A Hybrid Multi-Domain Color Image Encryption Algorithm Based on a 2D Fractional-Order Chaotic Map, 5D Gauss-Logistic Hyperchaotic System, and Iris-Biometric Key Distribution

This study proposes a hybrid multi-domain color image encryption algorithm that integrates a 2D Fractional-Order Chaotic Map (2D-FOCM), a 5D Gauss-Logistic Hyperchaotic System (5D-GLHS), two-level Discrete Wavelet Transform (DWT), and iris-biometric key distribution within a unified framework. The proposed architecture addresses three fundamental challenges simultaneously: the key distribution vulnerability of symmetric encryption, the limited dynamic complexity of integer-order chaotic systems, and the inadequacy of single-domain encryption approaches. The key distribution problem inherent in symmetric encryption is resolved through biometric uniqueness: rather than transmitting the encryption key directly, only an iris image is exchanged over a secure channel, and each party independently derives the chaotic control parameters from the iris ring region. Statistical features extracted from the iris ring region determine the control parameters of both the 2D-FOCM and the 5D-GLHS, establishing a user-specific, biometrically grounded dynamic key structure with an effective key space of 2149. The 2D-FOCM, constructed via the piecewise constant arguments method with a Caputo fractional-order derivative, exhibits a broader chaotic parameter range, higher Lyapunov exponents (LE1 ≈ 16.90, LE2 ≈ 16.96), and higher approximate entropy than its integer-order counterparts, thereby expanding the key space and suppressing periodic tendencies. The encryption pipeline combines two-level DWT-based frequency-domain subband permutation using 2D-FOCM sequences with five sequential spatial-domain operations directed by the 5D-GLHS: chaotic sequence sorting-based permutation, forward chaining diffusion, inter-block scrambling, intra-block permutation, and XOR diffusion. Comprehensive security evaluations demonstrate that the proposed method achieves the highest average information entropy (7.9975) among 14 compared methods, near-ideal differential attack resistance (NPCR: 99.6109–99.6292%; UACI: 33.3291–33.4308%), and near-zero pixel correlation coefficients across all channels and spatial directions. Chi-square test results confirm superior histogram uniformity in the G and B channels over all 12 compared methods. These results collectively validate the proposed algorithm as a robust and competitive solution for color image security.