Secure Color Image Encryption Using 9D Hyperchaotic System, Fibonacci Matrices of order m and Symplectic Quaternion-Fractional Hahn Moments

This work presents a novel scheme for encrypting color images. It leverages quaternion algebra, quaternion discrete fractional Hahn moments (QDFHM), Fibonacci matrices of order m, and a 9D complex chaotic system. The proposed scheme consists of two fundamental phases. The first phase leverages the capabilities of the 9D complex chaotic system with quaternions to generate a sequence of random numbers, which are used in the confusion process of the color image pixels, breaking the correlation between adjacent pixels. The second phase, diffusion, bolsters our scheme’s resistance to statistical attacks. To achieve this, the original image is subdivided into 2 × 2 blocks. Each block is then multiplied by a Fibonacci matrix of order m. Finally, for enhanced security, a proposed symplectic form of quaternion discrete fractional Hahn moments (QDFHM) transform is applied to these modified blocks, yielding the encrypted color image. The conducted simulation in this study rigorously evaluates the proposed algorithm’s validity and security by subjecting it to various attack scenarios and statistical analyses. These include correlation coefficient analysis, differential attacks, key-space analysis, entropy analysis, key sensitivity analysis, noise robustness, and data occlusion. The comprehensive assessments demonstrate both high security and outstanding efficiency in color image encryption.