Image Encryption Based on a Controllable Multi-Wing Chaotic System with Odd and Even Hidden Attractors

Abstract Multi-wing chaotic systems are highly valued for their complexity and pseudo-randomness, making them promising in applications like secure communication and image encryption. However, existing chaotic systems face limitations in attractor diversity and system dimensions, which restrict their effectiveness in complex encryption applications. In this paper, we construct a four-dimensional multi-wing chaotic system based on the Sprott-A chaotic system by introducing linear feedback control and additional state variables. Furthermore, by incorporating piecewise linear functions and new state variables, a five-dimensional multi-wing chaotic system with the characteristic of odd and even numbers of hidden attractors are developed. Odd multi-wing attractors have centrally symmetric complex trajectories, while even multi-wing attractors possess axisymmetric trajectories through the introduction of offset terms. This system overcomes the limitations of existing chaotic systems and significantly improves complexity, controllability, and pseudo-randomness, making it more suitable for encryption applications. Based on this system, we design a new color image encryption algorithm that uses chaotic sequences for pixel permutation and diffusion operations. The security analysis indicates that the algorithm offers a large key space, high sensitivity to initial conditions, and strong resistance to various attacks, providing a novel solution for complex encryption applications.