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An Image Encryption Algorithm Utilizing Julia Sets and Hilbert Curves

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  • Yuanyuan Sun
  • Lina Chen
  • Rudan Xu
  • Ruiqing Kong

Abstract

Image encryption is an important and effective technique to protect image security. In this paper, a novel image encryption algorithm combining Julia sets and Hilbert curves is proposed. The algorithm utilizes Julia sets’ parameters to generate a random sequence as the initial keys and gets the final encryption keys by scrambling the initial keys through the Hilbert curve. The final cipher image is obtained by modulo arithmetic and diffuse operation. In this method, it needs only a few parameters for the key generation, which greatly reduces the storage space. Moreover, because of the Julia sets’ properties, such as infiniteness and chaotic characteristics, the keys have high sensitivity even to a tiny perturbation. The experimental results indicate that the algorithm has large key space, good statistical property, high sensitivity for the keys, and effective resistance to the chosen-plaintext attack.

Suggested Citation

  • Yuanyuan Sun & Lina Chen & Rudan Xu & Ruiqing Kong, 2014. "An Image Encryption Algorithm Utilizing Julia Sets and Hilbert Curves," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-9, January.
    • Handle: RePEc:plo:pone00:0084655
    DOI: 10.1371/journal.pone.0084655
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    Cited by:

    1. Muhammad Tanveer & Waqas Nazeer & Krzysztof Gdawiec, 2020. "New Escape Criteria for Complex Fractals Generation in Jungck-CR Orbit," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1285-1303, December.
    2. Tassaddiq, Asifa, 2022. "General escape criteria for the generation of fractals in extended Jungck–Noor orbit," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 1-14.

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