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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
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    References listed on IDEAS

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    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. 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.
    4. 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.
    5. 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.
    6. 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.
    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.
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    Cited by:

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    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).

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