IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1027-d777697.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1027/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/7/1027/
    Download Restriction: no
    ---><---

    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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    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. Trujillo-Toledo, D.A. & López-Bonilla, O.R. & García-Guerrero, E.E. & Tlelo-Cuautle, E. & López-Mancilla, D. & Guillén-Fernández, O. & Inzunza-González, E., 2021. "Real-time RGB image encryption for IoT applications using enhanced sequences from chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    2. Bowen Zhang & Lingfeng Liu, 2023. "Chaos-Based Image Encryption: Review, Application, and Challenges," Mathematics, MDPI, vol. 11(11), pages 1-39, June.
    3. Gong, Li-Hua & Luo, Hui-Xin & Wu, Rou-Qing & Zhou, Nan-Run, 2022. "New 4D chaotic system with hidden attractors and self-excited attractors and its application in image encryption based on RNG," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    4. Tutueva, Aleksandra V. & Karimov, Artur I. & Moysis, Lazaros & Volos, Christos & Butusov, Denis N., 2020. "Construction of one-way hash functions with increased key space using adaptive chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Shihong Zhang & Hu Shi & Baizhong Wang & Chunlu Ma & Qinghua Li, 2024. "A Dynamic Hierarchical Improved Tyrannosaurus Optimization Algorithm with Hybrid Topology Structure," Mathematics, MDPI, vol. 12(10), pages 1-35, May.
    6. Yan, Yanjun & Chen, Kai & Zhao, Yijiu & Wang, Houjun & Xu, Bo & Wang, Yifan, 2024. "An innovative orthogonal matrix based on nonlinear chaotic system for compressive sensing," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    7. Dong, Youheng & Zhao, Geng, 2021. "A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    8. Moreira Bezerra, João Inácio & Valduga de Almeida Camargo, Vinícius & Molter, Alexandre, 2021. "A new efficient permutation-diffusion encryption algorithm based on a chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    9. Sahoo, Shilalipi & Roy, Binoy Krishna, 2022. "Design of multi-wing chaotic systems with higher largest Lyapunov exponent," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    10. Saha, Rahul & G, Geetha, 2017. "Symmetric random function generator (SRFG): A novel cryptographic primitive for designing fast and robust algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 371-377.
    11. Tutueva, Aleksandra V. & Moysis, Lazaros & Rybin, Vyacheslav G. & Kopets, Ekaterina E. & Volos, Christos & Butusov, Denis N., 2022. "Fast synchronization of symmetric Hénon maps using adaptive symmetry control," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    12. Xiong Wang & Akif Akgul & Sezgin Kacar & Viet-Thanh Pham, 2017. "Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium," Complexity, Hindawi, vol. 2017, pages 1-10, November.
    13. Yu, Jinwei & Xie, Wei & Zhong, Zhenyu & Wang, Huan, 2022. "Image encryption algorithm based on hyperchaotic system and a new DNA sequence operation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    14. Karakaya, Barış & Gülten, Arif & Frasca, Mattia, 2019. "A true random bit generator based on a memristive chaotic circuit: Analysis, design and FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 143-149.
    15. Motaeb Eid Alshammari & Makbul A. M. Ramli & Ibrahim M. Mehedi, 2021. "A New Chaotic Artificial Bee Colony for the Risk-Constrained Economic Emission Dispatch Problem Incorporating Wind Power," Energies, MDPI, vol. 14(13), pages 1-24, July.
    16. 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.
    17. 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).
    18. Wenqiang Yang & Li Xiao & Junjian Huang & Jinyue Yang, 2021. "Fixed-Time Synchronization of Neural Networks Based on Quantized Intermittent Control for Image Protection," Mathematics, MDPI, vol. 9(23), pages 1-14, November.
    19. Sukegawa, Noriyoshi & Ikeguchi, Tohru, 2022. "How to perturb Bernoulli shift map," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    20. Man, Zhenlong, 2023. "Biometric information security based on double chaotic rotating diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

    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:1027-:d:777697. 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 (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.