Efficient and Robust Image Cryptosystem Utilizing a Fractional-Order Discrete Cross-Coupled Map and Fractal Dragon Curve

Fractional-order chaotic systems have gained immense popularity in image encryption due to their complex nonlinear dynamics and infinite memory effects. However, their excessive computational complexity remains a persistent bottleneck, severely hindering real-time engineering applications. To address this issue, a lightweight Two-Dimensional Fractional-Order Discrete Cross-Coupled Map (2D-FODCCM) is constructed based on the Short Memory Principle (SMP). This simplified map exhibits excellent dynamical behaviors and cryptographic properties, while its physical realizability and computational efficiency are successfully verified on an STM32 microcontroller. Furthermore, guided by modern cryptanalysis, an efficient and robust image cryptosystem is developed. It integrates a plaintext-associated mechanism to thwart chosen-plaintext attacks, a dynamic fractal Dragon Curve for global spatial permutation, and an innovative pixel fusion strategy to significantly boost encryption throughput. Comprehensive experimental validations demonstrate that the proposed scheme achieves a massive key space of 2511, exceptional execution efficiency of 123.61 Mbit/s for standard 512×512×3 color images, and outstanding robustness against severe noise and data occlusion, offering a highly practical solution for secure real-time multimedia communication.