The large key space image encryption algorithm based on modulus synchronization between real and complex fractional-order dynamical systems

This paper constructs and analyzes the dynamical properties of a new fractional-order real hyper-chaotic system and its corresponding complex variable system. A thorough analysis was done by employing stability of equilibrium points, phase plots, Lyapunov spectrum, and bifurcation analysis for the consequences of varying fractional-order derivative and parameter values on the system. For the first time, a modulus synchronization scheme is proposed to synchronize real and complex fractional-order dynamical systems. Based on Lyapunov stability theory, non-linear controllers are designed to achieve the proposed modulus synchronization scheme. A new modulus synchronization encryption algorithm with a large key space size for digital images is introduced for the application. The experimental results and analysis validate the desired algorithm. Also, we compare our result of the new encryption algorithm with the previously published literature and verify the efficacy of the considered scheme. Numerical simulations are given to validate the theoretical analysis