Random number generation using chaotic dynamical maps

Abstract

Random numbers are necessary basic ingredients for simulation and modeling. Currently, linear congruential generators (LCGs) are typically used as random number generators (RNGs), which generate pseudorandom numbers (PRNs) by using linear functions and modulus. In this study, we propose some chaotic functions to generate PRNs, using the unpredictability property of dynamical chaotic maps. We suggest five different RNGs that are derived from three different chaotic maps: tent map, logistic map, and family of connecting maps. The uniformity and independence of the numbers generated through the five suggested RNGs are checked in three steps. Firstly, the histograms and serial plots are visually checked. Secondly, chi-square and Kolmogorov-Smirnov tests are applied to statistically test the uniformity of the generated numbers. Finally, runs tests and autocorrelation test are applied in order to check the independence of the numbers. The same tests are applied to compare the five suggested chaotic generators with some well-known conventionally used LCGs. It is concluded that the suggested generators perform nearly as well as LCGs and can lead to an alternative way of generating random numbers. More detailed mathematical, statistical, and numerical properties of the suggested generators constitute useful further research topics.