Exploiting multi-scroll hyperchaotic system and Heap-Queue cross-block permutation for visually meaningful medical image encryption

Abstract Medical images contain patients' private health information, which is crucial to protect their security. Chaotic systems are frequently used in medical image encryption owing to their advantages, including unpredictability and sensitivity to initial conditions. However, existing low-dimensional, small-scroll chaotic systems exhibit limitations, leading to poor security of relevant medical image encryption schemes due to insufficient complexity and randomness. To tackle these issues, a novel 6-scroll Jerk hyperchaotic system (6-SJHS) is constructed and we investigate its application in securing medical images. The 6-SJHS is developed by extending the classical Jerk chaotic system (JCS), and its performance is evaluated comprehensively using the Lyapunov exponent (LE), phase diagram (PD), and the NIST randomness test, demonstrating excellent chaotic robustness and randomness. To reduce the adjacent pixels’ strong correlation in medical images, a cross-block permutation method based on the max heap and queue (CPMHQ) is introduced. Compared with the traditional method, the CPMHQ introduces a dynamic sorting mechanism and efficient block-level disorder, which can better reduce the strong correlation between pixels in medical images. Additionally, to improve the diffusion process, an extended RNA coding scheme is proposed, enabling a cross-plane diffusion method with extended RNA coding (CDERC) that propagates minor alterations across the entire image. The diffused ciphertext image is then subjected to secret image sharing (SIS), generating shadow images (SDIs) that are embedded into carrier images based on their features, resulting in visually meaningful ciphertext images. The analysis of simulation results and experiments confirms that our proposed encryption system offers significant improvements in security and robustness, can achieve more than 49 dB visual quality of steganographic images, and is applicable to encrypt images of different types and sizes, providing an effective solution for protecting medical image confidentiality.