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

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  • 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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
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