A synergistic pseudo-random number generator based on training-free multi-scale autoregressive Transformer and 3D-Lü chaos with application to image encryption

Addressing the challenges of dynamical degradation and entropy loss in digital chaotic systems under finite precision, this study investigates the statistical complexity and nonlinear dynamics of a novel Heterogeneous Pseudo-Random Number Generator (H-PRNG). The proposed system achieves a synergistic coupling between a training-free modified Visual Autoregressive (VAR) Transformer and the 3D-Lü chaotic system, constructing a dual-modal framework termed “VAR High-Dimensional Manifold - Chaotic Dynamic Masking”. By exploiting the high-dimensional manifold projections of a randomly initialized VAR architecture, we generate high-complexity topological entropy sources without the need for large-scale data training, thereby overcoming the resource dependency of conventional deep learning schemes. Furthermore, the ergodicity and sensitivity of the 3D-Lü system are leveraged to enhance diffusion and confusion, effectively suppressing short-period collapse. A hash-based parameter decoupling and chain feedback loop are incorporated to expand the state–space complexity, achieving a massive key space of 2³²⁰. The statistical independence and randomness of the generated sequences are rigorously verified through the NIST SP 800-22a test suite and information-theoretic measures. In image encryption validation, the system exhibits an information entropy nearing the theoretical limit (≈7.999) and robust resistance to differential attacks (NPCR ≈99.6%, UACI ≈33.4%). This work demonstrates the feasibility of utilizing training-free generative architectures as high-security, lightweight entropy sources for complex dynamical applications.