{"id":73955,"date":"2018-03-09T23:18:53","date_gmt":"2018-03-09T23:18:53","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/sistemas-criptograficos-de-curva-ela%c2%adptica-basados-en-matrices\/"},"modified":"2018-03-09T23:18:53","modified_gmt":"2018-03-09T23:18:53","slug":"sistemas-criptograficos-de-curva-ela%c2%adptica-basados-en-matrices","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/sistemas-criptograficos-de-curva-ela%c2%adptica-basados-en-matrices\/","title":{"rendered":"Sistemas criptogr\u00e1ficos de curva el\u00edptica basados en matrices."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Francisco Ferr\u00e1ndez Agull\u00f3 <\/strong><\/h2>\n<p>El incremento de la velocidad de los ordenadores y los nuevos algoritmos de ataque que surgen continuamente hacen preciso el aumento constante de la seguridad de los sistemas criptogr\u00e1ficos. Lo que hoy en d\u00eda es seguro puede que no fo sea al cabo de pocos a\u00f1os. Esta necesidad en el aumento de la seguridad no est\u00e1 exenta de inconvenientes. La complejidad alcanzada actualmente (de orden exponencial) con los sistemas de curva eliptica no parece mejorable ya que existen determinados ataques que siempre son aplicables sobre grupos (los de ra\u00edz cuadrada, como el pollard-r). Otra opci\u00f3n para incrementar la seguridad consiste en aumentar el tama\u00f1o de los sistemas con claves m\u00e1s grandes. Pero esto requiere la utilizaci\u00f3n de claves de gran tama\u00f1o si utilizamos el dlp (discrete logarithm problem) en el que se basa el dsa (digital signature algorithm) o ellfp (integer factorization problem) en el que se basa el rsa. El ecdlp (elliptic curve dlp) utiliza claves mucho m\u00e1s cortas pero requiere de grandes recursos computacionales ya que es necesario calcular el orden del grupo de puntos racionales de la curva eliptica.  con el objetivo de dise\u00f1ar sistemas m\u00e1s seguros sin las dificultades comentadas, se proponen tres funciones unidireccionales que aumentan el tama\u00f1o del problema con claves cortas y sin apenas requerimientos de recursos. Los tres sistemas se han dise\u00f1ado como problemas matem\u00e1ticos complejos capaces de definir funciones unidireccionales con trampa, necesarias para el dise\u00f1o de sistemas criptogr\u00e1ficos de clave p\u00fablica.  la primera propuesta es un sistema criptogr\u00e1fico lineal de curva el\u00edptica basado en matrices que consiste en una aplicaci\u00f3n entre matrices construidas de forma polin6mica y n-tuplas de puntos en n-tuplas de puntos. Esta funci\u00f3n consigue aumentar la seguridad de los esquemas criptogr\u00e1ficos mediante el aumento de las instancias necesarias para resolverlo. Adem\u00e1s, se muestra adaptable a los protocolos<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Sistemas criptogr\u00e1ficos de curva el\u00edptica basados en matrices.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Sistemas criptogr\u00e1ficos de curva el\u00edptica basados en matrices. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Francisco Ferr\u00e1ndez Agull\u00f3 <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Alicante<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 13\/05\/2005<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li> Climent Colomina Joan Josep<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: guillermo Bernabeu pastor <\/li>\n<li>natividad Llorca pascual (vocal)<\/li>\n<li>Rafael Cant\u00f3 colomina (vocal)<\/li>\n<li>leandro Tortosa grau (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Francisco Ferr\u00e1ndez Agull\u00f3 El incremento de la velocidad de los ordenadores y los nuevos algoritmos de ataque [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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