Efficient Colour Image Encryption Algorithm Using a New Fractional-Order Memcapacitive Hyperchaotic System

In comparison with integer-order chaotic systems, fractional-order chaotic systems exhibit more complex dynamics. In recent years, research into fractional chaotic systems for the utilization of image cryptosystems has become increasingly highlighted. This paper describes the development, testing, numerical analysis, and electronic realization of a fractional-order memcapacitor. Then, a new four-dimensional (4D) fractional-order memcapacitive hyperchaotic system is suggested based on this memcapacitor. Analytically and numerically, the nonlinear dynamic properties of the hyperchaotic system have been explored, where various methods, including equilibrium points, phase portraits of chaotic attractors, bifurcation diagrams, and the Lyapunov exponent, are considered to demonstrate the chaos behaviour of this new hyperchaotic system. Consequently, an encryption cryptosystem algorithm is used for colour image encryption based on the chaotic behaviour of the memcapacitive model, where every pixel value of the original image is incorporated in the secret key to strengthen the encryption algorithm pirate anti-attack robustness. For generating the keyspace of that employed cryptosystem, the initial condition values, parameters, and fractional-order derivative value(s) (q) of the memcapacitive chaotic system are utilized. The common cryptanalysis metrics are verified in detail by histogram, keyspace, key sensitivity, correlation coefficient values, entropy, time efficiency, and comparisons with other recent related fieldwork in order to demonstrate the security level of the proposed cryptosystem approach. Finally, images of various sizes were encrypted and recovered to ensure that the utilized cryptosystem approach is capable of encrypting/decrypting images of various sizes. The obtained experimental results and security metrics analyses illustrate the excellent accuracy, high security, and perfect time efficiency of the utilized cryptosystem, which is highly resistant to various forms of pirate attacks.