A comparative analysis on chaos-based random number generation methods

This paper presents a comparative analysis on random number generation methods based on continuous-time chaos and Poincaré map transformations. Chaotic systems are appealing to use in random number generators (RNGs) as they suggest high throughput data without need for statistical post-processing, and they can be implemented as electrical circuits with relatively less complex hardware. In this study, four commonly used chaos-based random bit generation methods have been analyzed in a comparative manner: (1) regular sampling of chaotic waveform (RSCW), (2) Chaotic sampling of chaotic waveform (CSCW), (3) chaotic sampling of regular waveform (CSRW), and (4) chaos-modulated dual oscillator architecture (CMDOA). A double-scroll attractor system is chosen as the chaotic oscillator and it is numerically simulated in normalized time domain to generate random bit sequences using each of the aforementioned methods. The concepts of autocorrelation and approximate entropy are used to assess the randomness of the generated output bitstreams and to make quantitative comparisons between the bit generation methods. The chaos-based random bit generation methods are compared in terms of three aspects: (1) data throughput capability, (2) robustness against changes in chaos-controlling parameters, (3) robustness against external interference. It is demonstrated that chaotic sampling of chaotic waveform method which is based on Poincaré map transformation provides higher robustness against external interference in comparison with other three methods. On the other hand, chaos-modulated dual oscillator architecture method, which is based on the times related to the Poincaré map, is shown to enable the highest data throughput among the aforementioned chaos-based bit generation methods. Additionally, this paper presents general guidelines which can be applied to the design of random number generators based on continuous-time chaotic oscillators.