Advanced medical image encryption techniques using the fractional-order Halvorsen circulant systems: dynamics, control, synchronization and security applications

In this paper, we describe the Halvorsen circulant system (HCS) with a fractional-order Caputo derivative and its qualitative properties. The numerical solution of the fractional order Halvorsen circulant system (FO-HCS) is proposed based on the Adomian decomposition method (ADM). The ADM method is used to solve fractional-order systems. Then, dynamics is analyzed using different methods including Lyapunov exponents, bifurcation diagrams, complexity, and phase diagrams. This paper also investigates the stabilization and synchronization of identical FO-HCS, and stability theory proves adaptive feedback control and synchronization. In addition, using the fractional-order system's remarkable properties to develop the image encryption technique using the extended fractional sequences. The proposed method uses a keystream generator for high security based on the enhanced fractional Halvorsen circulant chaotic behavior. The simulation results confirm that it can resist various attacks, including statistical analysis, differential attacks, brute-force attacks, known plaintext attacks, and chosen plaintext attacks, with high security, and low computational complexity. Finally, the results of the simulation and its performance prove that it's effective and secure in image data.