{"id":33403,"date":"1997-01-12T00:00:00","date_gmt":"1997-01-12T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/orbitas-de-las-funciones-cuadraticas-sobre-cuerpos-finitos-aplicaciones-a-la-generacion-de-secuencias-pseudoaleatorios-y-al-diseno-de-criptosistemas\/"},"modified":"1997-01-12T00:00:00","modified_gmt":"1997-01-12T00:00:00","slug":"orbitas-de-las-funciones-cuadraticas-sobre-cuerpos-finitos-aplicaciones-a-la-generacion-de-secuencias-pseudoaleatorios-y-al-diseno-de-criptosistemas","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/orbitas-de-las-funciones-cuadraticas-sobre-cuerpos-finitos-aplicaciones-a-la-generacion-de-secuencias-pseudoaleatorios-y-al-diseno-de-criptosistemas\/","title":{"rendered":"Orbitas de las funciones cuadraticas sobre cuerpos finitos. aplicaciones a la generacion de secuencias pseudoaleatorios y al dise\u00f1o de criptosistemas."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Alberto Peinado Dom\u00ednguez <\/strong><\/h2>\n<p>El objeto de esta memoria es el estudio de los polinomios cuadr\u00e1ticos sobre cuerpos finitos y sus aplicaciones a la construccion de secuencias pseudo-aleatorias, al dise\u00f1o decifradores en flujo y al criptosistema de clave p\u00fablica definido por el generador bbs.  se obtienen tres resultados generales de inter\u00e9s te\u00f3rico:  1) se caracterizan los primos   para los cuales se alcanza exactamente la longitud m\u00e1xima de los cilos de la funci\u00f3n x1-x2 sobre zp. Este resultado tiene una aplicaci\u00f3n directa en el uso eficiente del generador bbs como criptosistema de clave p\u00fablica; 2) se aprueba que, contrariamente, los ciclos de las funciones cuadr\u00e1tica sobre gf(pn),p 2 son de longitud peque\u00f1a en relaci\u00f3n con pn, y su convergencia a cero es especialmente r\u00e1pida cuando n aumenta, de modo que tales funciones no son de inter\u00e9s en las aplicaciones; 3) se caracteriza los ciclos de longitud m\u00e1xima de las funciones cuadr\u00e1ticas sobre gf(2n), que resulta ser de longitud 2n1-2, para todo n -4. Tales funciones son especialmente \u00fatiles para la generaci\u00f3n de secuencias pseudoaleatorias, cuya complejidad respecto de diversos tests estad\u00edsticos tambi\u00e9n se analiza.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Orbitas de las funciones cuadraticas sobre cuerpos finitos. aplicaciones a la generacion de secuencias pseudoaleatorios y al dise\u00f1o de criptosistemas.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Orbitas de las funciones cuadraticas sobre cuerpos finitos. aplicaciones a la generacion de secuencias pseudoaleatorios y al dise\u00f1o de criptosistemas. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Alberto Peinado Dom\u00ednguez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/12\/1997<\/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>Faustino Montoya Vitini<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jorge D\u00e1vila muro <\/li>\n<li>Luis Hernandez encinas (vocal)<\/li>\n<li>Jos\u00e9 Javier Etayo gordejuela (vocal)<\/li>\n<li>amparo F\u00faster sabater (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Alberto Peinado Dom\u00ednguez El objeto de esta memoria es el estudio de los polinomios cuadr\u00e1ticos sobre cuerpos [&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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