A novel image encryption scheme using 3D chaotic maps with Josephus permutation and dynamic diffusion

Abstract

With the rapid development of digital communication, cloud computing, and intelligent applications such as smart healthcare and the Internet of Things (IoT), secure image transmission has become a critical challenge. Traditional encryption algorithms often face limitations including narrow key spaces, insufficient sensitivity to initial parameters, and weak resistance to statistical and differential attacks, leaving encrypted images vulnerable to security breaches. To address this gap, we propose a novel image encryption algorithm that integrates a three-dimensional Chebyshev-Henon hyperchaotic map (3D-CHM), Josephus permutation, wavelet transform, and a Gaussian noise-driven diffusion mechanism. First, the 3D-CHM generates complex, unpredictable chaotic sequences with high sensitivity to initial conditions, providing a substantially larger key space. Second, a pixel substitution strategy combining Josephus permutation and chaotic sequences ensures global pixel shuffling and effectively reduces inter-pixel correlation. Third, a dynamic diffusion process incorporating Gaussian noise further enhances robustness against various attacks. Experimental results demonstrate that the proposed algorithm achieves a vast key space of approximately 2256, strong resistance against brute-force, statistical, and differential attacks, and excellent performance metrics (Number of Pixels Change Rate (NPCR) = 99.609463%, Uniform Average Change Intensity (UACI) = 33.462821%). Comparative evaluations with state-of-the-art schemes confirm the superior security, efficiency, and robustness of our method across images of different resolutions. These results highlight the potential of the proposed scheme for practical deployment in privacy-critical scenarios such as medical image protection and IoT-based visual data security.