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An Image-Encipherment Algorithm Using a Combination of a One-Dimensional Chaotic Map and a Three-Dimensional Piecewise Chaotic Map

Author

Listed:
  • Sameh Askar

    (Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Ahmad Alshamrani

    (Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Aesha Elghandour

    (Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Abdelrahman Karawia

    (Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

One-dimensional and three-dimensional piecewise chaotic maps are used to propose an image-encipher technique in this article. First, the logistic map is used to construct the pseudo-random sequence. After that, this sequence is used to scramble the plain image. Next, the three-dimensional piecewise chaotic map has produced a mask of the chaotic sequence. After doing some preprocessing steps on the mask, a bit-wise XOR operation with the mask is applied to the shuffled image. The suggested algorithm is used to encipher and decipher a different range of images. To check the algorithm security and efficiency, the algorithm performance was calculated using multiple statistical tests and compared to several recent algorithms. Furthermore, numerical simulations and experimental data are also used to validate the proposed algorithm’s resistance to various attacks.

Suggested Citation

  • Sameh Askar & Ahmad Alshamrani & Aesha Elghandour & Abdelrahman Karawia, 2023. "An Image-Encipherment Algorithm Using a Combination of a One-Dimensional Chaotic Map and a Three-Dimensional Piecewise Chaotic Map," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:352-:d:1030215
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    References listed on IDEAS

    as
    1. S. S. Askar & A. A. Karawia & Ahmad Alshamrani, 2015. "Image Encryption Algorithm Based on Chaotic Economic Model," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, January.
    2. Wang, Xingyuan & Li, Yanpei & Jin, Jie, 2020. "A new one-dimensional chaotic system with applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Majid Khan & Fawad Masood & Abdullah Alghafis & Muhammad Amin & Syeda Iram Batool Naqvi, 2019. "A novel image encryption technique using hybrid method of discrete dynamical chaotic maps and Brownian motion," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-23, December.
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