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Image Encryption Schemes Based on a Class of Uniformly Distributed Chaotic Systems

Author

Listed:
  • Hongyan Zang

    (Mathematics and Physics School, University of Science and Technology Beijing, Beijing 100083, China)

  • Mengdan Tai

    (Mathematics and Physics School, University of Science and Technology Beijing, Beijing 100083, China)

  • Xinyuan Wei

    (Mathematics and Physics School, University of Science and Technology Beijing, Beijing 100083, China)

Abstract

This paper proposes a method to construct a one-dimensional discrete chaotic system. First, we define a generalized distance function to control the boundedness of the one-dimensional discrete system. Based on Marotto’s theorem, one-dimensional discrete systems are proven to be chaotic in the sense of Li–Yorke, and the corresponding chaos criterion theorem is proposed. The system can be distributed uniformly by adjusting the parameters. In this paper, we propose an image encryption scheme based on a uniformly distributed discrete chaotic system and DNA encoding. DNA encoding and decoding rules are determined by plain text. The experimental results demonstrate that our encryption algorithm has a large key space, high key sensitivity, and fast encryption speed and can resist differential and statistical attacks.

Suggested Citation

  • Hongyan Zang & Mengdan Tai & Xinyuan Wei, 2022. "Image Encryption Schemes Based on a Class of Uniformly Distributed Chaotic Systems," Mathematics, MDPI, vol. 10(7), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1027-:d:777697
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    References listed on IDEAS

    as
    1. Çavuşoğlu, Ünal & Kaçar, Sezgin & Pehlivan, Ihsan & Zengin, Ahmet, 2017. "Secure image encryption algorithm design using a novel chaos based S-Box," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 92-101.
    2. Shijie Zhang & Lingfeng Liu & Hongyue Xiang, 2021. "A Novel Plain-Text Related Image Encryption Algorithm Based on LB Compound Chaotic Map," Mathematics, MDPI, vol. 9(21), pages 1-25, November.
    3. Tutueva, Aleksandra V. & Nepomuceno, Erivelton G. & Karimov, Artur I. & Andreev, Valery S. & Butusov, Denis N., 2020. "Adaptive chaotic maps and their application to pseudo-random numbers generation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Zhu, Shenli & Deng, Xiaoheng & Zhang, Wendong & Zhu, Congxu, 2023. "Secure image encryption scheme based on a new robust chaotic map and strong S-box," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 322-346.
    2. Heping Wen & Zhen Liu & Haowen Lai & Chongfu Zhang & Linhao Liu & Jieyi Yang & Yiting Lin & Yunqi Li & Yunlong Liao & Linchao Ma & Zefeng Chen & Rui Li, 2022. "Secure DNA-Coding Image Optical Communication Using Non-Degenerate Hyperchaos and Dynamic Secret-Key," Mathematics, MDPI, vol. 10(17), pages 1-18, September.
    3. Shaista Mansoor & Parsa Sarosh & Shabir A. Parah & Habib Ullah & Mohammad Hijji & Khan Muhammad, 2022. "Adaptive Color Image Encryption Scheme Based on Multiple Distinct Chaotic Maps and DNA Computing," Mathematics, MDPI, vol. 10(12), pages 1-20, June.
    4. Shenli Zhu & Xiaoheng Deng & Wendong Zhang & Congxu Zhu, 2023. "Image Encryption Scheme Based on Newly Designed Chaotic Map and Parallel DNA Coding," Mathematics, MDPI, vol. 11(1), pages 1-22, January.
    5. Abed-Elhameed, Tarek M. & Mahmoud, Gamal M. & Elbadry, Motaz M. & Ahmed, Mansour E., 2023. "Nonlinear distributed-order models: Adaptive synchronization, image encryption and circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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