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Square-Based Division Scheme for Image Encryption Using Generalized Fibonacci Matrices

Author

Listed:
  • Panagiotis Oikonomou

    (Department of Computer Science & Telecommunications, University of Thessaly, 35100 Lamia, Greece)

  • George K. Kranas

    (Department of Computer Science & Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece)

  • Maria Sapounaki

    (Department of Computer Science & Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece)

  • Georgios Spathoulas

    (Department of Computer Science & Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece
    Department of Information Security and Communication Technology, Norwegian University of Science and Technology, NO-2815 Gjovik, Norway)

  • Aikaterini Aretaki

    (Department of Computer Science & Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece
    NASK National Research Institute, 01-045 Warsaw, Poland)

  • Athanasios Kakarountas

    (Department of Computer Science & Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece)

  • Maria Adam

    (Department of Computer Science & Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece)

Abstract

This paper proposes a novel image encryption and decryption scheme, called Square Block Division-Fibonacci (SBD-Fibonacci), which dynamically partitions any input image into optimally sized square blocks to enable efficient encryption without resizing or distortion. The proposed encryption scheme can dynamically adapt to the image dimensions and ensure compatibility with images of varying and high resolutions, while it serves as a yardstick for any symmetric-key image encryption algorithm. An optimization model, combined with the Lagrange Four-Square theorem, minimizes trivial block sizes, strengthening the encryption structure. Encryption keys are generated using the direct sum of generalized Fibonacci matrices, ensuring key matrix invertibility and strong diffusion properties and security levels. Experimental results on widely-used benchmark images and a comparative analysis against State-of-the-Art encryption algorithms demonstrate that SBD-Fibonacci achieves high entropy, strong resistance to differential and statistical attacks, and efficient runtime performance—even for large images.

Suggested Citation

  • Panagiotis Oikonomou & George K. Kranas & Maria Sapounaki & Georgios Spathoulas & Aikaterini Aretaki & Athanasios Kakarountas & Maria Adam, 2025. "Square-Based Division Scheme for Image Encryption Using Generalized Fibonacci Matrices," Mathematics, MDPI, vol. 13(11), pages 1-31, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1781-:d:1665570
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    References listed on IDEAS

    as
    1. 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.
    2. Biban, Geeta & Chugh, Renu & Panwar, Anju, 2023. "Image encryption based on 8D hyperchaotic system using Fibonacci Q-Matrix," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Mandeep Kaur & Surender Singh & Manjit Kaur, 2021. "Computational Image Encryption Techniques: A Comprehensive Review," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-17, July.
    4. Wei Feng & Jing Zhang & Zhentao Qin & Ahmed A. Abd El-Latif, 2021. "A Secure and Efficient Image Transmission Scheme Based on Two Chaotic Maps," Complexity, Hindawi, vol. 2021, pages 1-19, November.
    Full references (including those not matched with items on IDEAS)

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