Analytical Modeling of Continuous-Time Chaos Based Random Number Generators

This paper presents an analytical study about regular sampling of a continuous-time chaotic signal to make random number generators (RNGs). The procedure of choosing the sampling frequency to produce random bits is explored using the concept of autocorrelation. To mathematically describe the distribution and statistical properties of the underlying chaotic state variable, Kernel density estimation and polynomial regression methods have been studied. Applying these two methods, probability density function of the chaotic signal was defined analytically. Using the probability density function, bit distribution probability of the RNG has been investigated.