A Search for Good Pseudo-random Number Generators : Survey and Empirical Studies

Abstract

This paper targets to search so-called \emph{good} generators by doing a brief survey over the generators developed in the history of pseudo-random number generators (PRNGs), verify their claims and rank them based on strong empirical tests in same platforms. To do this, the genre of PRNGs developed so far are explored and classified into three groups -- linear congruential generator based, linear feedback shift register based and cellular automata based. From each group, the well-known widely used generators which claimed themselves to be `\emph{good}' are chosen. Overall $30$ PRNGs are selected in this way on which two types of empirical testing are done -- blind statistical tests with Diehard battery of tests, battery \emph{rabbit} of TestU01 library and NIST statistical test-suite as well as graphical tests (lattice test and space-time diagram test). Finally, the selected PRNGs are divided into $24$ groups and are ranked according to their overall performance in all empirical tests.