Image encryption algorithm based on matrix projective combination-combination synchronization of an 11-dimensional time delayed hyperchaotic system

Abstract Secure image transmission is critical to protect sensitive data from unauthorized access, especially in an era of increasing digital threats. Chaotic systems with their inherent complexity and unpredictability, provide a promising solution for enhancing encryption security. To contribute to this field, we investigate a new 11-dimensional hyperchaotic system by taking advantage of its complex dynamical properties to strengthen security. The high dimensional of the system intensifies chaotic behaviors such as stability, attractors and sensitive to initial conditions, making it particularly suitable for encrypted transmission.
 Time delay is an important factor to be considered affecting the control and synchronization in nonlinear system. Additionally, time delays include the effects of past states, further increasing the unpredictability of the system. To explore these dynamics, we analyze the Lyapunov exponents, stability of equilibrium points, symmetry and dissipation. A matrix projective combination-combination synchronization scheme is proposed to synchronize four identical 11-dimensional hyperchaotic systems with time delay. Nonlinear active controllers designed based on Lyapunov stability theory are used to achieve this synchronization. This work advances an important idea for encryption and decryption algorithms, which is the secure transmission of images using affine encryption. In the affine encryption algorithm, the key is based on the solution of synchronized chaotic delayed systems and the private message of the sender and receiver. This proposed encryption and decryption algorithms have been applied on plain images. Numerical simulations and security analysis including key space, histogram, information entropy and correlation analysis are conducted to validate the theoretical results and encryption algorithm. Experimental analysis and comparisons with existing literature confirm the effectiveness and security of the proposed approach for cryptographic purposes.