{"id":4198,"date":"2021-09-17T09:58:18","date_gmt":"2021-09-17T08:58:18","guid":{"rendered":"https:\/\/cyberschool.univ-rennes.fr\/?page_id=4198"},"modified":"2026-03-12T14:30:54","modified_gmt":"2026-03-12T13:30:54","slug":"algorithmique-de-base","status":"publish","type":"page","link":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/","title":{"rendered":"Algorithmique de base"},"content":{"rendered":"\n<section class=\"txt\">\n    <div class=\"container\">\n        <div class=\"bloc-txt\">\n                            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Course description<\/h2>\n                        <div class=\"contain-txt\">\n<ul>\n<li>Recherche dichotomique, tris, arbres. Complexit\u00e9. Algorithmes \u00e9l\u00e9mentaires pour les graphes.<\/li>\n<li>PGCD, PGCD \u00e9tendu, th\u00e9or\u00e8me chinois et arithm\u00e9tique modulaire.<\/li>\n<li>Op\u00e9rations sur les polyn\u00f4mes (op\u00e9rations \u00e9l\u00e9mentaires, PGCD, interpolation, relations coefficients\/racines).<\/li>\n<li>Multiplication rapide de polyn\u00f4mes (Schoolbook, Karatsuba, Toom-Cook, transformation de Fourier rapide, Number Theoretic Transform).<\/li>\n<li>Factorisation des polyn\u00f4mes, en particulier sur les corps finis.<\/li>\n<li>Localisation des racines de polyn\u00f4mes si le temps le permet.<\/li>\n<li>R\u00e9sultants, initiation aux bases de Groebner.<\/li>\n<li>Arithm\u00e9tique multipr\u00e9cision. Inversion multipr\u00e9cision (m\u00e9thode de Newton, exponentiation, \u2026 ). Autres applications de la m\u00e9thode de Newton (racine carr\u00e9e).<\/li>\n<li>R\u00e9duction modulaire (R\u00e9duction de Montgomery, bases normales et gaussiennes si le temps le permet).<\/li>\n<\/ul>\n<\/div>\n\n        <\/div>\n    <\/div>\n<\/section>\n\n\n<section class=\"tuiles\">\n    <div class=\"container\">\n                <div class=\"bloc\">\n            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Skills to acquire<\/h2>\n            <p>Notion de complexit\u00e9, algorithmique n\u00e9cessaire pour les codes correcteurs d\u2019erreurs et la cryptographie classique et post-quantique.<\/p>\n\n                    <\/div>\n                <div class=\"bloc\">\n            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Keywords<\/h2>\n            <p>Tri, graphes, arithm\u00e9tique, polyn\u00f4mes, calcul modulaire.<\/p>\n\n                    <\/div>\n            <\/div>\n<\/section>\n\n\n\n<section class=\"txt\">\n    <div class=\"container\">\n        <div class=\"bloc-txt\">\n                            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Biography<\/h2>\n                        <div class=\"contain-txt\"><strong>Gianira Alfarano<\/strong> est titulaire d\u2019une chaire de professeur junior \u00e0 l\u2019universit\u00e9 de Rennes depuis septembre 2024. Elle travaille sur les codes correcteurs d\u2019erreurs et leurs applications en cryptographie.<\/div>\n\n        <\/div>\n    <\/div>\n<\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":8,"featured_media":0,"parent":11605,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.13 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Algorithmique de base - CyberSchool<\/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:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Algorithmique de base - CyberSchool\" \/>\n<meta property=\"og:url\" content=\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/\" \/>\n<meta property=\"og:site_name\" content=\"CyberSchool\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/CSchoolRennes\/\" \/>\n<meta property=\"article:modified_time\" content=\"2026-03-12T13:30:54+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/cyberschool.univ-rennes.fr\/app\/uploads\/2021\/02\/cover-social-network.jpeg\" \/>\n\t<meta property=\"og:image:width\" content=\"1500\" \/>\n\t<meta property=\"og:image:height\" content=\"500\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@CSchoolRennes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/\",\"url\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/\",\"name\":\"Algorithmique de base - CyberSchool\",\"isPartOf\":{\"@id\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/#website\"},\"datePublished\":\"2021-09-17T08:58:18+00:00\",\"dateModified\":\"2026-03-12T13:30:54+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Education\",\"item\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Master\u2019s and postgraduate programmes\",\"item\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Master\u2019s in Mathematics and Applications \u2013 IT Mathematics and Cryptography\",\"item\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/\"},{\"@type\":\"ListItem\",\"position\":5,\"name\":\"Study programme of the Master&rsquo;s Mathematics and Applications \u2013 IT Mathematics and Cryptography\",\"item\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/\"},{\"@type\":\"ListItem\",\"position\":6,\"name\":\"Algorithmique de base\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/#website\",\"url\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/\",\"name\":\"CyberSchool\",\"description\":\"Just another WordPress site\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/cyberschool.univ-rennes.fr\/en\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Algorithmique de base - CyberSchool","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:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/","og_locale":"en_US","og_type":"article","og_title":"Algorithmique de base - CyberSchool","og_url":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/","og_site_name":"CyberSchool","article_publisher":"https:\/\/www.facebook.com\/CSchoolRennes\/","article_modified_time":"2026-03-12T13:30:54+00:00","og_image":[{"width":1500,"height":500,"url":"https:\/\/cyberschool.univ-rennes.fr\/app\/uploads\/2021\/02\/cover-social-network.jpeg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@CSchoolRennes","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/","url":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/","name":"Algorithmique de base - CyberSchool","isPartOf":{"@id":"https:\/\/cyberschool.univ-rennes.fr\/en\/#website"},"datePublished":"2021-09-17T08:58:18+00:00","dateModified":"2026-03-12T13:30:54+00:00","breadcrumb":{"@id":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algorithmique-de-base\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/cyberschool.univ-rennes.fr\/en\/"},{"@type":"ListItem","position":2,"name":"Education","item":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/"},{"@type":"ListItem","position":3,"name":"Master\u2019s and postgraduate programmes","item":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/"},{"@type":"ListItem","position":4,"name":"Master\u2019s in Mathematics and Applications \u2013 IT Mathematics and Cryptography","item":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/"},{"@type":"ListItem","position":5,"name":"Study programme of the Master&rsquo;s Mathematics and Applications \u2013 IT Mathematics and Cryptography","item":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/"},{"@type":"ListItem","position":6,"name":"Algorithmique de base"}]},{"@type":"WebSite","@id":"https:\/\/cyberschool.univ-rennes.fr\/en\/#website","url":"https:\/\/cyberschool.univ-rennes.fr\/en\/","name":"CyberSchool","description":"Just another WordPress site","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/cyberschool.univ-rennes.fr\/en\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/cyberschool.univ-rennes.fr\/en\/wp-json\/wp\/v2\/pages\/4198"}],"collection":[{"href":"https:\/\/cyberschool.univ-rennes.fr\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cyberschool.univ-rennes.fr\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cyberschool.univ-rennes.fr\/en\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/cyberschool.univ-rennes.fr\/en\/wp-json\/wp\/v2\/comments?post=4198"}],"version-history":[{"count":21,"href":"https:\/\/cyberschool.univ-rennes.fr\/en\/wp-json\/wp\/v2\/pages\/4198\/revisions"}],"predecessor-version":[{"id":18466,"href":"https:\/\/cyberschool.univ-rennes.fr\/en\/wp-json\/wp\/v2\/pages\/4198\/revisions\/18466"}],"up":[{"embeddable":true,"href":"https:\/\/cyberschool.univ-rennes.fr\/en\/wp-json\/wp\/v2\/pages\/11605"}],"wp:attachment":[{"href":"https:\/\/cyberschool.univ-rennes.fr\/en\/wp-json\/wp\/v2\/media?parent=4198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}