IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v185y2024ics0960077924007203.html
   My bibliography  Save this article

An n-dimensional polynomial modulo chaotic map with controllable range of Lyapunov exponents and its application in color image encryption

Author

Listed:
  • Ding, Dawei
  • Zhu, Haifei
  • Zhang, Hongwei
  • Yang, Zongli
  • Xie, Dong

Abstract

In chaos-based image encryption, better performance of the chaotic system represents higher security of the encryption algorithm, and the Lyapunov exponent (LE) is an important measure to evaluate the chaotic performance. In this paper, an n-dimensional(n-D) polynomial modulo chaotic map (nD-PMCM) is proposed as a general model, whose range of Lyapunov exponent is controlled by the system parameters and the robust chaotic behavior with the desired complexity can be obtained. And an instantiated 2D-PMCM is constructed by setting the corresponding parameters in nD-PMCM, which exhibits superior chaotic performance compared to other chaotic maps. Then a novel color image encryption scheme based on the 2D-PMCM is also constructed, which mainly uses cross-plane cyclic shift permutation and cross-plane XOR diffusion. Different from the traditional encryption scheme with separate processing of color planes, the cross-plane operation disrupts the correlation between color image planes and has higher encryption efficiency due to the ability to disrupt the pixel position while also changing the pixel value. The experimental simulation results show that this encryption scheme has better security and encryption effects.

Suggested Citation

  • Ding, Dawei & Zhu, Haifei & Zhang, Hongwei & Yang, Zongli & Xie, Dong, 2024. "An n-dimensional polynomial modulo chaotic map with controllable range of Lyapunov exponents and its application in color image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924007203
    DOI: 10.1016/j.chaos.2024.115168
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924007203
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115168?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Liu, Xilin & Tong, Xiaojun & Wang, Zhu & Zhang, Miao, 2022. "A new n-dimensional conservative chaos based on Generalized Hamiltonian System and its’ applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    3. Yildirim, Melih, 2022. "Optical color image encryption scheme with a novel DNA encoding algorithm based on a chaotic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Wu, Rui & Gao, Suo & Wang, Xingyuan & Liu, Songbo & Li, Qi & Erkan, Uğur & Tang, Xianglong, 2022. "AEA-NCS: An audio encryption algorithm based on a nested chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    5. Fan, Chunlei & Ding, Qun, 2023. "Design and geometric control of polynomial chaotic maps with any desired positive Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    6. Ding, Dawei & Wang, Wei & Yang, Zongli & Hu, Yongbing & Wang, Jin & Wang, Mouyuan & Niu, Yan & Zhu, Haifei, 2023. "An n-dimensional modulo chaotic system with expected Lyapunov exponents and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    7. Wang, Mingxu & Wang, Xingyuan & Wang, Chunpeng & Xia, Zhiqiu & Zhao, Hongyu & Gao, Suo & Zhou, Shuang & Yao, Nianmin, 2020. "Spatiotemporal chaos in cross coupled map lattice with dynamic coupling coefficient and its application in bit-level color image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    Full references (including those not matched with items on IDEAS)

    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. Ding, Dawei & Wang, Wei & Yang, Zongli & Hu, Yongbing & Wang, Jin & Wang, Mouyuan & Niu, Yan & Zhu, Haifei, 2023. "An n-dimensional modulo chaotic system with expected Lyapunov exponents and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Gao, Suo & Iu, Herbert Ho-Ching & Mou, Jun & Erkan, Uğur & Liu, Jiafeng & Wu, Rui & Tang, Xianglong, 2024. "Temporal action segmentation for video encryption," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    3. 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).
    4. Zou, Chengye & Wang, Xingyuan & Zhou, Changjun & Xu, Shujuan & Huang, Chun, 2022. "A novel image encryption algorithm based on DNA strand exchange and diffusion," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    5. Wu, Rui & Gao, Suo & Wang, Xingyuan & Liu, Songbo & Li, Qi & Erkan, Uğur & Tang, Xianglong, 2022. "AEA-NCS: An audio encryption algorithm based on a nested chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    6. Zou, Chengye & Li, Haifeng & Zhang, Xuncai & Liu, Yunong & Shang, Yubao & Zhou, Chuangjun, 2024. "Target localization image encryption of wind turbines based on DNA strand replacement rule," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    7. Qingye Huang & Linqing Huang & Shuting Cai & Xiaoming Xiong & Hui Zhang, 2023. "On a Symmetric Image Cryptosystem Based on a Novel One-Dimensional Chaotic System and Banyan Network," Mathematics, MDPI, vol. 11(21), pages 1-21, October.
    8. Yan, Minxiu & Jie, Jingfeng, 2022. "Fractional-order multiwing switchable chaotic system with a wide range of parameters," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    9. Man, Zhenlong & Li, Jinqing & Di, Xiaoqiang & Sheng, Yaohui & Liu, Zefei, 2021. "Double image encryption algorithm based on neural network and chaos," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Cang, Shijian & Wang, Luo & Zhang, Yapeng & Wang, Zenghui & Chen, Zengqiang, 2022. "Bifurcation and chaos in a smooth 3D dynamical system extended from Nosé-Hoover oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    11. Yan, Shaohui & Jiang, Defeng & Cui, Yu & Zhang, Hanbing & Li, Lin & Jiang, Jiawei, 2024. "A fractional-order hyperchaotic system that is period in integer-order case and its application in a novel high-quality color image encryption algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    12. 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.
    13. 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.
    14. Liu, Xilin & Tong, Xiaojun & Zhang, Miao & Wang, Zhu, 2023. "A highly secure image encryption algorithm based on conservative hyperchaotic system and dynamic biogenetic gene algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    15. Tuli, Rohan & Soneji, Hitesh Narayan & Churi, Prathamesh, 2022. "PixAdapt: A novel approach to adaptive image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    16. Man, Zhenlong, 2023. "Biometric information security based on double chaotic rotating diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    17. Reis, Eduardo V.M. & Savi, Marcelo A., 2022. "Spatiotemporal chaos in a conservative Duffing-type system," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    18. 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).
    19. 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.
    20. Shenli Zhu & Xiaoheng Deng & Wendong Zhang & Congxu Zhu, 2023. "Construction of a New 2D Hyperchaotic Map with Application in Efficient Pseudo-Random Number Generator Design and Color Image Encryption," Mathematics, MDPI, vol. 11(14), pages 1-23, July.

    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:eee:chsofr:v:185:y:2024:i:c:s0960077924007203. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.