Medical images contain rich individual health information, making the protection of their privacy and security crucial. This study first proposes a novel multi-segment memristor based on a multi-segment linear function. Then, building upon the Sprott-B chaotic system, a mirror-symmetric memristor multi-scroll chaotic attractor (MMSCAs) is introduced by incorporating logic pulse signals and the novel multi-segment memristor. Dynamic analysis of MMSCAs is conducted from four aspects: equilibrium points, Lyapunov exponents and bifurcations, coexisting attractors, and complexity. Lyapunov exponents and bifurcation diagram analysis reveal rich dynamical behaviors in MMSCAs, including inverse period-doubling bifurcations, burst chaotic, transient chaotic, and offset boosting. MMSCAs exhibit periodic and chaotic attractors co-existing under different initial conditions, along with multi-stability and super multi-stability. Complexity analysis results indicate that MMSCAs possess higher complexity and better randomness compared to other memristor chaotic systems. The accuracy of the MMSCAs mathematical model is verified through circuit design and simulation, and the implementation of MMSCAs in the embedded domain is extended using the STM32 microcontroller. Finally, a new cryptographic system is designed by integrating MMSCAs with RNA computation and applied to medical image encryption. The security of the cryptographic system is evaluated through key space and sensitivity, histogram, and correlation, while its robustness is evaluated through resistance to cropping and noise. The analysis results demonstrate high security and strong robustness of the cryptographic system, offering a novel solution for the protection of medical image information.

中文翻译：

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基于新型多段忆阻器的多涡卷混沌吸引子设计及其在医学图像加密中的应用

医学图像包含丰富的个人健康信息，保护其隐私和安全至关重要。本研究首先提出了一种基于多段线性函数的新型多段忆阻器。然后，在 Sprott-B 混沌系统的基础上，通过结合逻辑脉冲信号和新颖的多段忆阻器，引入了镜像对称忆阻器多涡卷混沌吸引器（MMSCA）。MMSCA的动态分析从平衡点、Lyapunov指数和分岔、共存吸引子和复杂度四个方面进行。Lyapunov 指数和分岔图分析揭示了 MMSCA 中丰富的动力学行为，包括反倍周期分岔、突发混沌、瞬态混沌和偏移增强。MMSCAs 表现出在不同初始条件下共存的周期性吸引子和混沌吸引子，以及多稳定性和超多稳定性。复杂性分析结果表明，与其他忆阻混沌系统相比，MMSCA 具有更高的复杂性和更好的随机性。通过电路设计和仿真验证了MMSCA数学模型的准确性，并利用STM32微控制器扩展了MMSCA在嵌入式领域的实现。最后，将MMSCA与RNA计算相结合，设计了一种新的密码系统，并将其应用于医学图像加密。密码系统的安全性通过密钥空间和敏感性、直方图和相关性来评估，而鲁棒性则通过抗剪裁和噪声来评估。分析结果表明该密码系统安全性高、鲁棒性强，为医学图像信息的保护提供了一种新颖的解决方案。