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A robust bit-level image encryption based on Bessel map

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  • Toktas, Abdurrahim
  • Erkan, Uğur
  • Gao, Suo
  • Pak, Chanil

Abstract

A chaotic map plays a critical role in image encryption (IME). The map used to generate chaotic sequences should perform high dynamic characteristics. In this study, a new chaotic system depending on the Bessel function, so-called Bessel map, and a novel Bessel map-based IME scheme are proposed for the IME. The Bessel map has three control parameters, which provide superior ergodicity and diversity. Bessel map has also order degree rather than Sine map, which is used as a control parameter boosting the security. The chaotic characteristic of the Bessel map is verified through different reliable measurements such as bifurcation diagram, trajectory phase, Lyapunov exponent (LE), sample entropy (SE), permutation entropy (PE), and 0-1 test. Then, the Bessel map is employed in a new bitwise IME (BIME) scheme based on bit-level permutation and diffusion processes. The Bessel map-based BIME is validated through various simulated cryptanalyses and cyberattacks as well as compared with the state-of-the-art schemes. The achieved results demonstrate that the BIME based on the Bessel map ensures the most secure ciphered images thanks to the excellent randomness and complexity performance.

Suggested Citation

  • Toktas, Abdurrahim & Erkan, Uğur & Gao, Suo & Pak, Chanil, 2024. "A robust bit-level image encryption based on Bessel map," Applied Mathematics and Computation, Elsevier, vol. 462(C).
    • Handle: RePEc:eee:apmaco:v:462:y:2024:i:c:s009630032300509x
    DOI: 10.1016/j.amc.2023.128340
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    References listed on IDEAS

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    1. Erkan, Uğur & Toktas, Abdurrahim & Lai, Qiang, 2023. "Design of two dimensional hyperchaotic system through optimization benchmark function," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Wang, Xingyuan & Guan, Nana & Yang, Jingjing, 2021. "Image encryption algorithm with random scrambling based on one-dimensional logistic self-embedding chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Castro, Julio Cesar Hernandez & Sierra, José María & Seznec, Andre & Izquierdo, Antonio & Ribagorda, Arturo, 2005. "The strict avalanche criterion randomness test," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(1), pages 1-7.
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    Citations

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    Cited by:

    1. Jinlong Zhang & Heping Wen, 2024. "Secure image communication based on two-layer dynamic feedback encryption and DWT information hiding," PLOS ONE, Public Library of Science, vol. 19(8), pages 1-25, August.
    2. Cao, Hongli & Wang, Yu & Banerjee, Santo & Cao, Yinghong & Mou, Jun, 2024. "A discrete Chialvo–Rulkov neuron network coupled with a novel memristor model: Design, Dynamical analysis, DSP implementation and its application," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. He, Shaobo & Hu, Kai & Wang, Mengjiao & Wang, Huihai & Wu, Xianming, 2024. "Design and dynamics of discrete dual-memristor chaotic maps and its application in speech encryption," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    4. Huang, Yibo & Wang, Ling & Li, Zhiyong & Zhang, Qiuyu, 2024. "A new 3D robust chaotic mapping and its application to speech encryption," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    5. Ustun, Deniz & Sahinkaya, Serap, 2025. "Design of secure S-Boxes via novel 2D-Zettle chaotic map and ABC algorithm for robust image encryption," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 235(C), pages 175-204.
    6. Hu, Long-Long & Chen, Ming-Xuan & Wang, Meng-Meng & Zhou, Nan-Run, 2024. "A multi-image encryption scheme based on block compressive sensing and nonlinear bifurcation diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    7. SaberiKamarposhti, Morteza & Ghorbani, Amirabbas & Yadollahi, Mehdi, 2024. "A comprehensive survey on image encryption: Taxonomy, challenges, and future directions," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    8. Zhou, Shuang & Yin, Yanli & Erkan, Uğur & Toktas, Abdurrahim & Zhang, Yingqian, 2025. "Novel hyperchaotic system: Implementation to audio encryption," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    9. Chai, Xiuli & Shang, Guangyu & Wang, Binjie & Gan, Zhihua & Zhang, Wenkai, 2024. "Exploiting 2D-SDMCHM and matching embedding driven by flag-shaped hexagon prediction for visually meaningful medical image cryptosystem," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).

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