric conservative chaotic systems and improved offset boosting control," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1202-:d:788311. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.