Classification of pseudo-random number generators by complex networks and computational geometry analysis

• Autor(a) principal: Alves, Marcela Lopes
• Data de Publicação: 2019
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/55/55134/tde-06012020-171245/
• topic: Aleatoriedade; Complex networks; Complex systems; Computational geometry; Geometria computacional; Randomness; Redes complexas; Sistemas complexos

Randomness has stimulated mankinds attention and imagination ever since we began to observe the behavior of nature. It was by understanding the randomness and patterns that humans learned to control crops, for example, which led to the creation of the first communities. In the modern world, with the aim of mimicking the randomness of natural phenomena, computers are used to generate sequences that look as random as possible running pseudo-random number generators (PRNG). PRNGs have diverse applications in information security, digital games, simulations, modeling, gambling, arts, among others. Despite this fact, existing methods of randomness measure do not offer a definitive solution to the need of classifying PRNGs. The main methods of randomness measurement consist of statistical tests through which the sequences generated by the algorithms are analyzed. Once PRNGs are analyzed by these test suits, they are considered (un)satisfactory random. This paper explores an aspect that has been neglected in statistical tests: the spatial distribution of pseudo-random sequences. It is conjectured that this distribution is the source of undisclosed patterns in test suites. One way to study this arrangement more depth is using models that explore the relation of values and iterations. The relation of elements in space has to be the basis of the paradigm. This work applies theory of graphs and computational geometry methods to find patterns in pseudo-random sequences. The analyzed sequences are plotted in a Cartesian plan generating a set of points that are converted into graphs considering the Euclidean distance between the points within a radius. The best combination of descriptors formed by measurements of graphs and geometric properties is selected. When patterns emerge, one can point out flaws in the widely used methods for measuring PRNGs quality. It is intended to suggest a complementary approach for the evaluation of PRNGs, contributing to a better classification of the PRNGs and, consequently, to cause improvements in the studies on information security. This includes identifying patterns in sequences generated by algorithms that are considered pseudo-random by current statistical tests and thus identifying the limitations of these assessments.