{"id":4245,"date":"2021-09-17T14:33:16","date_gmt":"2021-09-17T13:33:16","guid":{"rendered":"https:\/\/cyberschool.univ-rennes.fr\/?page_id=4245"},"modified":"2025-06-03T14:26:06","modified_gmt":"2025-06-03T13:26:06","slug":"courbes-elliptiques-pour-la-cryptographie","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\/courbes-elliptiques-pour-la-cryptographie\/","title":{"rendered":"Courbes elliptiques pour la cryptographie"},"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>Syst\u00e8mes d\u2019\u00e9quations alg\u00e9briques et g\u00e9n\u00e9ralit\u00e9s de g\u00e9om\u00e9trie alg\u00e9brique. Courbes alg\u00e9briques (th\u00e9or\u00e8me de B\u00e9zout, diviseurs, courbes alg\u00e9briques sur les corps finis). Illustration en th\u00e9orie des codes.<\/li>\n<li>Courbes elliptiques (g\u00e9n\u00e9ralit\u00e9s, loi de groupes, endomorphismes, isog\u00e9nies, Frobenius, polyn\u00f4mes de division, courbes elliptiques sur C, Q, Fq).<\/li>\n<li>Nombre de points sur les corps finis (borne de Hasse, Algorithme de Schoof)<\/li>\n<li>Utilisation des courbes elliptiques en cryptographie.<\/li>\n<li>Arithm\u00e9tique des courbes elliptiques sur les corps finis (syst\u00e8mes de coordonn\u00e9es, syst\u00e8mes de repr\u00e9sentation de la courbe)<\/li>\n<li>Multiplication scalaire efficace (Double and Add, Fen\u00eatre glissante, cha\u00eenes d\u2019addition, Yao, Lim-Lee, Montgomery ladder)<\/li>\n<li>Attaques par canaux cach\u00e9s basiques (SPA, DPA, fautes) et contre mesures<\/li>\n<li>Multiexponentiation et application \u00e0 la m\u00e9thode GLV\/GLS<\/li>\n<li>Attaques connues (courbes anormales, couplages, restriction aux scalaires de Weil)<\/li>\n<li>Protocoles standard (ECDSA, ECMQV, Nyberg Ruppel, GPS)<\/li>\n<li>Revues et conf\u00e9rences importantes, biblioth\u00e8ques de multipr\u00e9cision et de cryptographie<\/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>\u00catre en mesure de mettre en place de fa\u00e7on s\u00fbre et efficace un syst\u00e8me de s\u00e9curit\u00e9 bas\u00e9 sur l\u2019utilisation des normes les plus r\u00e9centes de cryptographie \u00e0 base de courbes elliptiques.<\/p>\n\n                    <\/div>\n                <div class=\"bloc\">\n            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Keywords<\/h2>\n            <p>Courbes elliptiques, multiplication scalaire, arithm\u00e9tique efficace, attaques par canaux cach\u00e9s.<\/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>Biographies<\/h2>\n                        <div class=\"contain-txt\">\n<div class=\"contain-txt\"><strong>Sylvain Duquesne <\/strong>est\u00a0 professeur \u00e0 l\u2019Universit\u00e9 de Rennes, responsable du master\u00a0 et ancien directeur de l\u2019IRMAR. \u00a0Son domaine de recherche concerne la th\u00e9orie des nombres et plus particuli\u00e8rement l\u2019arithm\u00e9tique et l\u2019algorithmique sur les courbes alg\u00e9briques, et les corps finis ainsi que les applications en cryptographie.<\/div>\n<div><\/div>\n<div class=\"contain-txt\"><strong>Niels Feld<\/strong> est ma\u00eetre de conf\u00e9rences \u00e0 l\u2019Universit\u00e9 de Rennes.<\/div>\n<\/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_changed":false,"footnotes":""},"class_list":["post-4245","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - 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