Haris Çalgan
Fractional-order chaotic systems have emerged as powerful tools in secure communications and multimedia protection owing to their memory-dependent dynamics, large key spaces, and high sensitivity to initial conditions. However, most existing fractional-order image encryption schemes rely on fixed-order chaos and conventional solvers, which limit their complexity and reduce unpredictability, while also neglecting the potential of variable fractional-order (VFO) dynamics. Although similar phenomena have been reported in some fractional-order systems, the coexistence of hidden attractors and stable equilibria has not been extensively investigated within VFO frameworks. To address these gaps, this paper introduces a novel discrete variable fractional-order dark matter–dark energy (VFODM-DE) chaotic system. The system is discretized using the piecewise constant argument discretization (PWCAD) method, enabling chaos to emerge at significantly lower fractional orders than previously reported. A comprehensive dynamic analysis is performed, revealing rich behaviors such as multistability, symmetry properties, and hidden attractors coexisting with stable equilibria. Leveraging these enhanced chaotic features, a pseudorandom number generator (PRNG) is constructed from the VFODM-DE system and applied to grayscale image encryption through permutation–diffusion operations. Security evaluations demonstrate that the proposed scheme offers a substantially large key space (approximately 2249) and exceptional key sensitivity. The scheme generates ciphertexts with nearly uniform histograms, extremely low pixel correlation coefficients (less than 0.04), and high information entropy values (close to 8 bits). Moreover, it demonstrates strong resilience against differential attacks, achieving average NPCR and UACI values of about 99.6% and 33.46%, respectively, while maintaining robustness under data loss conditions. In addition, the proposed framework achieves a high encryption throughput, reaching an average speed of 647.56 Mbps. These results confirm that combining VFO dynamics with PWCAD enriches the chaotic complexity and provides a powerful framework for developing efficient and robust chaos-based image encryption algorithms.