{"id":84291,"date":"2008-02-12T04:39:00","date_gmt":"2008-02-12T04:39:00","guid":{"rendered":"http:\/\/weblogs.madrimasd.org\/\/matematicas\/archive\/2008\/02\/12\/84291.aspx"},"modified":"2008-02-12T04:39:00","modified_gmt":"2008-02-12T04:39:00","slug":"matematicas-y-criptografia","status":"publish","type":"post","link":"https:\/\/www.madrimasd.org\/blogs\/matematicas\/2008\/02\/12\/84291","title":{"rendered":"MATEM\u00c1TICAS Y CRIPTOGRAF\u00cdA"},"content":{"rendered":"<p>A nadie parece extra\u00f1ar la frase \u201c\u2026hoy vivimos en la sociedad de la informaci\u00f3n\u2026\u201d, cada d\u00eda cualquiera de nosotros almacena, procesa e incluso transmite informaci\u00f3n de forma digital. Sin duda, desde los a\u00f1os ochenta, el uso de los ordenadores, de las redes locales, de Internet, del correo electr\u00f3nico, de la telefon\u00eda inal\u00e1mbrica, del wireless\u2026 es parte de nuestra vida diaria.<\/p>\n<p>La contrapartida del uso de toda esa informaci\u00f3n sobre redes abiertas son los problemas de privacidad y seguridad. Se deben pues buscar mecanismos tanto legales como cient\u00edfico-t\u00e9cnicos para garantizar ambas. Un ejemplo de plena actualidad es la puesta en marcha del Documento Nacional de Identidad electr\u00f3nico.<\/p>\n<p>La <a href=\"http:\/\/www.imdea.org\/Portals\/0\/Institutos\/Matematicas\/imdea_seminar_series_febrero.pdf\">Criptograf\u00eda<\/a> es la parte cient\u00edfico-t\u00e9cnica que trata de garantizar los fundamentos de la seguridad en la transmisi\u00f3n de la informaci\u00f3n.<br \/><!--more-->We live in an information-based society. The techniques to keep secret the information are the field of study of cryptography. The cryptography are the mathematical tools related to confidentiality, data integrity, entity authentication and data origin authentication.<\/p>\n<p>There are two forms of encryption: Symmetric Key Encryption which is fast but both parties need to know a shared secret key and Public Key Encryption which is show but only one party needs to keep a key private.<\/p>\n<p>The first and most popular public key exchange algorithm is <a href=\"http:\/\/www.math.uwaterloo.ca\/%7Eajmeneze\/publications\/publickey.pdf\">RSA<\/a>. The security of RSA is based on the intractability of the integer factorization problem. <a href=\"http:\/\/www.cs.berkeley.edu\/%7Echristos\/classics\/diffiehellman.pdf\">Diffie-Hellman<\/a> key exchange relies on difficulty of computing discrete logarithms. There are a few other key exchange schemes that used in practice, for example, the Digital Signature Algorithms (DSA) and the Elliptic Curve Digital Signature (ECDSA). The security of those schemes is based on the discrete logarithm problem in the multiplicative group of points of an elliptic curve over finite field.<\/p>\n<p>One of fundamental tools used in information security is the signature. From practical view point the main ingredient of signature in cryptology are the <a href=\"http:\/\/www.ams.org\/notices\/200603\/fea-landau.pdf\">hash functions<\/a>. The main role of crytographic hash function is in the provision of digital signatures. Since hash funtions are generally faster than digital signature algorithms, it is typical to compute the digital signature to some document by computing the signature on the document\u2019s hash value, which is small compared to the document itself. It was a big surprise that vulnerability of standart hash funciones was announced in Feb. 2005. The attack primarily affects some digital signature applications, including timestamping and certificate signing operations, where one party prepares a message form the generation of digital signature by second party, and third parties then virefy the signature.<\/p>\n<p>When quantum computers reach aproximately 30 to 40 q-bits they will start to have the speed (parallelism) needed to attack the methods society uses to Project data processes, including encryption, digital signatures, random number generators, key transmission, and other security algorithms. In particular all the standarts used nowdays will became obsolete and one should be prepared to have ready several other cryptosystems.<\/p>\n<p>Second Cryptografy Hash Workshop:<a href=\"http:\/\/csrc.nist.gov\/groups\/ST\/hash\/index.html\"> http:\/\/www.csrc.nist.gov\/pki\/HashWorkshop\/index.html<\/a><br \/>Mathematics and Internet security: <a href=\"http:\/\/www.mathaware.org\/mam\/06\/\">http:\/\/www.mathaware.org\/mam\/06\/<\/a><\/p>\n<p>Fuente: C. XIII, Matem\u00e1ticas y Criptograf\u00eda, de Matem\u00e1ticas en la Frontera, <a href=\"http:\/\/www.madrimasd.org\/informacionidi\/biblioteca\/Publicacion\/coleccion-madrimasd\/default.asp\">Colecci\u00f3n Madri+d<\/a>.<\/p>\n<div align=\"right\">Por Alejandro Melle Hern\u00e1ndez<br \/>Universidad Complutense de Madrid<br \/>Departamento de \u00c1lgebra<br \/>Facultad de Matem\u00e1ticas<\/div>\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A nadie parece extra\u00f1ar la frase \u201c\u2026hoy vivimos en la sociedad de la informaci\u00f3n\u2026\u201d, cada d\u00eda cualquiera de nosotros almacena, procesa e incluso transmite informaci\u00f3n de forma digital. Sin duda, desde los a\u00f1os ochenta, el uso de los ordenadores, de las redes locales, de Internet, del correo electr\u00f3nico, de la telefon\u00eda inal\u00e1mbrica, del wireless\u2026 es parte de nuestra vida diaria. La contrapartida del uso de toda esa informaci\u00f3n sobre redes abiertas son los problemas de privacidad y seguridad. Se deben pues buscar mecanismos tanto legales como cient\u00edfico-t\u00e9cnicos para garantizar ambas. Un ejemplo de plena actualidad es la puesta en marcha\u2026<\/p>\n","protected":false},"author":49,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[1],"tags":[],"blocksy_meta":{"styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":4}},"aioseo_notices":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v18.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>MATEM\u00c1TICAS Y CRIPTOGRAF\u00cdA - Matem\u00e1ticas y sus fronteras<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.madrimasd.org\/blogs\/matematicas\/2008\/02\/12\/84291\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"MATEM\u00c1TICAS Y CRIPTOGRAF\u00cdA - Matem\u00e1ticas y sus fronteras\" \/>\n<meta property=\"og:description\" content=\"A nadie parece extra\u00f1ar la frase \u201c\u2026hoy vivimos en la sociedad de la informaci\u00f3n\u2026\u201d, cada d\u00eda cualquiera de nosotros almacena, procesa e incluso transmite informaci\u00f3n de forma digital. 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Es adem\u00e1s Director del programa Estalmat.\",\"url\":\"https:\/\/www.madrimasd.org\/blogs\/matematicas\/author\/matematicas\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"MATEM\u00c1TICAS Y CRIPTOGRAF\u00cdA - Matem\u00e1ticas y sus fronteras","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.madrimasd.org\/blogs\/matematicas\/2008\/02\/12\/84291","og_locale":"es_ES","og_type":"article","og_title":"MATEM\u00c1TICAS Y CRIPTOGRAF\u00cdA - Matem\u00e1ticas y sus fronteras","og_description":"A nadie parece extra\u00f1ar la frase \u201c\u2026hoy vivimos en la sociedad de la informaci\u00f3n\u2026\u201d, cada d\u00eda cualquiera de nosotros almacena, procesa e incluso transmite informaci\u00f3n de forma digital. 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