Reconsidering the Generalized Logistic Map as a Pseudo Random Bit Generator

Abstract

The purpose of the paper is to evidence the possibilities to use the generalized logistic map, known until now for its inability togenerate uniform pseudo random numbers, as a source for such numbers when certain restriction have been imposed. The cases whenthis is possible are shown and the results of the statistical tests applied for to the numbers are revealed. A good pseudo random bitgenerator must pass certain statistical tests to be a good candidate for cryptographic algorithms. There are three principles that are crucialfor such a task and we shall remind them in brief: the distribution of the numbers must be uniform; the number of ones and zeros must berelatively equal and the number of long sequences of ones and zeros must not exceed certain, well established, limits. Ill. 5, bibl. 8 (inEnglish; summaries in Lithuanian, English and Russian).