A novel infinitely coexisting attractor and its application in image encryption.

The security performance of image encryption schemes based on chaotic systems has been greatly improved. Specifically, those chaotic systems with high-dimension or special attractors have shown more benefits for enhancing performance. By introducing the tangent function, a 4-dimensional chaotic system with infinite coexisting attractors is constructed. And the dynamical behaviors are analyzed through phase diagrams, bifurcation diagrams, Lyapunov exponent spectrum and spectral entropy complexity diagram. The results demonstrate that the system exhibits self-replication with respect to the initial value y₀ and possesses rich dynamical properties, such as infinite coexisting attractors, sensitivity to initial values and period-doubling bifurcation. These characteristics make it suitable for chaotic cryptography applications. Subsequently, a lossless double color image encryption scheme is designed based on the constructed system. The scheme adopts a diffusion-scrambling-diffusion processing method, and cleverly utilizes the information of the original plaintext image in the scrambling process, which significantly enhances the ability to resist known plaintext attacks or selected plaintext attacks. The experimental results verify that the designed algorithm not only effectively encrypts color and grayscale images, but also allows for encryption images of any size. Moreover, the algorithm implementation process is efficient and ensures high security performance, effectively resisting differential attacks, rotation attacks and cropping attacks. This research exploration on the chaotic characteristics of the nonlinear high-dimensional system and its application in image encryption is expected to provide theoretical guidance in the field of secure communication. [ABSTRACT FROM AUTHOR]