A Pseudo-Random Generator Whose Output is a Normal Sequence

Abstract

Pseudo-random number generators (PRNGs) are widely used in computer simulation, cryptography, and many other fields. In this paper, we describe a PRNG class, which, firstly, has been successfully tested using the most powerful modern test batteries, and secondly, is proved to consist of generators that generate normal sequences. The latter property means that, for any generated sequence [Formula: see text] and any binary word [Formula: see text], we have [Formula: see text] where [Formula: see text] is the number of occurrences of [Formula: see text] in the sequence [Formula: see text], [Formula: see text].