Algorithms for factoring large integers
Integer factorization is a problem of great interest considering that it allows us to better understand numbers and compute certain arithmetic functions more easily. Furthermore, safety of the famous RSA cryptosystem is based on the complexity of this problem, which makes the finding of new methods...
- Autores:
-
Escobar Sarmiento, Camilo Andrés
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2020
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/49078
- Acceso en línea:
- http://hdl.handle.net/1992/49078
- Palabra clave:
- Factorización (Matemáticas)
Programación entera
Algoritmo de Pollard
Ecuaciones integrales
Matemáticas
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
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Al consultar y hacer uso de este recurso, está aceptando las condiciones de uso establecidas por los autores.http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Bogart, Tristram47bee2c6-53e2-4211-831b-906b5a30b6ac600Escobar Sarmiento, Camilo Andrésd0d489f0-2cff-4ace-b5b2-6e3f892f1cdf500Karpuk, David AntonCortissoz Iriarte, Jean Carlos2021-02-18T12:40:41Z2021-02-18T12:40:41Z2020http://hdl.handle.net/1992/49078u833792.pdfinstname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/Integer factorization is a problem of great interest considering that it allows us to better understand numbers and compute certain arithmetic functions more easily. Furthermore, safety of the famous RSA cryptosystem is based on the complexity of this problem, which makes the finding of new methods of factorization an interesting chal- lenge. In this work we present some of the applications of integer factorization as well as some of the current methods of factorization such as Pollard?s p-1 algorithm, the elliptic curve method and the continued fraction factoring algoritm. We also implement these algorithms and do an analysis on their complexities. Finally, we explore the future of this problem"La factorización de enteros es un problema de gran interés ya que nos permite entender mejor este tipo de números y calcular funciones aritméticas facilmente. Ademas, la seguridad del famoso criptosistema RSA se basa en la complejidad de este problema, por lo cual hallar nuevos algoritmos de factorización es un desafio interesante. En este trabajo presento algunas de las aplicaciones de factorizar enteros y también presento alguno de los métodos actuales de factorización tales como el algoritmo P-1 de Pollard, el método de curvas elipticas y el algoritmo de fracciones continuas. También implementamos algunos de estos algoritmos y analizamos sus complejidades. Finalmente exploramos el futuro de este problema."--Tomado del Formato de Documento de GradoMatemáticoPregrado58 hojasapplication/pdfengUniversidad de los AndesMatemáticasFacultad de CienciasDepartamento de Matemáticasinstname:Universidad de los Andesreponame:Repositorio Institucional SénecaAlgorithms for factoring large integersTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesishttp://purl.org/coar/resource_type/c_7a1fhttp://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/TPFactorización (Matemáticas)Programación enteraAlgoritmo de PollardEcuaciones integralesMatemáticasPublicationORIGINALu833792.pdfapplication/pdf504005https://repositorio.uniandes.edu.co/bitstreams/e9467123-b49e-4b53-8790-f4be848dd921/download02872e9a4522e551c3a32d86ca1910bbMD51THUMBNAILu833792.pdf.jpgu833792.pdf.jpgIM Thumbnailimage/jpeg6530https://repositorio.uniandes.edu.co/bitstreams/a10079f9-9b35-4abb-9d4d-f71fffae8f5b/downloadc1006248e041cc8901bb5b40abfab633MD55TEXTu833792.pdf.txtu833792.pdf.txtExtracted texttext/plain87741https://repositorio.uniandes.edu.co/bitstreams/05b50e5e-668f-422b-862b-cf9df89379fc/download544ec8ad54994a131a28bc2cebb708afMD541992/49078oai:repositorio.uniandes.edu.co:1992/490782023-10-10 17:18:57.754http://creativecommons.org/licenses/by-nc-sa/4.0/open.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.co |
| dc.title.es_CO.fl_str_mv |
Algorithms for factoring large integers |
| title |
Algorithms for factoring large integers |
| spellingShingle |
Algorithms for factoring large integers Factorización (Matemáticas) Programación entera Algoritmo de Pollard Ecuaciones integrales Matemáticas |
| title_short |
Algorithms for factoring large integers |
| title_full |
Algorithms for factoring large integers |
| title_fullStr |
Algorithms for factoring large integers |
| title_full_unstemmed |
Algorithms for factoring large integers |
| title_sort |
Algorithms for factoring large integers |
| dc.creator.fl_str_mv |
Escobar Sarmiento, Camilo Andrés |
| dc.contributor.advisor.none.fl_str_mv |
Bogart, Tristram |
| dc.contributor.author.none.fl_str_mv |
Escobar Sarmiento, Camilo Andrés |
| dc.contributor.jury.none.fl_str_mv |
Karpuk, David Anton Cortissoz Iriarte, Jean Carlos |
| dc.subject.armarc.es_CO.fl_str_mv |
Factorización (Matemáticas) Programación entera Algoritmo de Pollard Ecuaciones integrales |
| topic |
Factorización (Matemáticas) Programación entera Algoritmo de Pollard Ecuaciones integrales Matemáticas |
| dc.subject.themes.none.fl_str_mv |
Matemáticas |
| description |
Integer factorization is a problem of great interest considering that it allows us to better understand numbers and compute certain arithmetic functions more easily. Furthermore, safety of the famous RSA cryptosystem is based on the complexity of this problem, which makes the finding of new methods of factorization an interesting chal- lenge. In this work we present some of the applications of integer factorization as well as some of the current methods of factorization such as Pollard?s p-1 algorithm, the elliptic curve method and the continued fraction factoring algoritm. We also implement these algorithms and do an analysis on their complexities. Finally, we explore the future of this problem |
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2020 |
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2020 |
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