Design of multi-scroll chaotic attractor based on a novel multi-segmented memristor and its application in medical image encryption

Abstract

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.