An Adaptive Bias-Corrected Pseudo-Random Number Generator Derived from Nondegenerate Chaotic Systems

The Pseudo-Random Number Generator (PRNG) designed using chaotic systems has been widely used in the field of security communication and some other privacy-required applications because of its excellent nonlinear dynamics. However, in practical engineering applications, the digital realization of chaotic systems on finite-precision hardware platforms inevitably triggers the problem of dynamics degradation, which, in turn, directly leads to the lack of stability of the PRNG in long-term operation, and seriously threatens the security and reliability of the system. In this paper, we construct an [Formula: see text]-dimensional nondegenerate chaotic system. Based on this system, we propose a PRNG construction method that employs a Graph Neural Network (GNN) for degradation detection and Light Gradient Boosting Machine (LightGBM) for adaptive bias correction. The method first models the higher-dimensional structured features of chaotic sequences by GNN, then realizes the accurate detection of degradation behaviors by the LightGBM, and finally introduces the discriminative result-driven state perturbation mechanism to realize the continuous nondegradation evolution of chaotic systems. The experimental results indicate that under the conditions of extremely scarce samples of degraded behaviors and highly unbalanced data, the proposed method exhibits excellent performance measured by all indicators of degradation detection, especially its Area Under the Receiver Operating Characteristic Curve (AUC) is as high as 0.9922, which indicates that the model has a very high confidence and differentiation ability in distinguishing degraded states from normal states. In addition, this PRNG significantly improves the statistical properties of its pseudo-random number sequence and successfully passes the NIST SP800-22 test, which effectively guarantees the long-term stability and reliability of the sequence. This study not only provides new ideas for the design of highly reliable nondegenerate PRNG, but also lays a theoretical foundation for the practical application of chaos theory in the field of secure communications.