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La Paz, Febrero De 2010 UNIVERSIDAD POLITÉCNICA DE MADRID ESCUELA TÉCNICA SUPERIOR DE INGENIEROS INFORMÁTICOS CAMPUS MONTEGANCEDO TRABAJO DE FIN DE MÁSTER MÁSTER UNIVERSITARIO EN SOFTWARE Y SISTEMAS CIFRADO DE IMÁGENES DIGITALES BASADO EN TEORÍA DEL CAOS – MAPAS LOGÍSTICOS POSTULANTE: Marcos Espinoza Illanes TUTOR: Raúl Alonso MADRID, JULIO 2015 DEDICATORIA A Dios, Mi Salvador y guía en mi proyecto de vida que ha iluminado toda acción, palabra y pensamiento; siendo Él obrando a través de mí. AGRADECIMIENTOS Mis más sinceros agradecimientos: A mi Padre de los Cielos por guiarme y acompañarme durante toda la vida; y llenarme de sabiduría y fortaleza durante este proyecto. A mi papá Ramiro Espinoza Delgado por enseñarme con palabras y acciones que todo esfuerzo siempre tiene su recompensa; convirtiéndose en mi referente y modelo de hombre a seguir. A mi mamá María Elena Illanes de Espinoza por alentarme en los momentos de mayor debilidad y aconsejarme en los momentos de mayor incertidumbre. A mi hermanita Andy porque hizo mis preocupaciones suyas y su apoyo incondicional fueron otro incentivo para seguir adelante. Al Ing. Raúl Alonso, por haber creído en mis capacidades al inicio; por haberme apoyado académicamente y disuelto dudas durante el proceso; y por haberme acompañado en la satisfacción de haber culminado nuestro proyecto. Finalmente, pero no menos importante, a mis amigos de curso de Máster por compartir todos los estos meses llenos de anécdotas inolvidables y por su constante apoyo moral y académico. RESUMEN Las nuevas tendencias de compartir archivos multimedia a través de redes abiertas, demanda el uso de mejores técnicas de encriptación que garanticen la integridad, disponibilidad y confidencialidad, manteniendo y/o mejorando la eficiencia del proceso de cifrado sobre estos archivos. Hoy en día es frecuente la transferencia de imágenes a través de medios tecnológicos, siendo necesario la actualización de las técnicas de encriptación existentes y mejor aún, la búsqueda de nuevas alternativas. Actualmente los algoritmos criptográficos clásicos son altamente conocidos en medio de la sociedad informática lo que provoca mayor vulnerabilidad, sin contar los altos tiempos de procesamiento al momento de ser utilizados, elevando la probabilidad de ser descifrados y minimizando la disponibilidad inmediata de los recursos. Para disminuir estas probabilidades, el uso de la teoría de caos surge como una buena opción para ser aplicada en un algoritmo que tome partida del comportamiento caótico de los sistemas dinámicos, y aproveche las propiedades de los mapas logísticos para elevar el nivel de robustez en el cifrado. Es por eso que este trabajo propone la creación de un sistema criptográfico basado sobre una arquitectura dividida en dos etapas de confusión y difusión. Cada una de ellas utiliza una ecuación logística para generar números pseudoaleatorios que permitan desordenar la posición del píxel y cambiar su intensidad en la escala de grises. Este proceso iterativo es determinado por la cantidad total de píxeles de una imagen. Finalmente, toda la lógica de cifrado es ejecutada sobre la tecnología CUDA que permite el procesamiento en paralelo. Como aporte sustancial, se propone una nueva técnica de encriptación vanguardista de alta sensibilidad ante ruidos externos manteniendo no solo la confidencialidad de la imagen, sino también la disponibilidad y la eficiencia en los tiempos de proceso. ABSTRACT New trends to share multimedia files over open networks, demand the best use of encryption techniques to ensure the integrity, availability and confidentiality, keeping and/or improving the efficiency of the encryption process on these files. Today it is common to transfer pictures through technological networks, thus, it is necessary to update existing techniques encryption, and even better, the searching of new alternatives. Nowadays, classic cryptographic algorithms are highly known in the midst of the information society which not only causes greater vulnerability, but high processing times when this algorithms are used. It raise the probability of being deciphered and minimizes the immediate availability of resources. To reduce these odds, the use of chaos theory emerged as a good option to be applied on an algorithm that takes advantage of chaotic behavior of dynamic systems, and take logistic maps’ properties to raise the level of robustness in the encryption. That is why this paper proposes the creation of a cryptographic system based on an architecture divided into two stages: confusion and diffusion. Each stage uses a logistic equation to generate pseudorandom numbers that allow mess pixel position and change their intensity in grayscale. This iterative process is determined by the total number of pixels of an image. Finally, the entire encryption logic is executed on the CUDA technology that enables parallel processing. As a substantial contribution, it propose a new encryption technique with high sensitivity on external noise not only keeping the confidentiality of the image, but also the availability and efficiency in processing times. CONTENIDO CAPÍTULO I GENERALIDADES ....................................................................... 7 1.1. INTRODUCCIÓN ........................................................................................ 8 1.2. MOTIVACIÓN ........................................................................................... 11 1.3. PLANTEAMIENTO DEL PROBLEMA ...................................................... 12 1.3.1. Problema principal ...................................................................................12 1.3.2. Problemas secundarios ..........................................................................12 1.4. OBJETIVOS ............................................................................................. 12 1.4.1. Objetivo principal .....................................................................................13 1.4.2. Objetivos específicos ..............................................................................13 1.5. ORGANIZACIÓN DE LA MEMORIA ........................................................ 13 CAPÍTULO II ESTADO DEL ARTE .................................................................. 16 2.1. ANTECEDENTES ..................................................................................... 17 CAPÍTULO III MARCO TEÓRICO .................................................................... 25 3.1. FUNDAMENTOS DE IMAGEN DIGITAL ....................................................... 26 3.1.1. Imagen Analógica ......................................................................................26 3.1.2. Imagen Digital ............................................................................................27 3.1.3. Pixeles .........................................................................................................29 3.2. TEORÍA DEL CAOS ...................................................................................... 31 3.2.1. Historia ........................................................................................................32 3.2.2. El caos ........................................................................................................33 3.2.3. Sistemas dinámicos...................................................................................34 3.2.3.1. Definición ......................................................................................... 34 3.2.3.2. Espacio de fases y órbitas ............................................................. 34 3.2.3.3. Atractores ........................................................................................ 35 3.2.3.4. Clasificación .................................................................................... 36 3.2.4. Mapas caóticos ..........................................................................................36 3.2.4.1. Mapas ............................................................................................... 37 3.2.4.2. Clasificación .................................................................................... 39 1 3.2.4.3. Mapas Unidimensionales................................................................ 40 3.2.5. Mapa logístico ............................................................................................43 3.2.5.1. Definición ......................................................................................... 43 3.2.5.2. Comportamiento caótico ................................................................ 43 3.3. SEGURIDAD Y CRIPTOGRAFÍA .................................................................. 48 3.3.1. Definición ....................................................................................................49 3.3.2. Cifrado de imágenes ..................................................................................49 3.3.3. Criptografía caótica ...................................................................................49 3.3.4. Confusión y Difusión .................................................................................50 CAPÍTULO IV TECNOLOGÍAS UTILIZADAS .................................................. 53 4.1. OPENCV ........................................................................................................ 54 4.1.1. Definición ....................................................................................................54 4.1.2. Estructura y contenido ..............................................................................54
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