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Introducción a la Criptografía post-cuántica basada en teoría de códigos
| dc.contributor.advisor | Gauthier-Umaña, Valérie | |
| dc.creator | Rambaut Lemus, Daniel Felipe | |
| dc.creator.degree | Profesional en Matemáticas Aplicadas y Ciencias de la Computación | spa |
| dc.creator.degreeLevel | Pregrado | |
| dc.creator.degreetype | Full time | spa |
| dc.date.accessioned | 2021-06-28T17:30:15Z | |
| dc.date.available | 2021-06-28T17:30:15Z | |
| dc.date.created | 2021-05-26 | |
| dc.description | La criptografía es la disciplina que estudia el arte de transformar un mensaje (llamado texto plano) en un mensaje no legible por un tercero (llamado texto cifrado) utilizando una clave secreta. Los protocolos de cifrado, descifrado y construcción de claves es lo que llamamos un criptosistema. Existen dos grandes familias: 1. Criptografía simétrica: conformada por los criptosistemas que utilizan una misma clave secreta para cifrar y descifrar mensajes. 2. Criptografía asimétrica o a clave pública: son aquellos en los que los procesos de cifrado y descifrado son llevados a cabo por dos claves, una pública para el proceso de cifrado y otra secreta para descifrado. La criptografía simétrica tiene dos principales problemas: las personas que van a comunicarse deben tener un primer encuentro para definir la clave secreta y por otro lado para cada pareja de personas que se quieran comunicar debe existir una clave secreta. Ambos problemas son resueltos por la criptografía a clave pública ya que en este caso no hay necesidad de ponerse de acuerdo con la clave y por otro lado una misma clave pública le permite a una persona recibir mensajes de muchas personas sin que estas tengan la posibilidad de descifrar el mensaje. Esto hace que la criptografía a clave pública sea la base del comercio electrónico. En 1978 se propuso el RSA, el cual fue el primer criptosistema a clave pública. Más de 40 años después los criptosistemas a clave pública que se utilizan dependen únicamente de dos problemas matemáticos: la factorización y el logaritmo discreto. Es decir que, si de alguna manera lográramos resolver estos problemas, toda la criptografía a clave pública quedaría expuesta e insegura. Sin embargo, en 1994, Peter Shor, publicó un algoritmo en el cual, de tener un computador cuántico suficientemente poderoso, podría resolver estos dos problemas. La carrera de varias empresas y centros de investigación por crear un computador cuántico ha sido bastante activa y ya se han creados algunos en los cuales se ha podido implementar el algoritmo de Shor y factorizar, por ejemplo, el número 15. Como respuesta a este nuevo escenario, en donde la computación cuántica pone en jaque a toda la criptografía a clave pública, se presenta la criptografía post-cuántica, la cual consiste en buscar criptosistemas que sean resistentes a ataques hechos en computadores convencionales y cuánticos. El instituto Nacional de estándares y Tecnología de Estados Unidos (llamado NIST por sus siglas en inglés, National Institute of Standards and Technology) preocupado por esta situación, y buscando promover la investigación en critpografía post-cuántica organizó un concurso público para buscar un criptosistema post-cuántico que se pueda convertir en el estándar. Existen diferentes familias que han inspirado algunas propuestas de criptosistemas post-cuánticos: la teoría de códigos, retículos funciones de Hash y álgebra multivariada que se vienen estudiando aproximadamente desde los años 2000 y recientemente se trabajan con isogeny en curvas elípticas. En este trabajo de grado nos concentramos en la criptografía post-cuántica basada en la teoría de códigos. En 1978, McEliece propuso un criptosistema que no tuvo mucha acogida dado su tamaño de la clave secreta, pero que resulta ser resistente a ataques post-cuánticos. En los últimos 20 años se han propuesto varias variantes del McEliece, que usan la misma idea de basarse en códigos correctores de errores, pero que usan protocolos diferentes para tratar de reducir el tamaño de la clave. Hasta el momento la mayoría han sido atacados, existen algunos vigentes, pero todavía la comunidad no tiene confianza en su seguridad ya que son muy recientes. En esta tesis se realizó un documento donde se introduce las bases matemáticas, la criptografía, la teoría de corrección de errores y la computación cuántica necesaria para poder entender la criptografía post-cuántica basada en teoría de códigos. Al final de la tesis introducimos los criptosistemas de McEliece y Niederreiter así como la versión del criptosistema de McEliece que llegó a la última etapa de la competencia de la NIST (todavía en curso). | spa |
| dc.description.abstract | Cryptography is the discipline that studies the art of transforming a message (called plaintext) into a message that is not readable by a third party (called ciphertext) using a secret key. The encryption, decryption and key construction protocols is what we call a cryptosystem. There are two great families: 1. Symmetric cryptography: made up of cryptosystems that use the same secret key to encrypt and decrypt messages. 2. Asymmetric or public key cryptography: those in which two keys carry the encryption and decryption processes out, one public for the encryption process and the other secret for decryption. Symmetric cryptography has two fundamental problems: the people who are going to communicate must have a first meeting to define the secret key and for each pair of people who want to communicate there must be a secret key. Public key cryptography solves both problems since in this case there is no need to agree on the key and the same public key allows a person to receive messages from many people without them having the possibility of decrypt the message. This makes public key cryptography the foundation of electronic commerce. In 1978 the RSA was proposed, which was the first public key cryptosystem. Over 40 years later, the public key cryptosystems that are used depend only on two mathematical problems: factoring and the discrete logarithm. If we somehow solved these problems, all public key cryptography would be exposed and insecure. However, in 1994, Peter Shor published an algorithm in which, if he had a powerful enough quantum computer, he could solve these two problems. The race of several companies and research centers to create a quantum computer has been quite active and we have already created some in which it has been possible to implement the Shor algorithm and factor, for example, the number 15. In response to this new scenario, where quantum computing puts all public key cryptography in check, post-quantum cryptography is presented, which comprises looking for cryptosystems that are resistant to attacks made on conventional and quantum computers. The National Institute of Standards and Technology of the United States (called NIST for its acronym in English, National Institute of Standards and Technology) concerned about this situation, and seeking to promote research in post-quantum cryptography organized a public contest to search for a post-cryptosystem -quantum that can become the standard. There are different families that have inspired some proposals for post-quantum cryptosystems: the theory of codes, Hash-function lattices and multivariate algebra that have been studied approximately since the 2000s and have recently been working with isogeny in elliptic curves. In this degree project, we focus on post-quantum cryptography based on code theory. In 1978, McEliece proposed a cryptosystem that was not very popular given its secret key size, but which turns out to be resistant to post-quantum attacks. Several variants of the McEliece have been proposed in the last 20 years, using the same idea of relying on error-correcting codes, but using different protocols to reduce the size of the key. So far must have been attacked, there are some in force, but the community still does not have confidence in their security since they are very recent. In this thesis, I made a document that introduces the mathematical bases, cryptography, error correction theory and the quantum computing necessary to understand post-quantum cryptography based on code theory. At the end of the thesis we introduce the McEliece and Niederreiter cryptosystems and the version of the McEliece cryptosystem that reached the last stage of the NIST competition (still ongoing). | spa |
| dc.format.extent | 102 pp. | spa |
| dc.format.mimetype | application/pdf | |
| dc.identifier.doi | https://doi.org/10.48713/10336_31688 | |
| dc.identifier.uri | https://repository.urosario.edu.co/handle/10336/31688 | |
| dc.language.iso | spa | spa |
| dc.publisher | Universidad del Rosario | |
| dc.publisher.department | Escuela de Ingeniería, Ciencia y Tecnología | |
| dc.publisher.program | Programa de Matemáticas Aplicadas y Ciencias de la Computación - MACC | |
| dc.rights | Atribución-NoComercial-SinDerivadas 2.5 Colombia | * |
| dc.rights.accesRights | info:eu-repo/semantics/openAccess | |
| dc.rights.acceso | Abierto (Texto Completo) | spa |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/co/ | |
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| dc.source.instname | instname:Universidad del Rosario | |
| dc.source.reponame | reponame:Repositorio Institucional EdocUR | |
| dc.subject | Criptografía post-cuántica basada en la teoría de códigos | spa |
| dc.subject | Criptosistemas de McEliece | spa |
| dc.subject | Criptosistema de Niederreiter | spa |
| dc.subject | Sistemas de encriptado de información de nueva generación frente a la computación cuántica | spa |
| dc.subject | Desarrollo de sistemas criptográficos post-cuánticos | spa |
| dc.subject | Seguridad informática en el contexto de la computación cuántica | spa |
| dc.subject.ddc | Métodos especiales de computación | spa |
| dc.subject.keyword | Post-quantum cryptography based on code theory | spa |
| dc.subject.keyword | McEliece Cryptosystems | spa |
| dc.subject.keyword | Niederreiter cryptosystem | spa |
| dc.subject.keyword | Next-generation information encryption systems vs. quantum computing | spa |
| dc.subject.keyword | Development of post-quantum cryptographic systems | spa |
| dc.subject.keyword | Computer security in the context of quantum computing | spa |
| dc.title | Introducción a la Criptografía post-cuántica basada en teoría de códigos | spa |
| dc.title.TranslatedTitle | Introduction to post-quantum cryptography based on code theory | spa |
| dc.type | bachelorThesis | eng |
| dc.type.document | Monografía | spa |
| dc.type.hasVersion | info:eu-repo/semantics/acceptedVersion | |
| dc.type.spa | Trabajo de grado | spa |
