nD-NDHS: An n-Dimensional Non-Degenerate Hyperchaotic System with Controllable All-Positive Lyapunov Exponents

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.