Analytical Modeling of Chaotic Sampling of Regular Waveform for Random Number Generation

Abstract

In this paper, an analytic approach is taken towards the analysis of a class of true random generators where an irregular square wave generated by a continuous-time chaotic oscillator and a comparator structure is used to sample a regular continuous-time waveform. Numerical and analytic equations for probability distribution have been derived for D flip-flop topology. Kernel density estimation method is utilized to describe bit distribution in the output. Then random bits are generated using analytical formulas and results from numerical simulations. Using the concepts of auto correlation and approximate entropy, the relationship between the regular and the chaotic waveform frequencies needed to generate uncorrelated bit stream have been investigated.