Medical image encryption based on RNG with an autonomous piecewise damping Josephson junction jerk oscillator embedded in FPGA

This paper explore the dynamics, Field Programmable Gate Array (FPGA) validation of an autonomous piecewise damping Josephson junction jerk oscillator (APDJJJO) and uses it to protect medical images based on random number generator (RNG). APDJJJO is derived from a piecewise damping Josephson junction (JJ) model and has either no equilibrium points or two unstable equilibrium points. One-scroll chaotic hidden attractor, one-scroll sovereign complex attractor, periodic and one-scroll complex self-driven attractors coexisting, and bistable limit cycles are found in APDJJJO during the investigation based on numerical simulations. Additionally, the FPGA validation of the APDJJJO shows similar complex characteristics to those obtained during the investigation via numerical simulations. Lastly, the chaotic characteristics depicted by the APDJJJO are used to design a RNG for the encryption of medical images. The generated random bits are validated successfully by standard statistical tool set by the National Institute of Standards and Technology (NIST-800-22). Encryption algorithm is developed to secure a medical image by exploring the unpredicted bits generated. The safety and performances analysis are done to prove the robustness and efficiency of the image encryption algorithm.