Image Encryption Scheme Based on Hyper-Chaotic Map and Self-Adaptive Diffusion

TL;DR

This work tackles secure image encryption by jointly optimizing chaotic dynamics and diffusion effectiveness. It introduces the 2D-RA chaotic map, a hyper-chaotic function built from the Rastrigin and Ackley bases, and a self-adaptive diffusion method that promotes near-uniform grayscale distribution. The authors demonstrate strong chaotic properties (e.g., LE and KE) and superior encryption metrics (histogram flatness, NPCR, CC, and IE) compared with state-of-the-art schemes, using SHA-256-derived keys and a reversible encryption pipeline. While effective, the method shows limitations against cropping and certain image patterns, pointing to directions for robustifying diffusion and expanding applicability to varied image types. Overall, the approach offers a high-security, diffusion-driven encryption framework with practical potential for color images and secure communications.

Abstract

In the digital age, image encryption technology acts as a safeguard, preventing unauthorized access to images. This paper proposes an innovative image encryption scheme that integrates a novel 2D hyper-chaotic map with a newly developed self-adaptive diffusion method. The 2D hyper-chaotic map, namely the 2D-RA map, is designed by hybridizing the Rastrigin and Ackley functions. The chaotic performance of the 2D-RA map is validated through a series of measurements, including the Bifurcation Diagram, Lyapunov Exponent (LE), Initial Value Sensitivity, 0 - 1 Test, Correlation Dimension (CD), and Kolmogorov Entropy (KE). The results demonstrate that the chaotic performance of the 2D-RA map surpasses that of existing advanced chaotic functions. Additionally, the self-adaptive diffusion method is employed to enhance the uniformity of grayscale distribution. The performance of the image encryption scheme is evaluated using a series of indicators. The results show that the proposed image encryption scheme significantly outperforms current state-of-the-art image encryption techniques. Code is available at: https://github.com/Tang-Yiqi/Image-Encryption-Scheme-Based-on-Hyper-Chaotic-Mapping-and-Self-Adaptive-Diffusion Code is available at: https://github.com/Tang-Yiqi/Image-Encryption-Scheme-Based-on-Hyper-Chaotic-Mapping-and-Self-Adaptive-Diffusion

Figures (19)

• Figure 1: Bifurcation Diagram of 2D-RA Function. a) $\alpha \in [0,200], \beta=1, x_{init}=0.5, y_{init}=0.5$ b) $\alpha=1, \beta \in [0,200], x_{init}=0.5, y_{init}=0.5$
• Figure 2: Attractor Phase Diagram of 2D-RA chaotic map. $\alpha=1,\beta=1,x_{init}=0.5,y_{init}=0.5$
• Figure 3: Lyapunov Exponent of 2D-RA map. a) $\alpha \in [0,100], \beta=1, x_{init}=0.5, y_{init}=0.5$ b) $\alpha=1, \beta \in [0,100], x_{init}=0.5, y_{init}=0.5$
• Figure 4: Initial Value Sensitivity Test of 2D-RA Function ($\alpha=1,\beta=1,x_{init0}=0.5,x_{init1}=0.5+10^{-9},y_{init0}=y_{init1}=0.5$)
• Figure 5: 0-1 Test of 2D-RA map. a) $\alpha \in [0,100], \beta=1, x_0=0.5, y_0=0.5$ b) $\alpha=1, \beta \in [0,100], x_0=0.5, y_0=0.5$