IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i1p362-369.html
   My bibliography  Save this article

Cryptography based on chaotic random maps with position dependent weighting probabilities

Author

Listed:
  • Behnia, S.
  • Akhshani, A.
  • Ahadpour, S.
  • Akhavan, A.
  • Mahmodi, H.

Abstract

Chaotic cryptology has been widely investigated recently. A common feature in the most recent developments of chaotic cryptosystems is the use of a single dynamical rule in the encoding–decoding process. The main objective of this paper is to provide a set of chaotic systems instead of a single one for cryptography. In this paper, we introduce a chaotic cryptosystem based on the symbolic dynamics of random maps with position dependent weighting probabilities. The random maps model is a deterministic dynamical system in a finite phase space with n points. The maps that establish the dynamics of the system are chosen randomly for every point. The essential idea of this paper is that, given two dynamical systems that behave in a certain way, it is possible to combine them (by composing) into a new dynamical system. This dynamically composed system behaves in a completely different way compared to the constituent systems. The proposed scheme exploits the symbolic dynamics of a set of chaotic maps in order to encode the binary information. The performance of the new cryptosystem based on chaotic dynamical systems properties is examined. Both theoretical and experimental results demonstrate that the proposed algorithm using symbolic dynamics achieves the optimal security criteria.

Suggested Citation

  • Behnia, S. & Akhshani, A. & Ahadpour, S. & Akhavan, A. & Mahmodi, H., 2009. "Cryptography based on chaotic random maps with position dependent weighting probabilities," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 362-369.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:362-369
    DOI: 10.1016/j.chaos.2007.07.070
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790700584X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.07.070?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. Lian, Shiguo & Sun, Jinsheng & Wang, Zhiquan, 2005. "A block cipher based on a suitable use of the chaotic standard map," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 117-129.
    2. Mi, Bo & Liao, Xiaofeng & Chen, Yong, 2008. "A novel chaotic encryption scheme based on arithmetic coding," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1523-1531.
    3. Lian, Shiguo & Sun, Jinsheng & Wang, Jinwei & Wang, Zhiquan, 2007. "A chaotic stream cipher and the usage in video protection," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 851-859.
    4. Wei, Jun & Liao, Xiaofeng & Wong, Kwok-wo & Xiang, Tao, 2006. "A new chaotic cryptosystem," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1143-1152.
    5. Behnia, S. & Akhshani, A. & Mahmodi, H. & Akhavan, A., 2008. "A novel algorithm for image encryption based on mixture of chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 408-419.
    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. Smaoui, Nejib & Kanso, Ali, 2009. "Cryptography with chaos and shadowing," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2312-2321.
    2. Xiang, Tao & Wong, Kwok-Wo & Liao, Xiaofeng, 2009. "On the security of a novel key agreement protocol based on chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 672-675.
    3. Wong, Kwok-Wo & Kwok, Bernie Sin-Hung & Yuen, Ching-Hung, 2009. "An efficient diffusion approach for chaos-based image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2652-2663.
    4. Behnia, S. & Akhshani, A. & Akhavan, A. & Mahmodi, H., 2009. "Applications of tripled chaotic maps in cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 505-519.
    5. Bowen Zhang & Lingfeng Liu, 2023. "Chaos-Based Image Encryption: Review, Application, and Challenges," Mathematics, MDPI, vol. 11(11), pages 1-39, June.
    6. Wang, Yong & Wong, Kwok-Wo & Liao, Xiaofeng & Xiang, Tao & Chen, Guanrong, 2009. "A chaos-based image encryption algorithm with variable control parameters," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1773-1783.
    7. Lian, Shiguo, 2009. "Efficient image or video encryption based on spatiotemporal chaos system," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2509-2519.
    8. Yang, Jiyun & Liao, Xiaofeng & Yu, Wenwu & Wong, Kwok-wo & Wei, Jun, 2009. "Cryptanalysis of a cryptographic scheme based on delayed chaotic neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 821-825.
    9. Akhavan, A. & Samsudin, A. & Akhshani, A., 2009. "Hash function based on piecewise nonlinear chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1046-1053.
    10. Mazloom, Sahar & Eftekhari-Moghadam, Amir Masud, 2009. "Color image encryption based on Coupled Nonlinear Chaotic Map," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1745-1754.
    11. Mi, Bo & Liao, Xiaofeng & Chen, Yong, 2008. "A novel chaotic encryption scheme based on arithmetic coding," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1523-1531.
    12. Runze Zhang & Yujie Zhu & Zhongshen Liu & Guohong Feng & Pengfei Diao & Hongen Wang & Shenghong Fu & Shuo Lv & Chen Zhang, 2023. "A Back Propagation Neural Network Model for Postharvest Blueberry Shelf-Life Prediction Based on Feature Selection and Dung Beetle Optimizer," Agriculture, MDPI, vol. 13(9), pages 1-31, September.
    13. Han, S. & Chang, E. & Dillon, T. & Hwang, M. & Lee, C., 2009. "Identifying attributes and insecurity of a public-channel key exchange protocol using chaos synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2569-2575.
    14. YuYan Bian & WenXin Yu, 2021. "A secure communication method based on 6-D hyperchaos and circuit implementation," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 77(4), pages 731-751, August.
    15. Yang, Degang & Liao, Xiaofeng & Wang, Yong & Yang, Huaqian & Wei, Pengcheng, 2009. "A novel chaotic block cryptosystem based on iterating map with output-feedback," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 505-510.
    16. Rhouma, Rhouma & Meherzi, Soumaya & Belghith, Safya, 2009. "OCML-based colour image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 309-318.
    17. Rech, Paulo C., 2009. "A coupling of three quadratic maps," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1949-1952.
    18. Zhang, Linhua, 2008. "Cryptanalysis of the public key encryption based on multiple chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 669-674.
    19. Borislav Stoyanov & Gyurhan Nedzhibov & Dimitar Dobrev & Tsvetelina Ivanova, 2023. "Application of Decimated Mathematical Equations and Polynomial Root-Finding Method in Protection of Text Messages," Mathematics, MDPI, vol. 11(24), pages 1-13, December.
    20. Yang, Huaqian & Liao, Xiaofeng & Wong, Kwok-wo & Zhang, Wei & Wei, Pengcheng, 2009. "A new cryptosystem based on chaotic map and operations algebraic," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2520-2531.

    More about this item

    Statistics

    Access and download statistics

    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:40:y:2009:i:1:p:362-369. 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.