Innovative Multiscroll 6-D Jerk Chaotic System and Its Application in Telemedicine

The rapid growth of telemedicine has intensified the need for advanced security mechanisms to protect medical images transmitted over open communication networks. Conventional encryption algorithms, while effective for general data protection, often struggle to achieve high security and real-time performance. Chaotic systems have gained considerable attention due to their deterministic yet unpredictable behavior, which makes them promising candidates for cryptographic applications. However, most existing jerk-based chaotic systems exhibit limited dimensionality and restricted control over multi-scroll attractors, thereby constraining their potential for secure image encryption. To overcome these limitations, this study proposes a modified six-dimensional jerk system formulated by integrating three nonlinear control functions into the classical jerk model while preserving its original state variables. The resulting system exhibits rich and tunable chaotic dynamics, capable of producing one-, two-, and three-dimensional multi-scroll attractors and coexisting attractors under different initial conditions. The system’s dynamic characteristics are comprehensively analyzed through bifurcation diagrams, Lyapunov exponents, Poincaré maps, and phase diagrams, confirming its broad chaotic range and high sensitivity to parameters and initial states. Furthermore, a chaos-based medical image encryption scheme is constructed using the proposed system by utilizing SHA-512 key generation and adaptive diffusion mechanisms. Experimental analyses demonstrate near-ideal information entropy ≈ 8.0, low pixel correlation, and strong key sensitivity. The extensive key space of 2512ensures robustness against brute-force attacks, while NPCR and UACI values are consistent with theoretical expectations, confirming resistance to differential attacks.