An Efficient Image Encryption Method Based on Enhanced Josephus Problem and a Non-Invertible Economic Map


  • Ahmed Kareem Shibeeb
  • Mohammed Hussein Ahmed
  • Salah Albermany



Josephus problem, Image encryption, Two-dimensional chaotic map, Chaos-based cryptography


As an increasing number of digital images are created and transmitted over the internet, there is growing concern over their unauthorized use, which has a big impact on both security and privacy concerns. In this research, we provide a fast and secure image encryption scheme by using an enhanced Josephus problem and two-dimensional non-invertible economic chaotic map (2D-ECM) to safely and covertly protect digital image information throughout public channel transmission. First, the initial values of the 2D-ECM map are generated based on Secure Hash Algorithm (SHA-256) and the input secret key. Then, the Josephus problem is enhanced by substituting the extract operation with location exchange and dynamic start location and step size is employed to scramble the image pixels. In order to integrate the confusion process and diffusion process, the enhanced Josephus problem is utilized indirectly to choose two random columns from the scrambled image and random image to XOR them with the current column. The evaluation results prove that the proposed image cryptosystem is more efficient compared to existing cryptosystems.


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How to Cite

Shibeeb, A. K., Ahmed, M. H., & Albermany, S. (2023). An Efficient Image Encryption Method Based on Enhanced Josephus Problem and a Non-Invertible Economic Map. International Journal of Computing, 22(4), 493-501.