Fast and Secure Image Encryption Using Josephus Ring Permutation and Logistic Map Diffusion

Subject Areas : Computer Engineering

Zahra Rafieian Bahabadi ¹ , Ali Nodehi ^{2 *} , Rasul Enayatifar ³

1 - Department of Computer Engineering, Go.C., Islamic Azad University, Gorgan, Iran
2 - Department of Computer Engineering, Go.C., Islamic Azad University, Gorgan, Iran
3 - Department of Computer Engineering, Fi.C., Islamic Azad ‎University, Firoozkooh, Iran

Received: 2025-04-12 Accepted : 2025-07-16 Published : 2025-06-25

Keywords: Image encryption, Josephus Ring, logistic map chaotic function,

Abstract :

In recent years, the demand for efficient and secure image encryption techniques has grown significantly due to the increasing transmission of sensitive visual data. This paper proposes a novel hybrid image encryption scheme combining a Josephus Ring-based permutation phase with a logistic map-based diffusion phase to achieve both high security and computational efficiency. In the permutation phase, pixel positions are dynamically swapped using a Josephus Ring traversal, effectively disrupting spatial correlations. Subsequently, the diffusion phase employs a chaotic logistic map to generate temporary keys, which are XORed with permuted pixel values to enhance randomness and resist statistical attacks. The proposed method leverages the simplicity of the Josephus Ring for fast permutation and the inherent unpredictability of chaotic maps for robust diffusion. Experimental results demonstrate that the algorithm achieves strong encryption performance, with high sensitivity to initial keys, resistance against differential attacks, and low computational overhead. Security analysis confirms its effectiveness in terms of key space robustness, statistical entropy, and resistance to common cryptographic threats. The combination of these two lightweight mechanisms makes the proposed scheme suitable for real-time secure image transmission applications.

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