Constructing scalable, non-degenerate, and intensity-tunable high-dimensional hyperchaotic maps is a key challenge for chaotic cryptography. Existing n-dimensional real-valued chaotic systems frequently suffer from dynamical degradation, limited adjustability of Lyapunov exponents, and reduced complexity under high-dimensional settings. To mitigate these drawbacks, this paper proposes an n-dimensional non-degenerate hyperchaotic system (nD-NDHS). Rigorous theoretical derivations demonstrate that all Lyapunov exponents can be continuously adjusted to positive values using a single global control parameter, which guarantees stable hyperchaotic behavior for different tested dimensions. Four evaluation metrics including Lyapunov exponents, correlation dimension, sample entropy, and Kolmogorov entropy are adopted for comprehensive assessment, alongside comparisons with state-of-the-art n-dimensional chaotic maps. Bifurcation diagrams, phase trajectories and Lyapunov exponent spectra are employed to analyze multiple instantiations and validate the generality of the presented framework. A 4D instantiation is physically realized on an STM32 embedded platform, and the corresponding pseudorandom number generator is subjected to the complete NIST SP800-22 and TestU01 test suites. Experimental results reveal that nD-NDHS exhibits compelling chaotic properties and improved dimensional robustness, where all statistical tests are passed to confirm favorable statistical randomness. The proposed model provides a novel complexity-controllable and degradation-resistant hyperchaotic paradigm, which is well adapted to high-dimensional encryption and lightweight hardware-oriented pseudorandom number generation.

Pseudo-random number generators (PRNGs) are essential for cryptography, secure communications, and simulations. Traditional chaos-based PRNGs suffer from periodicity degradation, inadequate statistical properties, and security vulnerabilities. To address these limitations, this paper proposes a novel PRNG model based on a generative adversarial network (GAN) integrating BiLSTM and Transformer architectures, termed BiLSTM-Transformer-GAN. A hybrid training set constructed from multiple chaotic systems provides rich samples. Within the generator, BiLSTM captures short-term dependencies, a lightweight sparse Transformer enhances long-range features, and chaotic positional encoding improves sensitivity to initial conditions. The discriminator employs parallel multi-branch dilated convolutions to capture multi-scale temporal features. The model adopts the Wasserstein GAN with gradient penalty (WGAN-GP) framework to ensure statistical matching with real chaotic sequences while avoiding mode collapse. Experimental results show that the generated sequences pass all NIST SP 800-22 and TestU01 tests, achieving an information entropy of 7.98 and a Lyapunov exponent of 10.23. Furthermore, by embedding chaotic signals during training, the generator produces sequences in a single forward pass at inference, significantly reducing per-step computational cost compared with traditional iterative chaotic PRNGs. These results validate the model’s superior randomness, chaotic properties, computational efficiency, and cryptographic security, offering an innovative approach for high-security PRNG applications.