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On the synchronization techniques of chaotic oscillators and their FPGA-based implementation for secure image transmission

Author

Listed:
  • Omar Guillén-Fernández
  • Ashley Meléndez-Cano
  • Esteban Tlelo-Cuautle
  • Jose Cruz Núñez-Pérez
  • Jose de Jesus Rangel-Magdaleno

Abstract

Synchronizing chaotic oscillators has been a challenge to guarantee successful applications in secure communications. That way, three synchronization techniques are applied herein to twenty two chaotic oscillators, three of them based on piecewise-linear functions and nineteen proposed by Julien C. Sprott. These chaotic oscillators are simulated to generate chaotic time series that are used to evaluate their Lyapunov exponents and Kaplan-Yorke dimension to rank their unpredictability. The oscillators with the high positive Lyapunov exponent are implemented into a field-programmable gate array (FPGA), and afterwards they are synchronized in a master-slave topology applying three techniques: the seminal work introduced by Pecora-Carroll, Hamiltonian forms and observer approach, and open-plus-closed-loop (OPCL). These techniques are compared with respect to their synchronization error and latency that is associated to the FPGA implementation. Finally, the chaotic oscillators providing the high positive Lyapunov exponent are synchronized and applied to a communication system with chaotic masking to perform a secure image transmission. Correlation analysis is performed among the original image, the chaotic channel and the recovered image for the three synchronization schemes. The experimental results show that both Hamiltonian forms and OPCL can recover the original image and its correlation with the chaotic channel is as low as 0.00002, demonstrating the advantage of synchronizing chaotic oscillators with high positive Lyapunov exponent to guarantee high security in data transmission.

Suggested Citation

  • Omar Guillén-Fernández & Ashley Meléndez-Cano & Esteban Tlelo-Cuautle & Jose Cruz Núñez-Pérez & Jose de Jesus Rangel-Magdaleno, 2019. "On the synchronization techniques of chaotic oscillators and their FPGA-based implementation for secure image transmission," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-34, February.
  • Handle: RePEc:plo:pone00:0209618
    DOI: 10.1371/journal.pone.0209618
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    References listed on IDEAS

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    1. Esteban Tlelo-Cuautle & Antonio de Jesus Quintas-Valles & Luis Gerardo de la Fraga & Jose de Jesus Rangel-Magdaleno, 2016. "VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-32, December.
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    Cited by:

    1. García-Guerrero, E.E. & Inzunza-González, E. & López-Bonilla, O.R. & Cárdenas-Valdez, J.R. & Tlelo-Cuautle, E., 2020. "Randomness improvement of chaotic maps for image encryption in a wireless communication scheme using PIC-microcontroller via Zigbee channels," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Martínez-Fuentes, Oscar & Díaz-Muñoz, Jonathan Daniel & Muñoz-Vázquez, Aldo Jonathan & Tlelo-Cuautle, Esteban & Fernández-Anaya, Guillermo & Cruz-Vega, Israel, 2024. "Family of controllers for predefined-time synchronization of Lorenz-type systems and the Raspberry Pi-based implementation," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. Muhammad Marwan & Vagner Dos Santos & Muhammad Zainul Abidin & Anda Xiong, 2022. "Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems," Mathematics, MDPI, vol. 10(11), pages 1-15, June.

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