Sistema de Lorenz i criptosistemes caòtics

Abstract

[en] In this work we study the Lorenz system and its application in the field of cryptography. Initially, from a theoretical point of view, we describe the most important properties and basic concepts of the system, in particular, we study the symmetry of the system, the invariance of the $z$ axis, the existence of a global attractor, the stability of the equilibrium points, bifurcations and we present basic notations of chaos theory in order to understand the main features of the behavior of the Lorenz system and its strange attractor. To do this, we use analytical and numerical tools. Later, from a more practical point of view, we present the synchronization of chaos that will allow us to introduce the concept of chaotic cryptography. Finally, we implement algorithms (in C) to encrypt and decrypt signals using the Lorenz system and analyze the dependence that exists between the error committed when recovering the original signal and the same signal.