Integrating Fractional-Order Hopfield Neural Network with Differentiated Encryption: Achieving High-Performance Privacy Protection for Medical Images

Medical images demand robust privacy protection, driving research into advanced image encryption (IE) schemes. However, current IE schemes still encounter certain challenges in both security and efficiency. Fractional-order Hopfield neural networks (HNNs) demonstrate unique advantages in IE. The introduction of fractional-order calculus operators enables them to possess more complex dynamical behaviors, creating more random and unpredictable keystreams. To enhance privacy protection, this paper introduces a high-performance medical IE scheme that integrates a novel 4D fractional-order HNN with a differentiated encryption strategy (MIES-FHNN-DE). Specifically, MIES-FHNN-DE leverages this 4D fractional-order HNN alongside a 2D hyperchaotic map to generate keystreams collaboratively. This design not only capitalizes on the 4D fractional-order HNN’s intricate dynamics but also sidesteps the efficiency constraints of recent IE schemes. Moreover, MIES-FHNN-DE boosts encryption efficiency through pixel bit splitting and weighted accumulation, ensuring robust security. Rigorous evaluations confirm that MIES-FHNN-DE delivers cutting-edge security performance. It features a large key space (2383), exceptional key sensitivity, extremely low ciphertext pixel correlations (<0.002), excellent ciphertext entropy values (>7.999 bits), uniform ciphertext pixel distributions, outstanding resistance to differential attacks (with average NPCR and UACI values of 99.6096% and 33.4638%, respectively), and remarkable robustness against data loss. Most importantly, MIES-FHNN-DE achieves an average encryption rate as high as 102.5623 Mbps. Compared with recent leading counterparts, MIES-FHNN-DE better meets the privacy protection demands for medical images in emerging fields like medical intelligent analysis and medical cloud services.