This paper presents an analysis of random number generators based on continuous-time chaotic oscillators. Two different methods for random number generation have been studied: 1) Regular sampling of a chaotic waveform, and 2) Chaotic sampling of a regular waveform. Kernel density estimation is used to analytically describe the distribution of chaotic state variables and the probability density function corresponding to the output bit stream. Random bit sequences are generated using analytical equations and results from numerical simulations. Applying the concepts of autocorrelation and approximate entropy, randomness quality of the generated bit sequences are assessed to analyze relationships between the frequencies of the regular and chaotic waveforms used in both random number generation methods. It is demonstrated that in both methods, there exists certain ratios between the frequencies of regular and chaotic signal at which the randomness of the output bit stream changes abruptly. Furthermore, both random number generation methods have been compared against their immunity to interference from external signals. Analysis shows that chaotic sampling of regular waveform method provides more robustness against interference compared to regular sampling of chaotic waveform method.

This paper deals with the security of chaos-based “true” random number generators (RNG)s. An attack method is proposed to analyze the security weaknesses of chaos-based RNGs and its convergence is proved using a master slave synchronization scheme. Attack on a RNG based on a double-scroll attractor is also presented as an example. All secret parameters of the RNG are revealed where the only information available is the structure of the RNG and a scalar time series observed from the double-scroll attractor. Simulation and numerical results of the proposed attack method are given such that the RNG doesn't fulfill NIST-800-22 statistical test suite, not only the next bit but also the same output bit stream of the RNG can be reproduced.