IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v123y2019icp69-78.html
   My bibliography  Save this article

Image encryption using finite-precision error

Author

Listed:
  • Nardo, Lucas G.
  • Nepomuceno, Erivelton G.
  • Arias-Garcia, Janier
  • Butusov, Denis N.

Abstract

Chaotic systems are broadly adopted to generate pseudo-random numbers used in encryption schemes. However, when implemented on a finite precision computer, chaotic systems end up in dynamical degradation of chaotic properties. Many works have been proposed to address this issue. Nevertheless, little attention has been paid to exploit the finite precision as a source of randomness rather a feature that should be mitigated. This paper proposes a novel plain-image encryption using finite-precision error. The error is obtained by means of the implementation of a chaotic system using two natural different interval extensions. The generated sequence has passed all NIST test, which means it has sufficient randomness to be used in encryption. Several benchmark images have been effectively encrypted using the proposed approach.

Suggested Citation

  • Nardo, Lucas G. & Nepomuceno, Erivelton G. & Arias-Garcia, Janier & Butusov, Denis N., 2019. "Image encryption using finite-precision error," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 69-78.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:69-78
    DOI: 10.1016/j.chaos.2019.03.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919300918
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.03.026?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. Wafaa S. Sayed & Ahmed G. Radwan & Ahmed A. Rezk & Hossam A. H. Fahmy, 2017. "Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications," Complexity, Hindawi, vol. 2017, pages 1-21, February.
    2. 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.
    3. Nepomuceno, Erivelton G. & Martins, Samir A.M. & Silva, Bruno C. & Amaral, Gleison F.V. & Perc, Matjaž, 2018. "Detecting unreliable computer simulations of recursive functions with interval extensions," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 408-419.
    4. Nepomuceno, Erivelton Geraldo & Mendes, Eduardo M.A.M., 2017. "On the analysis of pseudo-orbits of continuous chaotic nonlinear systems simulated using discretization schemes in a digital computer," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 21-32.
    5. Peixoto, Márcia L.C. & Nepomuceno, Erivelton G. & Martins, Samir A.M. & Lacerda, Márcio J., 2018. "Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 36-43.
    6. Nepomuceno, Erivelton G. & Lima, Arthur M. & Arias-García, Janier & Perc, Matjaž & Repnik, Robert, 2019. "Minimal digital chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 62-66.
    7. Yashuang Deng & Hanping Hu & Lingfeng Liu, 2015. "Feedback control of digital chaotic systems with application to pseudorandom number generator," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 26(02), pages 1-20.
    8. Elmanfaloty, Rania A. & Abou-Bakr, Ehab, 2019. "Random property enhancement of a 1D chaotic PRNG with finite precision implementation," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 134-144.
    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. Kamal, F.M. & Elsonbaty, A. & Elsaid, A., 2021. "A novel fractional nonautonomous chaotic circuit model and its application to image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Bowen Zhang & Lingfeng Liu, 2023. "Chaos-Based Image Encryption: Review, Application, and Challenges," Mathematics, MDPI, vol. 11(11), pages 1-39, June.
    3. Wang, Xingyuan & Yang, Jingjing & Guan, Nana, 2021. "High-sensitivity image encryption algorithm with random cross diffusion based on dynamically random coupled map lattice model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Zhang, Sen & Zheng, Jiahao & Wang, Xiaoping & Zeng, Zhigang, 2021. "A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. 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).
    6. 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.
    7. 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).
    8. Fan, Chunlei & Ding, Qun, 2023. "Constructing n-dimensional discrete non-degenerate hyperchaotic maps using QR decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    9. Jaishree Jain & Arpit Jain & Saurabh Kumar Srivastava & Chaman Verma & Maria Simona Raboaca & Zoltán Illés, 2022. "Improved Security of E-Healthcare Images Using Hybridized Robust Zero-Watermarking and Hyper-Chaotic System along with RSA," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    10. Ali Kanso & Mohammad Ghebleh & Mazen Bou Khuzam, 2022. "A Probabilistic Chaotic Image Encryption Scheme," Mathematics, MDPI, vol. 10(11), pages 1-26, June.
    11. 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).
    12. 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).

    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. 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).
    2. Guedes, Priscila F.S. & Mendes, Eduardo M.A.M. & Nepomuceno, Erivelton, 2022. "Effective computational discretization scheme for nonlinear dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    3. Mehmood, Ammara & Raja, Muhammad Asif Zahoor & Ninness, Brett, 2024. "Design of fractional-order hammerstein control auto-regressive model for heat exchanger system identification: Treatise on fuzzy-evolutionary computing," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. Elmanfaloty, Rania A. & Abou-Bakr, Ehab, 2019. "Random property enhancement of a 1D chaotic PRNG with finite precision implementation," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 134-144.
    5. Zheng, Jun & Hu, Hanping & Ming, Hao & Zhang, Yanxia, 2021. "Design of a hybrid model for construction of digital chaos and local synchronization," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    6. Amaral, Gleison F.V. & Nepomuceno, Erivelton G., 2018. "A smooth-piecewise model to the Cord Attractor," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 31-35.
    7. Ren, Weikai & Jin, Zhijun, 2023. "Phase space visibility graph," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    8. Nepomuceno, Erivelton G. & Martins, Samir A.M. & Silva, Bruno C. & Amaral, Gleison F.V. & Perc, Matjaž, 2018. "Detecting unreliable computer simulations of recursive functions with interval extensions," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 408-419.
    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. Nepomuceno, Erivelton G. & Lima, Arthur M. & Arias-García, Janier & Perc, Matjaž & Repnik, Robert, 2019. "Minimal digital chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 62-66.
    11. Yang, Zhen & Liu, Yinzhe & Wu, Yuqi & Qi, Yunliang & Ren, Fengyuan & Li, Shouliang, 2023. "A high speed pseudo-random bit generator driven by 2D-discrete hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    12. Peixoto, Márcia L.C. & Nepomuceno, Erivelton G. & Martins, Samir A.M. & Lacerda, Márcio J., 2018. "Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 36-43.
    13. 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).
    14. 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.
    15. Lai, Qiang & Hu, Genwen & Erkan, Uǧur & Toktas, Abdurrahim, 2023. "High-efficiency medical image encryption method based on 2D Logistic-Gaussian hyperchaotic map," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    16. Yildirim, Gokce & Tanyildizi, Erkan, 2023. "An innovative approach based on optimization for the determination of initial conditions of continuous-time chaotic system as a random number generator," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    17. Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Khalaf, Abdul Jalil M. & Alsaedi, Ahmed & Pham, Viet-Thanh & Hayat, Tasawar, 2018. "Investigation of dynamical properties in a chaotic flow with one unstable equilibrium: Circuit design and entropy analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 7-13.
    18. Valle, João & Bruno, Odemir M., 2024. "Dynamics and patterns of the least significant digits of the infinite-arithmetic precision logistic map orbits," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    19. Çavuşoğlu, Ünal & Akgül, Akif & Zengin, Ahmet & Pehlivan, Ihsan, 2017. "The design and implementation of hybrid RSA algorithm using a novel chaos based RNG," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 655-667.
    20. Liu, Hongjun & Kadir, Abdurahman & Xu, Chengbo, 2020. "Cryptanalysis and constructing S-Box based on chaotic map and backtracking," Applied Mathematics and Computation, Elsevier, vol. 376(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:eee:chsofr:v:123:y:2019:i:c:p:69-78. 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.