2D-Cosine power sine coupled map with fractal-Fibonacci fusion for hyperchaotic image encryption

Image security is vital in sectors such as healthcare, defence, finance, and personal data exchange, where breaches of image integrity can result in severe consequences. To address this challenge, we propose a novel image encryption framework. It combines a Fractal-Fibonacci diffusion process based on the Hilbert curve, recursive scrambling guided by chaotic sequences, and a new chaotic map entitled the Two Dimensional Cosine Power Sine Coupled Map (2D-CPSCM). These components enhance randomness and ensure maximum efficiency, resistance against cryptographic attacks. The proposed two-dimensional chaotic system exhibits positive Lyapunov exponents and superior statistical properties compared to traditional systems, as demonstrated by high sample entropy, permutation entropy, and Kolmogorov entropy, confirming its hyperchaotic behaviour. The encryption system has been evaluated using extensive simulations on benchmark images. The findings demonstrate strong key sensitivity, with an entropy of 7.9994, Number of Pixel Change Rate (NPCR) of 99.6%, Unified Average Changing Intensity (UACI) of 33.47%, and Number of Bit Change Rate (NBCR) of 50%. Additionally, Structural Similarity Index Metric (SSIM) and Visual Information Fidelity (VIF) values of 1 between input and decrypted images guarantee successful decryption, whereas low Peak Signal to Noise Ratio (PSNR), SSIM, and VIF between input and encrypted images reduce information leakage. The superior security, resilience, and robustness of the 2D-CPSCM based approach against statistical, noise, and cropping attacks highlights its potential for safe multimedia transmission and useful cryptographic applications.