3D-multiscroll chaotic attractors design, circuit implementation and application to medical image encryption

Compared to traditional chaotic attractors, multiscroll chaotic attractors (MSCAs) have broad application potential in fields such as dynamical system research and information processing. This paper introduces 1D-MSCAs, 2D-MSCAs, and 3D-MSCAs based on the Sprott-A system by incorporating piecewise linear functions. Through a dynamical analysis using equilibrium points, Lyapunov exponents, and bifurcation diagrams, it is found that the MSCAs have no equilibrium points and possess hidden attractors. The system exhibits a rich variety of dynamical behaviors, including reverse multiplicative cycle bifurcation, transient chaos, and bursting chaos, as the parameters vary. Additionally, the system demonstrates initial offset behavior in response to changes in initial conditions. The MSCAs are validated through an analog circuit implementation. Furthermore, a novel cryptosystem is designed by integrating 3D-MSCAs with RNA operations, and its security performance is evaluated in terms of key sensitivity, histogram analysis, correlation, and information entropy. The analysis results indicate that the proposed cryptosystem offers high-security performance, providing a promising solution for medical image encryption.