Methods to improve the pseudo-random properties of chaotic maps

Abstract

The chaos theory has received increasing interest in the most diverse areas of knowledge. Recently a study introduced the approach called deep-zoom, through which it is possible to observe the change of the chaotic dynamics of the system making it more chaotic and its orbits with properties more appropriate for generators of pseudorandom numbers (PRNG). In this same line of research that was coined for “randomization“ of chaotic maps are the methods of \textit {discretization} and skipping. Recently the candidate carried out research using the mapping method with which improvement of chaotic properties was observed as a pseudorandom number generator (PRNG). Although there are many proposals that have been using chaos theory to propose PRNGs, few are concerned with improving the randomization of chaotic maps and consequently improving such PRNGs. Thus, this project aims to study and compare new ways of randomizing chaotic maps. For this, the four main methods that have been proposed in the literature will be investigated and compared when effectively used in PRNGs. The proposed methods will be evaluated by statistical tests of the traditional randomness of the literature. Mainly in relation to randomization, the project proposal addresses a recent field that presents a new challenge to the community and has a wide field of unexplored research to be developed. (AU)