Ultra-complex 5D cubic–trigonometric memristive hyperchaos featuring phase-space folding, fractal basins and high-entropy PRNG

This study presents a novel five-dimensional cubic–trigonometric memristive hyperchaotic system (5D-CTMHS) that exhibits dynamical complexity through the integration of flux-controlled memristive feedback, cubic nonlinearities, and trigonometric functions. The system generates hidden attractors and demonstrates two positive Lyapunov exponents (LEs), resulting in a Kaplan–Yorke dimension of D K Y ≈ 4 , achieving dynamical complexity. Bifurcation analysis reveals dense chaotic regimes and an early onset of chaos, while multistability analysis confirms the coexistence of over 140 distinct chaotic attractors, manifesting as a shattered phase space. The basin of attraction exhibits fractal boundaries with a box-counting dimension of D ≈ 1 . 75 and a basin entropy of H ≈ 5 . 19 bits, quantifying the high unpredictability and the system’s intricate structure. High-quality pseudorandom number generators (PRNGs) are fundamental primitives for robust encryption and authentication, where statistical fidelity and unpredictability are prerequisites for security. Two sequences of PRNGs are designed using the system’s state trajectories. The generated 640K-bit sequences pass all NIST SP 800-22 tests, all DIEHARD tests, and the TestU01 Crush battery with zero failures, demonstrating exceptional statistical randomness. The PRNG achieves an information entropy of 7.9998 bits, a key space of 2 684 , and a Hamming distance of 49.98%, with key sensitivity to the initial conditions confirmed at perturbations as 1 0 − 16 . These results represent an increase in chaotic complexity and an improvement in entropy over existing methods, demonstrating that the proposed PRNG provides the necessary statistical robustness to resist differential and brute-force attacks when integrated into cryptographic schemes.