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position","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fconfidentialite-position","0.snt-2nde\u002Fse-localisation-cartographie\u002F5.confidentialite-position",{"title":145,"path":146,"stem":147,"children":148},"Informatique embarquée et objets connectés","\u002Fsnt-2nde\u002Fsf-info-embarquee","0.snt-2nde\u002Fsf-info-embarquee\u002F0.index",[149,150,154,158],{"title":145,"path":146,"stem":147},{"title":151,"path":152,"stem":153},"Systèmes informatiques embarqués","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fsystemes-embarques","0.snt-2nde\u002Fsf-info-embarquee\u002F1.systemes-embarques",{"title":155,"path":156,"stem":157},"Capteurs et actionneurs","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fcapteurs-actionneurs","0.snt-2nde\u002Fsf-info-embarquee\u002F2.capteurs-actionneurs",{"title":159,"path":160,"stem":161},"IHM et objets 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Python","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Ftraitement-rgb","0.snt-2nde\u002Fsg-photo-numerique\u002F4.traitement-rgb",{"title":185,"path":186,"stem":187,"children":188},"Notions transversales de programmation","\u002Fsnt-2nde\u002Fsh-prog-notions","0.snt-2nde\u002Fsh-prog-notions\u002F0.index",[189,190,194,198,202],{"title":185,"path":186,"stem":187},{"title":191,"path":192,"stem":193},"Séquences d'instructions et variables","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fsequences-affectations","0.snt-2nde\u002Fsh-prog-notions\u002F1.sequences-affectations",{"title":195,"path":196,"stem":197},"Instructions conditionnelles","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fconditionnelles","0.snt-2nde\u002Fsh-prog-notions\u002F2.conditionnelles",{"title":199,"path":200,"stem":201},"Boucles bornées et non bornées","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fboucles","0.snt-2nde\u002Fsh-prog-notions\u002F3.boucles",{"title":203,"path":204,"stem":205},"Définitions et appels de fonctions","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Ffonctions","0.snt-2nde\u002Fsh-prog-notions\u002F4.fonctions",{"title":207,"path":208,"stem":209,"children":210},"Démo des widgets MDC","\u002Fsnt-2nde\u002Fzz-demo-widgets","0.snt-2nde\u002Fzz-demo-widgets\u002F0.index",[211,212,216,220],{"title":207,"path":208,"stem":209},{"title":213,"path":214,"stem":215},"Démo statique — callouts, code, BO, illustration","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fstatique","0.snt-2nde\u002Fzz-demo-widgets\u002F1.statique",{"title":217,"path":218,"stem":219},"Démo interactive — self-eval et python-snippet","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Finteractif","0.snt-2nde\u002Fzz-demo-widgets\u002F2.interactif",{"title":221,"path":222,"stem":223},"Démo · 14 widgets de manipulation NSI","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fwidgets-manipulation","0.snt-2nde\u002Fzz-demo-widgets\u002F3.widgets-manipulation",{"title":225,"path":226,"stem":227,"children":228},"NSI — 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deux","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fentiers-relatifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F2.entiers-relatifs",{"title":271,"path":272,"stem":273},"Nombres flottants et virgule flottante","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fflottants","1.nsi-1ere\u002Fpb-types-valeurs\u002F3.flottants",{"title":275,"path":276,"stem":277},"Textes et encodages — ASCII, ISO-8859-1, Unicode","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Ftextes-encodages","1.nsi-1ere\u002Fpb-types-valeurs\u002F4.textes-encodages",{"title":279,"path":280,"stem":281},"Valeurs booléennes et opérateurs logiques","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fbooleens","1.nsi-1ere\u002Fpb-types-valeurs\u002F5.booleens",{"title":283,"path":284,"stem":285,"children":286},"Représentation des données : types construits","\u002Fnsi-1ere\u002Fpc-types-construits","1.nsi-1ere\u002Fpc-types-construits\u002F0.index",[287,288,292,296,300],{"title":283,"path":284,"stem":285},{"title":289,"path":290,"stem":291},"Tableaux et listes","\u002Fnsi-1ere\u002Fpc-types-construits\u002Ftableaux-listes","1.nsi-1ere\u002Fpc-types-construits\u002F1.tableaux-listes",{"title":293,"path":294,"stem":295},"Listes en compréhension","\u002Fnsi-1ere\u002Fpc-types-construits\u002Fcomprehension","1.nsi-1ere\u002Fpc-types-construits\u002F2.comprehension",{"title":297,"path":298,"stem":299},"Tuples et p-uplets nommés","\u002Fnsi-1ere\u002Fpc-types-construits\u002Ftuples","1.nsi-1ere\u002Fpc-types-construits\u002F3.tuples",{"title":301,"path":302,"stem":303},"Dictionnaires","\u002Fnsi-1ere\u002Fpc-types-construits\u002Fdictionnaires","1.nsi-1ere\u002Fpc-types-construits\u002F4.dictionnaires",{"title":305,"path":306,"stem":307,"children":308},"Traitement de données en tables","\u002Fnsi-1ere\u002Fpd-tables-donnees","1.nsi-1ere\u002Fpd-tables-donnees\u002F0.index",[309,310,314,318,322],{"title":305,"path":306,"stem":307},{"title":311,"path":312,"stem":313},"Tables et CSV","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftables-csv","1.nsi-1ere\u002Fpd-tables-donnees\u002F1.tables-csv",{"title":315,"path":316,"stem":317},"Recherche et filtrage","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Frecherche","1.nsi-1ere\u002Fpd-tables-donnees\u002F2.recherche",{"title":319,"path":320,"stem":321},"Trier une table","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftri","1.nsi-1ere\u002Fpd-tables-donnees\u002F3.tri",{"title":323,"path":324,"stem":325,"children":326},"Fusion et indexation","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ffusion-indexation","1.nsi-1ere\u002Fpd-tables-donnees\u002F4.fusion-indexation",[327],{"title":323,"path":324,"stem":325},{"title":329,"path":330,"stem":331,"children":332},"IHM sur le Web","\u002Fnsi-1ere\u002Fpe-ihm-web","1.nsi-1ere\u002Fpe-ihm-web\u002F0.index",[333,334,338,342,346,350],{"title":329,"path":330,"stem":331},{"title":335,"path":336,"stem":337},"HTML et CSS — rappel de structure","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fhtml-css-bases","1.nsi-1ere\u002Fpe-ihm-web\u002F1.html-css-bases",{"title":339,"path":340,"stem":341},"Formulaires HTML","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fformulaires","1.nsi-1ere\u002Fpe-ihm-web\u002F2.formulaires",{"title":343,"path":344,"stem":345},"Événements JavaScript","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fevenements-js","1.nsi-1ere\u002Fpe-ihm-web\u002F3.evenements-js",{"title":347,"path":348,"stem":349},"Manipulation du DOM","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fdom-interaction","1.nsi-1ere\u002Fpe-ihm-web\u002F4.dom-interaction",{"title":351,"path":352,"stem":353},"Client, serveur et HTTP","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fclient-serveur-http","1.nsi-1ere\u002Fpe-ihm-web\u002F5.client-serveur-http",{"title":355,"path":356,"stem":357,"children":358},"Architectures matérielles et systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os","1.nsi-1ere\u002Fpf-archi-os\u002F0.index",[359,360,364,368,372,376],{"title":355,"path":356,"stem":357},{"title":361,"path":362,"stem":363},"Le modèle de von Neumann","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fvon-neumann","1.nsi-1ere\u002Fpf-archi-os\u002F1.von-neumann",{"title":365,"path":366,"stem":367},"Périphériques et interface homme-machine","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fperipheriques-ihm","1.nsi-1ere\u002Fpf-archi-os\u002F2.peripheriques-ihm",{"title":369,"path":370,"stem":371},"Les systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fsystemes-exploitation","1.nsi-1ere\u002Fpf-archi-os\u002F3.systemes-exploitation",{"title":373,"path":374,"stem":375},"Linux et le shell","\u002Fnsi-1ere\u002Fpf-archi-os\u002Flinux-shell","1.nsi-1ere\u002Fpf-archi-os\u002F4.linux-shell",{"title":377,"path":378,"stem":379},"Réseaux et protocoles","\u002Fnsi-1ere\u002Fpf-archi-os\u002Freseaux","1.nsi-1ere\u002Fpf-archi-os\u002F5.reseaux",{"title":381,"path":382,"stem":383,"children":384},"Langages et programmation","\u002Fnsi-1ere\u002Fpg-langages-prog","1.nsi-1ere\u002Fpg-langages-prog\u002F0.index",[385,386,390,394,398,402,406],{"title":381,"path":382,"stem":383},{"title":387,"path":388,"stem":389},"Diversité et unité des langages de programmation","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fdiversite-langages","1.nsi-1ere\u002Fpg-langages-prog\u002F1.diversite-langages",{"title":391,"path":392,"stem":393},"Constructions élémentaires","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fconstructions-elementaires","1.nsi-1ere\u002Fpg-langages-prog\u002F2.constructions-elementaires",{"title":395,"path":396,"stem":397},"Fonctions","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Ffonctions","1.nsi-1ere\u002Fpg-langages-prog\u002F3.fonctions",{"title":399,"path":400,"stem":401},"Spécification d'une 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complexité","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fcomplexite-bases","1.nsi-1ere\u002Fph-algorithmique\u002F2.complexite-bases",{"title":425,"path":426,"stem":427},"Tris par sélection et par insertion","\u002Fnsi-1ere\u002Fph-algorithmique\u002Ftris","1.nsi-1ere\u002Fph-algorithmique\u002F3.tris",{"title":429,"path":430,"stem":431},"Recherche dichotomique","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fdichotomie","1.nsi-1ere\u002Fph-algorithmique\u002F4.dichotomie",{"title":433,"path":434,"stem":435},"Algorithmes gloutons","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fgloutons","1.nsi-1ere\u002Fph-algorithmique\u002F5.gloutons",{"title":437,"path":438,"stem":439},"Les k plus proches voisins (k-NN)","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fknn","1.nsi-1ere\u002Fph-algorithmique\u002F6.knn",{"title":441,"path":442,"stem":443,"children":444},"NSI — 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symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fhttps-tls","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F8.https-tls",{"title":381,"path":537,"stem":538,"children":539},"\u002Fnsi-tale\u002Ftd-langages-prog","2.nsi-tale\u002Ftd-langages-prog\u002F0.index",[540,541,544,548,552,556],{"title":381,"path":537,"stem":538},{"title":403,"path":542,"stem":543},"\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmise-au-point","2.nsi-tale\u002Ftd-langages-prog\u002F1.mise-au-point",{"title":545,"path":546,"stem":547},"Modularité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmodularite","2.nsi-tale\u002Ftd-langages-prog\u002F2.modularite",{"title":549,"path":550,"stem":551},"Récursivité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Frecursivite","2.nsi-tale\u002Ftd-langages-prog\u002F3.recursivite",{"title":553,"path":554,"stem":555},"Paradigmes de programmation","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fparadigmes","2.nsi-tale\u002Ftd-langages-prog\u002F4.paradigmes",{"title":557,"path":558,"stem":559},"Programme comme donnée — calculabilité et indécidabilité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fprogramme-comme-donnee","2.nsi-tale\u002Ftd-langages-prog\u002F5.programme-comme-donnee",{"title":411,"path":561,"stem":562,"children":563},"\u002Fnsi-tale\u002Fte-algorithmique","2.nsi-tale\u002Fte-algorithmique\u002F0.index",[564,565,569,573,577,581],{"title":411,"path":561,"stem":562},{"title":566,"path":567,"stem":568},"Algorithmes sur les arbres binaires","\u002Fnsi-tale\u002Fte-algorithmique\u002Farbres-binaires-algos","2.nsi-tale\u002Fte-algorithmique\u002F1.arbres-binaires-algos",{"title":570,"path":571,"stem":572},"Parcours de graphes — DFS, BFS, cycles, chemins","\u002Fnsi-tale\u002Fte-algorithmique\u002Fgraphes-parcours","2.nsi-tale\u002Fte-algorithmique\u002F2.graphes-parcours",{"title":574,"path":575,"stem":576},"Diviser pour régner","\u002Fnsi-tale\u002Fte-algorithmique\u002Fdiviser-pour-regner","2.nsi-tale\u002Fte-algorithmique\u002F3.diviser-pour-regner",{"title":578,"path":579,"stem":580},"Programmation dynamique","\u002Fnsi-tale\u002Fte-algorithmique\u002Fprogrammation-dynamique","2.nsi-tale\u002Fte-algorithmique\u002F4.programmation-dynamique",{"title":582,"path":583,"stem":584},"Recherche textuelle — l'algorithme de 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La cryptographie a\ntrouvé la réponse en 1976 avec une ",[602,611,612],{},"idée révolutionnaire"," : utiliser\n",[602,615,616],{},"deux clés différentes"," par personne, l'une ",[602,619,620],{},"publiable"," et l'autre\n",[602,623,624],{},"gardée secrète",", mathématiquement liées de telle façon que l'une\nchiffre et l'autre seule sait déchiffrer. C'est le ",[602,627,628],{},"chiffrement\nasymétrique",", et c'est ce que demande ",[631,632],"bo-ref",{"code":588},".",[593,635,637],{"id":636},"le-principe-deux-clés-par-personne","Le principe — deux clés par personne",[598,639,640,641,644],{},"Chaque utilisateur dispose d'une ",[602,642,643],{},"paire de clés"," :",[646,647,648,784],"ul",{},[649,650,651,652,655,656,779,780,783],"li",{},"une ",[602,653,654],{},"clé publique"," 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sur sa machine",", jamais\ntransmise à personne.",[598,890,891],{},"Les deux fonctions sont :",[657,893,896],{"className":894},[895],"katex-display",[657,897,899,979],{"className":898},[660],[657,900,902],{"className":901},[664],[666,903,905],{"xmlns":668,"display":904},"block",[670,906,907,976],{},[673,908,909,912,916,933,937,940,943,947,949,951,970,972,974],{},[679,910,911],{},"C",[913,914,915],"mo",{},"=",[676,917,918,921],{},[679,919,920],{},"E",[676,922,923,925],{},[679,924,681],{},[673,926,927,929,931],{},[679,928,598],{},[679,930,688],{},[679,932,691],{},[913,934,936],{"stretchy":935},"false","(",[679,938,939],{},"M",[913,941,942],{"stretchy":935},")",[944,945],"mspace",{"width":946},"2em",[679,948,939],{},[913,950,915],{},[676,952,953,956],{},[679,954,955],{},"D",[676,957,958,960],{},[679,959,681],{},[673,961,962,964,966,968],{},[679,963,598],{},[679,965,811],{},[679,967,814],{},[679,969,817],{},[913,971,936],{"stretchy":935},[679,973,911],{},[913,975,942],{"stretchy":935},[693,977,978],{"encoding":695},"C = E_{K_{pub}}(M) \\qquad M = D_{K_{priv}}(C)",[657,980,982,1003,1137],{"className":981,"ariaHidden":701},[700],[657,983,985,989,992,996,1000],{"className":984},[705],[657,986],{"className":987,"style":988},[709],"height:0.6833em;",[657,990,911],{"className":991,"style":719},[714,718],[657,993],{"className":994,"style":995},[944],"margin-right:0.2778em;",[657,997,915],{"className":998},[999],"mrel",[657,1001],{"className":1002,"style":995},[944],[657,1004,1006,1010,1109,1113,1117,1121,1125,1128,1131,1134],{"className":1005},[705],[657,1007],{"className":1008,"style":1009},[709],"height:1.1031em;vertical-align:-0.3531em;",[657,1011,1013,1017],{"className":1012},[714],[657,1014,920],{"className":1015,"style":1016},[714,718],"margin-right:0.0576em;",[657,1018,1020],{"className":1019},[723],[657,1021,1023,1100],{"className":1022},[727,728],[657,1024,1026,1097],{"className":1025},[732],[657,1027,1030],{"className":1028,"style":1029},[736],"height:0.3283em;",[657,1031,1033,1036],{"style":1032},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[657,1034],{"className":1035,"style":745},[744],[657,1037,1039],{"className":1038},[749,750,751,752],[657,1040,1042],{"className":1041},[714,752],[657,1043,1045,1048],{"className":1044},[714,752],[657,1046,681],{"className":1047,"style":719},[714,718,752],[657,1049,1051],{"className":1050},[723],[657,1052,1054,1088],{"className":1053},[727,728],[657,1055,1057,1085],{"className":1056},[732],[657,1058,1061],{"className":1059,"style":1060},[736],"height:0.3448em;",[657,1062,1064,1068],{"style":1063},"top:-2.3488em;margin-left:-0.0715em;margin-right:0.0714em;",[657,1065],{"className":1066,"style":1067},[744],"height:2.5em;",[657,1069,1073],{"className":1070},[749,1071,1072,752],"reset-size3","size1",[657,1074,1076,1079,1082],{"className":1075},[714,752],[657,1077,598],{"className":1078},[714,718,752],[657,1080,688],{"className":1081},[714,718,752],[657,1083,691],{"className":1084},[714,718,752],[657,1086,769],{"className":1087},[768],[657,1089,1091],{"className":1090},[732],[657,1092,1095],{"className":1093,"style":1094},[736],"height:0.2901em;",[657,1096],{},[657,1098,769],{"className":1099},[768],[657,1101,1103],{"className":1102},[732],[657,1104,1107],{"className":1105,"style":1106},[736],"height:0.3531em;",[657,1108],{},[657,1110,936],{"className":1111},[1112],"mopen",[657,1114,939],{"className":1115,"style":1116},[714,718],"margin-right:0.109em;",[657,1118,942],{"className":1119},[1120],"mclose",[657,1122],{"className":1123,"style":1124},[944],"margin-right:2em;",[657,1126,939],{"className":1127,"style":1116},[714,718],[657,1129],{"className":1130,"style":995},[944],[657,1132,915],{"className":1133},[999],[657,1135],{"className":1136,"style":995},[944],[657,1138,1140,1144,1241,1244,1247],{"className":1139},[705],[657,1141],{"className":1142,"style":1143},[709],"height:1.0973em;vertical-align:-0.3473em;",[657,1145,1147,1150],{"className":1146},[714],[657,1148,955],{"className":1149,"style":866},[714,718],[657,1151,1153],{"className":1152},[723],[657,1154,1156,1232],{"className":1155},[727,728],[657,1157,1159,1229],{"className":1158},[732],[657,1160,1162],{"className":1161,"style":1029},[736],[657,1163,1165,1168],{"style":1164},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[657,1166],{"className":1167,"style":745},[744],[657,1169,1171],{"className":1170},[749,750,751,752],[657,1172,1174],{"className":1173},[714,752],[657,1175,1177,1180],{"className":1176},[714,752],[657,1178,681],{"className":1179,"style":719},[714,718,752],[657,1181,1183],{"className":1182},[723],[657,1184,1186,1220],{"className":1185},[727,728],[657,1187,1189,1217],{"className":1188},[732],[657,1190,1193],{"className":1191,"style":1192},[736],"height:0.3281em;",[657,1194,1196,1199],{"style":1195},"top:-2.357em;margin-left:-0.0715em;margin-right:0.0714em;",[657,1197],{"className":1198,"style":1067},[744],[657,1200,1202],{"className":1201},[749,1071,1072,752],[657,1203,1205,1208,1211,1214],{"className":1204},[714,752],[657,1206,598],{"className":1207},[714,718,752],[657,1209,811],{"className":1210,"style":866},[714,718,752],[657,1212,814],{"className":1213},[714,718,752],[657,1215,817],{"className":1216,"style":873},[714,718,752],[657,1218,769],{"className":1219},[768],[657,1221,1223],{"className":1222},[732],[657,1224,1227],{"className":1225,"style":1226},[736],"height:0.2819em;",[657,1228],{},[657,1230,769],{"className":1231},[768],[657,1233,1235],{"className":1234},[732],[657,1236,1239],{"className":1237,"style":1238},[736],"height:0.3473em;",[657,1240],{},[657,1242,936],{"className":1243},[1112],[657,1245,911],{"className":1246,"style":719},[714,718],[657,1248,942],{"className":1249},[1120],[646,1251,1252,1343],{},[649,1253,1254,1257,1258,1342],{},[602,1255,1256],{},"N'importe qui"," peut chiffrer un message avec ",[657,1259,1261,1284],{"className":1260},[660],[657,1262,1264],{"className":1263},[664],[666,1265,1266],{"xmlns":668},[670,1267,1268,1282],{},[673,1269,1270],{},[676,1271,1272,1274],{},[679,1273,681],{},[673,1275,1276,1278,1280],{},[679,1277,598],{},[679,1279,688],{},[679,1281,691],{},[693,1283,696],{"encoding":695},[657,1285,1287],{"className":1286,"ariaHidden":701},[700],[657,1288,1290,1293],{"className":1289},[705],[657,1291],{"className":1292,"style":710},[709],[657,1294,1296,1299],{"className":1295},[714],[657,1297,681],{"className":1298,"style":719},[714,718],[657,1300,1302],{"className":1301},[723],[657,1303,1305,1334],{"className":1304},[727,728],[657,1306,1308,1331],{"className":1307},[732],[657,1309,1311],{"className":1310,"style":737},[736],[657,1312,1313,1316],{"style":740},[657,1314],{"className":1315,"style":745},[744],[657,1317,1319],{"className":1318},[749,750,751,752],[657,1320,1322,1325,1328],{"className":1321},[714,752],[657,1323,598],{"className":1324},[714,718,752],[657,1326,688],{"className":1327},[714,718,752],[657,1329,691],{"className":1330},[714,718,752],[657,1332,769],{"className":1333},[768],[657,1335,1337],{"className":1336},[732],[657,1338,1340],{"className":1339,"style":776},[736],[657,1341],{}," de Bob.",[649,1344,1345,1348,1349,633],{},[602,1346,1347],{},"Seul Bob"," peut le déchiffrer avec ",[657,1350,1352,1377],{"className":1351},[660],[657,1353,1355],{"className":1354},[664],[666,1356,1357],{"xmlns":668},[670,1358,1359,1375],{},[673,1360,1361],{},[676,1362,1363,1365],{},[679,1364,681],{},[673,1366,1367,1369,1371,1373],{},[679,1368,598],{},[679,1370,811],{},[679,1372,814],{},[679,1374,817],{},[693,1376,820],{"encoding":695},[657,1378,1380],{"className":1379,"ariaHidden":701},[700],[657,1381,1383,1386],{"className":1382},[705],[657,1384],{"className":1385,"style":710},[709],[657,1387,1389,1392],{"className":1388},[714],[657,1390,681],{"className":1391,"style":719},[714,718],[657,1393,1395],{"className":1394},[723],[657,1396,1398,1430],{"className":1397},[727,728],[657,1399,1401,1427],{"className":1400},[732],[657,1402,1404],{"className":1403,"style":848},[736],[657,1405,1406,1409],{"style":740},[657,1407],{"className":1408,"style":745},[744],[657,1410,1412],{"className":1411},[749,750,751,752],[657,1413,1415,1418,1421,1424],{"className":1414},[714,752],[657,1416,598],{"className":1417},[714,718,752],[657,1419,811],{"className":1420,"style":866},[714,718,752],[657,1422,814],{"className":1423},[714,718,752],[657,1425,817],{"className":1426,"style":873},[714,718,752],[657,1428,769],{"className":1429},[768],[657,1431,1433],{"className":1432},[732],[657,1434,1436],{"className":1435,"style":776},[736],[657,1437],{},[598,1439,1440,1441,1444,1445,1448,1449,1538,1539,1623],{},"L'asymétrie est dans le nom : la clé qui chiffre ",[602,1442,1443],{},"n'est pas"," celle qui\ndéchiffre. Et il est ",[602,1446,1447],{},"calculatoirement impossible"," de retrouver\n",[657,1450,1452,1477],{"className":1451},[660],[657,1453,1455],{"className":1454},[664],[666,1456,1457],{"xmlns":668},[670,1458,1459,1475],{},[673,1460,1461],{},[676,1462,1463,1465],{},[679,1464,681],{},[673,1466,1467,1469,1471,1473],{},[679,1468,598],{},[679,1470,811],{},[679,1472,814],{},[679,1474,817],{},[693,1476,820],{"encoding":695},[657,1478,1480],{"className":1479,"ariaHidden":701},[700],[657,1481,1483,1486],{"className":1482},[705],[657,1484],{"className":1485,"style":710},[709],[657,1487,1489,1492],{"className":1488},[714],[657,1490,681],{"className":1491,"style":719},[714,718],[657,1493,1495],{"className":1494},[723],[657,1496,1498,1530],{"className":1497},[727,728],[657,1499,1501,1527],{"className":1500},[732],[657,1502,1504],{"className":1503,"style":848},[736],[657,1505,1506,1509],{"style":740},[657,1507],{"className":1508,"style":745},[744],[657,1510,1512],{"className":1511},[749,750,751,752],[657,1513,1515,1518,1521,1524],{"className":1514},[714,752],[657,1516,598],{"className":1517},[714,718,752],[657,1519,811],{"className":1520,"style":866},[714,718,752],[657,1522,814],{"className":1523},[714,718,752],[657,1525,817],{"className":1526,"style":873},[714,718,752],[657,1528,769],{"className":1529},[768],[657,1531,1533],{"className":1532},[732],[657,1534,1536],{"className":1535,"style":776},[736],[657,1537],{}," à partir de ",[657,1540,1542,1565],{"className":1541},[660],[657,1543,1545],{"className":1544},[664],[666,1546,1547],{"xmlns":668},[670,1548,1549,1563],{},[673,1550,1551],{},[676,1552,1553,1555],{},[679,1554,681],{},[673,1556,1557,1559,1561],{},[679,1558,598],{},[679,1560,688],{},[679,1562,691],{},[693,1564,696],{"encoding":695},[657,1566,1568],{"className":1567,"ariaHidden":701},[700],[657,1569,1571,1574],{"className":1570},[705],[657,1572],{"className":1573,"style":710},[709],[657,1575,1577,1580],{"className":1576},[714],[657,1578,681],{"className":1579,"style":719},[714,718],[657,1581,1583],{"className":1582},[723],[657,1584,1586,1615],{"className":1585},[727,728],[657,1587,1589,1612],{"className":1588},[732],[657,1590,1592],{"className":1591,"style":737},[736],[657,1593,1594,1597],{"style":740},[657,1595],{"className":1596,"style":745},[744],[657,1598,1600],{"className":1599},[749,750,751,752],[657,1601,1603,1606,1609],{"className":1602},[714,752],[657,1604,598],{"className":1605},[714,718,752],[657,1607,688],{"className":1608},[714,718,752],[657,1610,691],{"className":1611},[714,718,752],[657,1613,769],{"className":1614},[768],[657,1616,1618],{"className":1617},[732],[657,1619,1621],{"className":1620,"style":776},[736],[657,1622],{}," — c'est ce qui rend le système sûr.",[1625,1626,1627],"tip",{},[598,1628,1629,1632,1633,1636],{},[602,1630,1631],{},"Analogie du cadenas ouvert."," Imaginez que Bob distribue partout des\n",[602,1634,1635],{},"cadenas ouverts"," dont lui seul possède la clé. Alice prend un cadenas,\nreferme une boîte avec, et expédie. Seul Bob, avec sa clé, peut rouvrir.\nLe cadenas (clé publique) est public, la clé (clé privée) est privée.",[593,1638,1640],{"id":1639},"lidée-de-rsa-modulo-et-exponentiation","L'idée de RSA — modulo et exponentiation",[598,1642,1643,1644,1647,1648,1651,1652,1655,1656,1659,1660,633],{},"Le représentant le plus connu de chiffrement asymétrique est ",[602,1645,1646],{},"RSA","\n(Rivest, Shamir, Adleman, 1977). Vous n'avez ",[602,1649,1650],{},"pas"," à connaître la\ndémonstration complète au niveau Terminale, mais vous devez en\n",[602,1653,1654],{},"reconnaître les ingrédients"," : le ",[602,1657,1658],{},"modulo"," et l'",[602,1661,1662],{},"exponentiation\nmodulaire",[598,1664,1665],{},"L'idée tient en trois étapes (très simplifiées) :",[1667,1668,1669,1925,2075],"ol",{},[649,1670,1671,1672,1701,1702,1731,1732,1811,1812,1840,1841,633],{},"Bob choisit deux grands nombres premiers ",[657,1673,1675,1688],{"className":1674},[660],[657,1676,1678],{"className":1677},[664],[666,1679,1680],{"xmlns":668},[670,1681,1682,1686],{},[673,1683,1684],{},[679,1685,598],{},[693,1687,598],{"encoding":695},[657,1689,1691],{"className":1690,"ariaHidden":701},[700],[657,1692,1694,1698],{"className":1693},[705],[657,1695],{"className":1696,"style":1697},[709],"height:0.625em;vertical-align:-0.1944em;",[657,1699,598],{"className":1700},[714,718]," et ",[657,1703,1705,1719],{"className":1704},[660],[657,1706,1708],{"className":1707},[664],[666,1709,1710],{"xmlns":668},[670,1711,1712,1717],{},[673,1713,1714],{},[679,1715,1716],{},"q",[693,1718,1716],{"encoding":695},[657,1720,1722],{"className":1721,"ariaHidden":701},[700],[657,1723,1725,1728],{"className":1724},[705],[657,1726],{"className":1727,"style":1697},[709],[657,1729,1716],{"className":1730,"style":873},[714,718],". Il calcule leur\nproduit ",[657,1733,1735,1759],{"className":1734},[660],[657,1736,1738],{"className":1737},[664],[666,1739,1740],{"xmlns":668},[670,1741,1742,1756],{},[673,1743,1744,1747,1749,1751,1754],{},[679,1745,1746],{},"n",[913,1748,915],{},[679,1750,598],{},[913,1752,1753],{},"×",[679,1755,1716],{},[693,1757,1758],{"encoding":695},"n = p \\times q",[657,1760,1762,1781,1802],{"className":1761,"ariaHidden":701},[700],[657,1763,1765,1769,1772,1775,1778],{"className":1764},[705],[657,1766],{"className":1767,"style":1768},[709],"height:0.4306em;",[657,1770,1746],{"className":1771},[714,718],[657,1773],{"className":1774,"style":995},[944],[657,1776,915],{"className":1777},[999],[657,1779],{"className":1780,"style":995},[944],[657,1782,1784,1788,1791,1795,1799],{"className":1783},[705],[657,1785],{"className":1786,"style":1787},[709],"height:0.7778em;vertical-align:-0.1944em;",[657,1789,598],{"className":1790},[714,718],[657,1792],{"className":1793,"style":1794},[944],"margin-right:0.2222em;",[657,1796,1753],{"className":1797},[1798],"mbin",[657,1800],{"className":1801,"style":1794},[944],[657,1803,1805,1808],{"className":1804},[705],[657,1806],{"className":1807,"style":1697},[709],[657,1809,1716],{"className":1810,"style":873},[714,718],". Ce ",[657,1813,1815,1828],{"className":1814},[660],[657,1816,1818],{"className":1817},[664],[666,1819,1820],{"xmlns":668},[670,1821,1822,1826],{},[673,1823,1824],{},[679,1825,1746],{},[693,1827,1746],{"encoding":695},[657,1829,1831],{"className":1830,"ariaHidden":701},[700],[657,1832,1834,1837],{"className":1833},[705],[657,1835],{"className":1836,"style":1768},[709],[657,1838,1746],{"className":1839},[714,718]," devient public — il fait partie de\n",[657,1842,1844,1867],{"className":1843},[660],[657,1845,1847],{"className":1846},[664],[666,1848,1849],{"xmlns":668},[670,1850,1851,1865],{},[673,1852,1853],{},[676,1854,1855,1857],{},[679,1856,681],{},[673,1858,1859,1861,1863],{},[679,1860,598],{},[679,1862,688],{},[679,1864,691],{},[693,1866,696],{"encoding":695},[657,1868,1870],{"className":1869,"ariaHidden":701},[700],[657,1871,1873,1876],{"className":1872},[705],[657,1874],{"className":1875,"style":710},[709],[657,1877,1879,1882],{"className":1878},[714],[657,1880,681],{"className":1881,"style":719},[714,718],[657,1883,1885],{"className":1884},[723],[657,1886,1888,1917],{"className":1887},[727,728],[657,1889,1891,1914],{"className":1890},[732],[657,1892,1894],{"className":1893,"style":737},[736],[657,1895,1896,1899],{"style":740},[657,1897],{"className":1898,"style":745},[744],[657,1900,1902],{"className":1901},[749,750,751,752],[657,1903,1905,1908,1911],{"className":1904},[714,752],[657,1906,598],{"className":1907},[714,718,752],[657,1909,688],{"className":1910},[714,718,752],[657,1912,691],{"className":1913},[714,718,752],[657,1915,769],{"className":1916},[768],[657,1918,1920],{"className":1919},[732],[657,1921,1923],{"className":1922,"style":776},[736],[657,1924],{},[649,1926,1927,1928,1986,1987,2015,2016,2044,2045,2074],{},"Bob calcule un couple d'exposants ",[657,1929,1931,1956],{"className":1930},[660],[657,1932,1934],{"className":1933},[664],[666,1935,1936],{"xmlns":668},[670,1937,1938,1953],{},[673,1939,1940,1942,1945,1948,1951],{},[913,1941,936],{"stretchy":935},[679,1943,1944],{},"e",[913,1946,1947],{"separator":701},",",[679,1949,1950],{},"d",[913,1952,942],{"stretchy":935},[693,1954,1955],{"encoding":695},"(e, d)",[657,1957,1959],{"className":1958,"ariaHidden":701},[700],[657,1960,1962,1966,1969,1972,1976,1980,1983],{"className":1961},[705],[657,1963],{"className":1964,"style":1965},[709],"height:1em;vertical-align:-0.25em;",[657,1967,936],{"className":1968},[1112],[657,1970,1944],{"className":1971},[714,718],[657,1973,1947],{"className":1974},[1975],"mpunct",[657,1977],{"className":1978,"style":1979},[944],"margin-right:0.1667em;",[657,1981,1950],{"className":1982},[714,718],[657,1984,942],{"className":1985},[1120]," liés par une relation\nmodulaire. ",[657,1988,1990,2003],{"className":1989},[660],[657,1991,1993],{"className":1992},[664],[666,1994,1995],{"xmlns":668},[670,1996,1997,2001],{},[673,1998,1999],{},[679,2000,1944],{},[693,2002,1944],{"encoding":695},[657,2004,2006],{"className":2005,"ariaHidden":701},[700],[657,2007,2009,2012],{"className":2008},[705],[657,2010],{"className":2011,"style":1768},[709],[657,2013,1944],{"className":2014},[714,718]," est public (avec ",[657,2017,2019,2032],{"className":2018},[660],[657,2020,2022],{"className":2021},[664],[666,2023,2024],{"xmlns":668},[670,2025,2026,2030],{},[673,2027,2028],{},[679,2029,1746],{},[693,2031,1746],{"encoding":695},[657,2033,2035],{"className":2034,"ariaHidden":701},[700],[657,2036,2038,2041],{"className":2037},[705],[657,2039],{"className":2040,"style":1768},[709],[657,2042,1746],{"className":2043},[714,718],"), ",[657,2046,2048,2061],{"className":2047},[660],[657,2049,2051],{"className":2050},[664],[666,2052,2053],{"xmlns":668},[670,2054,2055,2059],{},[673,2056,2057],{},[679,2058,1950],{},[693,2060,1950],{"encoding":695},[657,2062,2064],{"className":2063,"ariaHidden":701},[700],[657,2065,2067,2071],{"className":2066},[705],[657,2068],{"className":2069,"style":2070},[709],"height:0.6944em;",[657,2072,1950],{"className":2073},[714,718]," est privé.",[649,2076,2077,2078,2106,2107,2252,2253],{},"Pour chiffrer un message ",[657,2079,2081,2094],{"className":2080},[660],[657,2082,2084],{"className":2083},[664],[666,2085,2086],{"xmlns":668},[670,2087,2088,2092],{},[673,2089,2090],{},[679,2091,939],{},[693,2093,939],{"encoding":695},[657,2095,2097],{"className":2096,"ariaHidden":701},[700],[657,2098,2100,2103],{"className":2099},[705],[657,2101],{"className":2102,"style":988},[709],[657,2104,939],{"className":2105,"style":1116},[714,718]," représenté comme un entier, on calcule :\n",[657,2108,2110],{"className":2109},[895],[657,2111,2113,2158],{"className":2112},[660],[657,2114,2116],{"className":2115},[664],[666,2117,2118],{"xmlns":668,"display":904},[670,2119,2120,2155],{},[673,2121,2122,2124,2126,2133,2137,2151,2153],{},[679,2123,911],{},[913,2125,915],{},[2127,2128,2129,2131],"msup",{},[679,2130,939],{},[679,2132,1944],{},[2134,2135,2136],"mtext",{}," ",[913,2138,2140],{"lspace":2139,"rspace":2139},"0.22em",[673,2141,2142,2146,2149],{},[679,2143,2145],{"mathvariant":2144},"normal","m",[679,2147,2148],{"mathvariant":2144},"o",[679,2150,1950],{"mathvariant":2144},[2134,2152,2136],{},[679,2154,1746],{},[693,2156,2157],{"encoding":695},"C = M^{e} \\bmod n",[657,2159,2161,2179,2243],{"className":2160,"ariaHidden":701},[700],[657,2162,2164,2167,2170,2173,2176],{"className":2163},[705],[657,2165],{"className":2166,"style":988},[709],[657,2168,911],{"className":2169,"style":719},[714,718],[657,2171],{"className":2172,"style":995},[944],[657,2174,915],{"className":2175},[999],[657,2177],{"className":2178,"style":995},[944],[657,2180,2182,2186,2219,2223,2226,2237,2240],{"className":2181},[705],[657,2183],{"className":2184,"style":2185},[709],"height:0.7144em;",[657,2187,2189,2192],{"className":2188},[714],[657,2190,939],{"className":2191,"style":1116},[714,718],[657,2193,2195],{"className":2194},[723],[657,2196,2198],{"className":2197},[727],[657,2199,2201],{"className":2200},[732],[657,2202,2204],{"className":2203,"style":2185},[736],[657,2205,2207,2210],{"style":2206},"top:-3.113em;margin-right:0.05em;",[657,2208],{"className":2209,"style":745},[744],[657,2211,2213],{"className":2212},[749,750,751,752],[657,2214,2216],{"className":2215},[714,752],[657,2217,1944],{"className":2218},[714,718,752],[657,2220],{"className":2221,"style":2222},[944],"margin-right:0.0556em;",[657,2224],{"className":2225,"style":1794},[944],[657,2227,2229],{"className":2228},[1798],[657,2230,2232],{"className":2231},[714],[657,2233,2236],{"className":2234},[714,2235],"mathrm","mod",[657,2238],{"className":2239,"style":2222},[944],[657,2241],{"className":2242,"style":1794},[944],[657,2244,2246,2249],{"className":2245},[705],[657,2247],{"className":2248,"style":1768},[709],[657,2250,1746],{"className":2251},[714,718],"\nEt pour déchiffrer :\n",[657,2254,2256],{"className":2255},[895],[657,2257,2259,2297],{"className":2258},[660],[657,2260,2262],{"className":2261},[664],[666,2263,2264],{"xmlns":668,"display":904},[670,2265,2266,2294],{},[673,2267,2268,2270,2272,2278,2280,2290,2292],{},[679,2269,939],{},[913,2271,915],{},[2127,2273,2274,2276],{},[679,2275,911],{},[679,2277,1950],{},[2134,2279,2136],{},[913,2281,2282],{"lspace":2139,"rspace":2139},[673,2283,2284,2286,2288],{},[679,2285,2145],{"mathvariant":2144},[679,2287,2148],{"mathvariant":2144},[679,2289,1950],{"mathvariant":2144},[2134,2291,2136],{},[679,2293,1746],{},[693,2295,2296],{"encoding":695},"M = C^{d} \\bmod n",[657,2298,2300,2318,2378],{"className":2299,"ariaHidden":701},[700],[657,2301,2303,2306,2309,2312,2315],{"className":2302},[705],[657,2304],{"className":2305,"style":988},[709],[657,2307,939],{"className":2308,"style":1116},[714,718],[657,2310],{"className":2311,"style":995},[944],[657,2313,915],{"className":2314},[999],[657,2316],{"className":2317,"style":995},[944],[657,2319,2321,2325,2357,2360,2363,2372,2375],{"className":2320},[705],[657,2322],{"className":2323,"style":2324},[709],"height:0.8991em;",[657,2326,2328,2331],{"className":2327},[714],[657,2329,911],{"className":2330,"style":719},[714,718],[657,2332,2334],{"className":2333},[723],[657,2335,2337],{"className":2336},[727],[657,2338,2340],{"className":2339},[732],[657,2341,2343],{"className":2342,"style":2324},[736],[657,2344,2345,2348],{"style":2206},[657,2346],{"className":2347,"style":745},[744],[657,2349,2351],{"className":2350},[749,750,751,752],[657,2352,2354],{"className":2353},[714,752],[657,2355,1950],{"className":2356},[714,718,752],[657,2358],{"className":2359,"style":2222},[944],[657,2361],{"className":2362,"style":1794},[944],[657,2364,2366],{"className":2365},[1798],[657,2367,2369],{"className":2368},[714],[657,2370,2236],{"className":2371},[714,2235],[657,2373],{"className":2374,"style":2222},[944],[657,2376],{"className":2377,"style":1794},[944],[657,2379,2381,2384],{"className":2380},[705],[657,2382],{"className":2383,"style":1768},[709],[657,2385,1746],{"className":2386},[714,718],[2388,2389,2390],"note",{},[598,2391,2392,2393,2477,2478,1701,2506,2534,2535,1701,2563,2591,2592,2620,2621,2649],{},"La sécurité de RSA repose sur le fait que ",[602,2394,2395,2396,2424,2425,2476],{},"factoriser ",[657,2397,2399,2412],{"className":2398},[660],[657,2400,2402],{"className":2401},[664],[666,2403,2404],{"xmlns":668},[670,2405,2406,2410],{},[673,2407,2408],{},[679,2409,1746],{},[693,2411,1746],{"encoding":695},[657,2413,2415],{"className":2414,"ariaHidden":701},[700],[657,2416,2418,2421],{"className":2417},[705],[657,2419],{"className":2420,"style":1768},[709],[657,2422,1746],{"className":2423},[714,718]," en ",[657,2426,2428,2446],{"className":2427},[660],[657,2429,2431],{"className":2430},[664],[666,2432,2433],{"xmlns":668},[670,2434,2435,2443],{},[673,2436,2437,2439,2441],{},[679,2438,598],{},[913,2440,1753],{},[679,2442,1716],{},[693,2444,2445],{"encoding":695},"p \\times q",[657,2447,2449,2467],{"className":2448,"ariaHidden":701},[700],[657,2450,2452,2455,2458,2461,2464],{"className":2451},[705],[657,2453],{"className":2454,"style":1787},[709],[657,2456,598],{"className":2457},[714,718],[657,2459],{"className":2460,"style":1794},[944],[657,2462,1753],{"className":2463},[1798],[657,2465],{"className":2466,"style":1794},[944],[657,2468,2470,2473],{"className":2469},[705],[657,2471],{"className":2472,"style":1697},[709],[657,2474,1716],{"className":2475,"style":873},[714,718],"\nest extrêmement coûteux"," quand ",[657,2479,2481,2494],{"className":2480},[660],[657,2482,2484],{"className":2483},[664],[666,2485,2486],{"xmlns":668},[670,2487,2488,2492],{},[673,2489,2490],{},[679,2491,598],{},[693,2493,598],{"encoding":695},[657,2495,2497],{"className":2496,"ariaHidden":701},[700],[657,2498,2500,2503],{"className":2499},[705],[657,2501],{"className":2502,"style":1697},[709],[657,2504,598],{"className":2505},[714,718],[657,2507,2509,2522],{"className":2508},[660],[657,2510,2512],{"className":2511},[664],[666,2513,2514],{"xmlns":668},[670,2515,2516,2520],{},[673,2517,2518],{},[679,2519,1716],{},[693,2521,1716],{"encoding":695},[657,2523,2525],{"className":2524,"ariaHidden":701},[700],[657,2526,2528,2531],{"className":2527},[705],[657,2529],{"className":2530,"style":1697},[709],[657,2532,1716],{"className":2533,"style":873},[714,718]," sont très grands (typiquement\n1024 ou 2048 bits chacun). Sans ",[657,2536,2538,2551],{"className":2537},[660],[657,2539,2541],{"className":2540},[664],[666,2542,2543],{"xmlns":668},[670,2544,2545,2549],{},[673,2546,2547],{},[679,2548,598],{},[693,2550,598],{"encoding":695},[657,2552,2554],{"className":2553,"ariaHidden":701},[700],[657,2555,2557,2560],{"className":2556},[705],[657,2558],{"className":2559,"style":1697},[709],[657,2561,598],{"className":2562},[714,718],[657,2564,2566,2579],{"className":2565},[660],[657,2567,2569],{"className":2568},[664],[666,2570,2571],{"xmlns":668},[670,2572,2573,2577],{},[673,2574,2575],{},[679,2576,1716],{},[693,2578,1716],{"encoding":695},[657,2580,2582],{"className":2581,"ariaHidden":701},[700],[657,2583,2585,2588],{"className":2584},[705],[657,2586],{"className":2587,"style":1697},[709],[657,2589,1716],{"className":2590,"style":873},[714,718],", on ne peut pas retrouver ",[657,2593,2595,2608],{"className":2594},[660],[657,2596,2598],{"className":2597},[664],[666,2599,2600],{"xmlns":668},[670,2601,2602,2606],{},[673,2603,2604],{},[679,2605,1950],{},[693,2607,1950],{"encoding":695},[657,2609,2611],{"className":2610,"ariaHidden":701},[700],[657,2612,2614,2617],{"className":2613},[705],[657,2615],{"className":2616,"style":2070},[709],[657,2618,1950],{"className":2619},[714,718],".\nAvec les ordinateurs actuels, factoriser un ",[657,2622,2624,2637],{"className":2623},[660],[657,2625,2627],{"className":2626},[664],[666,2628,2629],{"xmlns":668},[670,2630,2631,2635],{},[673,2632,2633],{},[679,2634,1746],{},[693,2636,1746],{"encoding":695},[657,2638,2640],{"className":2639,"ariaHidden":701},[700],[657,2641,2643,2646],{"className":2642},[705],[657,2644],{"className":2645,"style":1768},[709],[657,2647,1746],{"className":2648},[714,718]," de 2048 bits prendrait\ndes siècles.",[598,2651,2652,2653,644],{},"Pour comprendre l'opération centrale, regardez ce qu'est l'",[602,2654,1662],{},[2656,2657,2662],"pre",{"className":2658,"code":2659,"language":2660,"meta":2661,"style":2661},"language-python shiki shiki-themes github-light github-light github-dark","def exp_modulaire(base: int, exposant: int, modulo: int) -> int:\n    \"\"\"Calcule (base ** exposant) % modulo, efficacement.\"\"\"\n    return pow(base, exposant, modulo)\n\n# Exemple jouet avec p=11, q=13 → n=143, e=7, d=103\nn, e, d = 143, 7, 103\nM = 42\nC = exp_modulaire(M, e, n)\nprint(C)                              # 81\nM_restitue = exp_modulaire(C, d, n)\nprint(M_restitue)                     # 42\n","python","",[2663,2664,2665,2703,2710,2722,2729,2736,2758,2769,2780,2792,2803],"code",{"__ignoreMap":2661},[657,2666,2669,2673,2677,2681,2685,2688,2690,2693,2695,2698,2700],{"class":2667,"line":2668},"line",1,[657,2670,2672],{"class":2671},"s8jYJ","def",[657,2674,2676],{"class":2675},"snPdu"," exp_modulaire",[657,2678,2680],{"class":2679},"sxrX7","(base: ",[657,2682,2684],{"class":2683},"sBjJW","int",[657,2686,2687],{"class":2679},", exposant: ",[657,2689,2684],{"class":2683},[657,2691,2692],{"class":2679},", modulo: ",[657,2694,2684],{"class":2683},[657,2696,2697],{"class":2679},") -> ",[657,2699,2684],{"class":2683},[657,2701,2702],{"class":2679},":\n",[657,2704,2706],{"class":2667,"line":2705},2,[657,2707,2709],{"class":2708},"sIIMD","    \"\"\"Calcule (base ** exposant) % modulo, efficacement.\"\"\"\n",[657,2711,2713,2716,2719],{"class":2667,"line":2712},3,[657,2714,2715],{"class":2671},"    return",[657,2717,2718],{"class":2683}," pow",[657,2720,2721],{"class":2679},"(base, exposant, modulo)\n",[657,2723,2725],{"class":2667,"line":2724},4,[657,2726,2728],{"emptyLinePlaceholder":2727},true,"\n",[657,2730,2732],{"class":2667,"line":2731},5,[657,2733,2735],{"class":2734},"sCsY4","# Exemple jouet avec p=11, q=13 → n=143, e=7, d=103\n",[657,2737,2739,2742,2744,2747,2750,2753,2755],{"class":2667,"line":2738},6,[657,2740,2741],{"class":2679},"n, e, d ",[657,2743,915],{"class":2671},[657,2745,2746],{"class":2683}," 143",[657,2748,2749],{"class":2679},", ",[657,2751,2752],{"class":2683},"7",[657,2754,2749],{"class":2679},[657,2756,2757],{"class":2683},"103\n",[657,2759,2761,2764,2766],{"class":2667,"line":2760},7,[657,2762,2763],{"class":2679},"M ",[657,2765,915],{"class":2671},[657,2767,2768],{"class":2683}," 42\n",[657,2770,2772,2775,2777],{"class":2667,"line":2771},8,[657,2773,2774],{"class":2679},"C ",[657,2776,915],{"class":2671},[657,2778,2779],{"class":2679}," exp_modulaire(M, e, n)\n",[657,2781,2783,2786,2789],{"class":2667,"line":2782},9,[657,2784,2785],{"class":2683},"print",[657,2787,2788],{"class":2679},"(C)                              ",[657,2790,2791],{"class":2734},"# 81\n",[657,2793,2795,2798,2800],{"class":2667,"line":2794},10,[657,2796,2797],{"class":2679},"M_restitue ",[657,2799,915],{"class":2671},[657,2801,2802],{"class":2679}," exp_modulaire(C, d, n)\n",[657,2804,2806,2808,2811],{"class":2667,"line":2805},11,[657,2807,2785],{"class":2683},[657,2809,2810],{"class":2679},"(M_restitue)                     ",[657,2812,2813],{"class":2734},"# 42\n",[598,2815,2816,2817,2820,2821,3008],{},"L'instruction ",[2663,2818,2819],{},"pow(base, exposant, modulo)"," de Python calcule\n",[657,2822,2824,2895],{"className":2823},[660],[657,2825,2827],{"className":2826},[664],[666,2828,2829],{"xmlns":668},[670,2830,2831,2892],{},[673,2832,2833,2835,2838,2841,2865,2867,2877,2879,2881,2883,2885,2887,2890],{},[679,2834,691],{},[679,2836,2837],{},"a",[679,2839,2840],{},"s",[2127,2842,2843,2845],{},[679,2844,1944],{},[673,2846,2847,2849,2852,2854,2856,2858,2860,2862],{},[679,2848,1944],{},[679,2850,2851],{},"x",[679,2853,598],{},[679,2855,2148],{},[679,2857,2840],{},[679,2859,2837],{},[679,2861,1746],{},[679,2863,2864],{},"t",[2134,2866,2136],{},[913,2868,2869],{"lspace":2139,"rspace":2139},[673,2870,2871,2873,2875],{},[679,2872,2145],{"mathvariant":2144},[679,2874,2148],{"mathvariant":2144},[679,2876,1950],{"mathvariant":2144},[2134,2878,2136],{},[679,2880,2145],{},[679,2882,2148],{},[679,2884,1950],{},[679,2886,688],{},[679,2888,2889],{},"l",[679,2891,2148],{},[693,2893,2894],{"encoding":695},"base^{exposant} \\bmod modulo",[657,2896,2898,2983],{"className":2897,"ariaHidden":701},[700],[657,2899,2901,2905,2909,2912,2962,2965,2968,2977,2980],{"className":2900},[705],[657,2902],{"className":2903,"style":2904},[709],"height:0.7936em;",[657,2906,2908],{"className":2907},[714,718],"ba",[657,2910,2840],{"className":2911},[714,718],[657,2913,2915,2918],{"className":2914},[714],[657,2916,1944],{"className":2917},[714,718],[657,2919,2921],{"className":2920},[723],[657,2922,2924],{"className":2923},[727],[657,2925,2927],{"className":2926},[732],[657,2928,2930],{"className":2929,"style":2904},[736],[657,2931,2933,2936],{"style":2932},"top:-3.063em;margin-right:0.05em;",[657,2934],{"className":2935,"style":745},[744],[657,2937,2939],{"className":2938},[749,750,751,752],[657,2940,2942,2945,2948,2951,2955,2959],{"className":2941},[714,752],[657,2943,1944],{"className":2944},[714,718,752],[657,2946,2851],{"className":2947},[714,718,752],[657,2949,598],{"className":2950},[714,718,752],[657,2952,2954],{"className":2953},[714,718,752],"os",[657,2956,2958],{"className":2957},[714,718,752],"an",[657,2960,2864],{"className":2961},[714,718,752],[657,2963],{"className":2964,"style":2222},[944],[657,2966],{"className":2967,"style":1794},[944],[657,2969,2971],{"className":2970},[1798],[657,2972,2974],{"className":2973},[714],[657,2975,2236],{"className":2976},[714,2235],[657,2978],{"className":2979,"style":2222},[944],[657,2981],{"className":2982,"style":1794},[944],[657,2984,2986,2989,2992,2995,2998,3001,3005],{"className":2985},[705],[657,2987],{"className":2988,"style":2070},[709],[657,2990,2145],{"className":2991},[714,718],[657,2993,2148],{"className":2994},[714,718],[657,2996,1950],{"className":2997},[714,718],[657,2999,688],{"className":3000},[714,718],[657,3002,2889],{"className":3003,"style":3004},[714,718],"margin-right:0.0197em;",[657,3006,2148],{"className":3007},[714,718]," efficacement, sans construire l'entier\ngéant intermédiaire. C'est l'opération de base de RSA.",[3010,3011,3014,3020],"self-eval-qcm",{"correct":3012,"slug":3013},"1","chiffrement-asymetrique-c1",[3015,3016,3017],"template",{"v-slot:question":2661},[598,3018,3019],{},"Dans RSA, la sécurité repose sur la difficulté de…",[3015,3021,3022],{"v-slot:choices":2661},[646,3023,3024,3027,3030],{},[649,3025,3026],{},"multiplier deux grands nombres",[649,3028,3029],{},"factoriser un grand nombre en deux premiers",[649,3031,3032],{},"additionner modulo n",[593,3034,3036],{"id":3035},"que-peut-on-faire-avec-une-paire-de-clés","Que peut-on faire avec une paire de clés ?",[598,3038,3039],{},"L'asymétrie autorise deux usages complémentaires :",[3041,3042,3043,3062],"table",{},[3044,3045,3046],"thead",{},[3047,3048,3049,3053,3056,3059],"tr",{},[3050,3051,3052],"th",{},"Opération",[3050,3054,3055],{},"Clé utilisée pour chiffrer",[3050,3057,3058],{},"Clé utilisée pour déchiffrer",[3050,3060,3061],{},"But",[3063,3064,3065,3254],"tbody",{},[3047,3066,3067,3073,3160,3251],{},[3068,3069,3070],"td",{},[602,3071,3072],{},"Confidentialité",[3068,3074,3075,3159],{},[657,3076,3078,3101],{"className":3077},[660],[657,3079,3081],{"className":3080},[664],[666,3082,3083],{"xmlns":668},[670,3084,3085,3099],{},[673,3086,3087],{},[676,3088,3089,3091],{},[679,3090,681],{},[673,3092,3093,3095,3097],{},[679,3094,598],{},[679,3096,688],{},[679,3098,691],{},[693,3100,696],{"encoding":695},[657,3102,3104],{"className":3103,"ariaHidden":701},[700],[657,3105,3107,3110],{"className":3106},[705],[657,3108],{"className":3109,"style":710},[709],[657,3111,3113,3116],{"className":3112},[714],[657,3114,681],{"className":3115,"style":719},[714,718],[657,3117,3119],{"className":3118},[723],[657,3120,3122,3151],{"className":3121},[727,728],[657,3123,3125,3148],{"className":3124},[732],[657,3126,3128],{"className":3127,"style":737},[736],[657,3129,3130,3133],{"style":740},[657,3131],{"className":3132,"style":745},[744],[657,3134,3136],{"className":3135},[749,750,751,752],[657,3137,3139,3142,3145],{"className":3138},[714,752],[657,3140,598],{"className":3141},[714,718,752],[657,3143,688],{"className":3144},[714,718,752],[657,3146,691],{"className":3147},[714,718,752],[657,3149,769],{"className":3150},[768],[657,3152,3154],{"className":3153},[732],[657,3155,3157],{"className":3156,"style":776},[736],[657,3158],{}," du destinataire",[3068,3161,3162,3159],{},[657,3163,3165,3190],{"className":3164},[660],[657,3166,3168],{"className":3167},[664],[666,3169,3170],{"xmlns":668},[670,3171,3172,3188],{},[673,3173,3174],{},[676,3175,3176,3178],{},[679,3177,681],{},[673,3179,3180,3182,3184,3186],{},[679,3181,598],{},[679,3183,811],{},[679,3185,814],{},[679,3187,817],{},[693,3189,820],{"encoding":695},[657,3191,3193],{"className":3192,"ariaHidden":701},[700],[657,3194,3196,3199],{"className":3195},[705],[657,3197],{"className":3198,"style":710},[709],[657,3200,3202,3205],{"className":3201},[714],[657,3203,681],{"className":3204,"style":719},[714,718],[657,3206,3208],{"className":3207},[723],[657,3209,3211,3243],{"className":3210},[727,728],[657,3212,3214,3240],{"className":3213},[732],[657,3215,3217],{"className":3216,"style":848},[736],[657,3218,3219,3222],{"style":740},[657,3220],{"className":3221,"style":745},[744],[657,3223,3225],{"className":3224},[749,750,751,752],[657,3226,3228,3231,3234,3237],{"className":3227},[714,752],[657,3229,598],{"className":3230},[714,718,752],[657,3232,811],{"className":3233,"style":866},[714,718,752],[657,3235,814],{"className":3236},[714,718,752],[657,3238,817],{"className":3239,"style":873},[714,718,752],[657,3241,769],{"className":3242},[768],[657,3244,3246],{"className":3245},[732],[657,3247,3249],{"className":3248,"style":776},[736],[657,3250],{},[3068,3252,3253],{},"Seul le destinataire lit",[3047,3255,3256,3261,3353,3439],{},[3068,3257,3258],{},[602,3259,3260],{},"Signature",[3068,3262,3263,3352],{},[657,3264,3266,3291],{"className":3265},[660],[657,3267,3269],{"className":3268},[664],[666,3270,3271],{"xmlns":668},[670,3272,3273,3289],{},[673,3274,3275],{},[676,3276,3277,3279],{},[679,3278,681],{},[673,3280,3281,3283,3285,3287],{},[679,3282,598],{},[679,3284,811],{},[679,3286,814],{},[679,3288,817],{},[693,3290,820],{"encoding":695},[657,3292,3294],{"className":3293,"ariaHidden":701},[700],[657,3295,3297,3300],{"className":3296},[705],[657,3298],{"className":3299,"style":710},[709],[657,3301,3303,3306],{"className":3302},[714],[657,3304,681],{"className":3305,"style":719},[714,718],[657,3307,3309],{"className":3308},[723],[657,3310,3312,3344],{"className":3311},[727,728],[657,3313,3315,3341],{"className":3314},[732],[657,3316,3318],{"className":3317,"style":848},[736],[657,3319,3320,3323],{"style":740},[657,3321],{"className":3322,"style":745},[744],[657,3324,3326],{"className":3325},[749,750,751,752],[657,3327,3329,3332,3335,3338],{"className":3328},[714,752],[657,3330,598],{"className":3331},[714,718,752],[657,3333,811],{"className":3334,"style":866},[714,718,752],[657,3336,814],{"className":3337},[714,718,752],[657,3339,817],{"className":3340,"style":873},[714,718,752],[657,3342,769],{"className":3343},[768],[657,3345,3347],{"className":3346},[732],[657,3348,3350],{"className":3349,"style":776},[736],[657,3351],{}," de l'expéditeur",[3068,3354,3355,3352],{},[657,3356,3358,3381],{"className":3357},[660],[657,3359,3361],{"className":3360},[664],[666,3362,3363],{"xmlns":668},[670,3364,3365,3379],{},[673,3366,3367],{},[676,3368,3369,3371],{},[679,3370,681],{},[673,3372,3373,3375,3377],{},[679,3374,598],{},[679,3376,688],{},[679,3378,691],{},[693,3380,696],{"encoding":695},[657,3382,3384],{"className":3383,"ariaHidden":701},[700],[657,3385,3387,3390],{"className":3386},[705],[657,3388],{"className":3389,"style":710},[709],[657,3391,3393,3396],{"className":3392},[714],[657,3394,681],{"className":3395,"style":719},[714,718],[657,3397,3399],{"className":3398},[723],[657,3400,3402,3431],{"className":3401},[727,728],[657,3403,3405,3428],{"className":3404},[732],[657,3406,3408],{"className":3407,"style":737},[736],[657,3409,3410,3413],{"style":740},[657,3411],{"className":3412,"style":745},[744],[657,3414,3416],{"className":3415},[749,750,751,752],[657,3417,3419,3422,3425],{"className":3418},[714,752],[657,3420,598],{"className":3421},[714,718,752],[657,3423,688],{"className":3424},[714,718,752],[657,3426,691],{"className":3427},[714,718,752],[657,3429,769],{"className":3430},[768],[657,3432,3434],{"className":3433},[732],[657,3435,3437],{"className":3436,"style":776},[736],[657,3438],{},[3068,3440,3441],{},"N'importe qui peut vérifier que c'est bien l'expéditeur",[598,3443,3444,3445,3448,3449,3538,3539,3567,3568,3757,3758,3761,3762,3765],{},"Dans le cas de la ",[602,3446,3447],{},"signature",", on inverse les rôles : seul Bob, qui\ndétient ",[657,3450,3452,3477],{"className":3451},[660],[657,3453,3455],{"className":3454},[664],[666,3456,3457],{"xmlns":668},[670,3458,3459,3475],{},[673,3460,3461],{},[676,3462,3463,3465],{},[679,3464,681],{},[673,3466,3467,3469,3471,3473],{},[679,3468,598],{},[679,3470,811],{},[679,3472,814],{},[679,3474,817],{},[693,3476,820],{"encoding":695},[657,3478,3480],{"className":3479,"ariaHidden":701},[700],[657,3481,3483,3486],{"className":3482},[705],[657,3484],{"className":3485,"style":710},[709],[657,3487,3489,3492],{"className":3488},[714],[657,3490,681],{"className":3491,"style":719},[714,718],[657,3493,3495],{"className":3494},[723],[657,3496,3498,3530],{"className":3497},[727,728],[657,3499,3501,3527],{"className":3500},[732],[657,3502,3504],{"className":3503,"style":848},[736],[657,3505,3506,3509],{"style":740},[657,3507],{"className":3508,"style":745},[744],[657,3510,3512],{"className":3511},[749,750,751,752],[657,3513,3515,3518,3521,3524],{"className":3514},[714,752],[657,3516,598],{"className":3517},[714,718,752],[657,3519,811],{"className":3520,"style":866},[714,718,752],[657,3522,814],{"className":3523},[714,718,752],[657,3525,817],{"className":3526,"style":873},[714,718,752],[657,3528,769],{"className":3529},[768],[657,3531,3533],{"className":3532},[732],[657,3534,3536],{"className":3535,"style":776},[736],[657,3537],{}," de Bob, peut produire ",[657,3540,3542,3555],{"className":3541},[660],[657,3543,3545],{"className":3544},[664],[666,3546,3547],{"xmlns":668},[670,3548,3549,3553],{},[673,3550,3551],{},[679,3552,911],{},[693,3554,911],{"encoding":695},[657,3556,3558],{"className":3557,"ariaHidden":701},[700],[657,3559,3561,3564],{"className":3560},[705],[657,3562],{"className":3563,"style":988},[709],[657,3565,911],{"className":3566,"style":719},[714,718]," tel que ",[657,3569,3571,3619],{"className":3570},[660],[657,3572,3574],{"className":3573},[664],[666,3575,3576],{"xmlns":668},[670,3577,3578,3616],{},[673,3579,3580,3606,3608,3610,3612,3614],{},[676,3581,3582,3584],{},[679,3583,955],{},[676,3585,3586,3588],{},[679,3587,681],{},[673,3589,3590,3592,3594,3596,3599,3602,3604],{},[679,3591,598],{},[679,3593,688],{},[679,3595,691],{},[913,3597,3598],{},"−",[679,3600,3601],{},"B",[679,3603,2148],{},[679,3605,691],{},[913,3607,936],{"stretchy":935},[679,3609,911],{},[913,3611,942],{"stretchy":935},[913,3613,915],{},[679,3615,939],{},[693,3617,3618],{"encoding":695},"D_{K_{pub-Bob}}(C)\n= M",[657,3620,3622,3748],{"className":3621,"ariaHidden":701},[700],[657,3623,3625,3628,3730,3733,3736,3739,3742,3745],{"className":3624},[705],[657,3626],{"className":3627,"style":1009},[709],[657,3629,3631,3634],{"className":3630},[714],[657,3632,955],{"className":3633,"style":866},[714,718],[657,3635,3637],{"className":3636},[723],[657,3638,3640,3722],{"className":3639},[727,728],[657,3641,3643,3719],{"className":3642},[732],[657,3644,3646],{"className":3645,"style":1029},[736],[657,3647,3648,3651],{"style":1164},[657,3649],{"className":3650,"style":745},[744],[657,3652,3654],{"className":3653},[749,750,751,752],[657,3655,3657],{"className":3656},[714,752],[657,3658,3660,3663],{"className":3659},[714,752],[657,3661,681],{"className":3662,"style":719},[714,718,752],[657,3664,3666],{"className":3665},[723],[657,3667,3669,3711],{"className":3668},[727,728],[657,3670,3672,3708],{"className":3671},[732],[657,3673,3675],{"className":3674,"style":1060},[736],[657,3676,3677,3680],{"style":1063},[657,3678],{"className":3679,"style":1067},[744],[657,3681,3683],{"className":3682},[749,1071,1072,752],[657,3684,3686,3689,3692,3695,3698,3702,3705],{"className":3685},[714,752],[657,3687,598],{"className":3688},[714,718,752],[657,3690,688],{"className":3691},[714,718,752],[657,3693,691],{"className":3694},[714,718,752],[657,3696,3598],{"className":3697},[1798,752],[657,3699,3601],{"className":3700,"style":3701},[714,718,752],"margin-right:0.0502em;",[657,3703,2148],{"className":3704},[714,718,752],[657,3706,691],{"className":3707},[714,718,752],[657,3709,769],{"className":3710},[768],[657,3712,3714],{"className":3713},[732],[657,3715,3717],{"className":3716,"style":1094},[736],[657,3718],{},[657,3720,769],{"className":3721},[768],[657,3723,3725],{"className":3724},[732],[657,3726,3728],{"className":3727,"style":1106},[736],[657,3729],{},[657,3731,936],{"className":3732},[1112],[657,3734,911],{"className":3735,"style":719},[714,718],[657,3737,942],{"className":3738},[1120],[657,3740],{"className":3741,"style":995},[944],[657,3743,915],{"className":3744},[999],[657,3746],{"className":3747,"style":995},[944],[657,3749,3751,3754],{"className":3750},[705],[657,3752],{"className":3753,"style":988},[709],[657,3755,939],{"className":3756,"style":1116},[714,718],". C'est une ",[602,3759,3760],{},"preuve d'identité"," vérifiable par tous. La signature\nest essentielle pour les ",[602,3763,3764],{},"certificats"," que vous croiserez avec HTTPS.",[3767,3768,3769],"warning",{},[598,3770,3771,3774,3775,3777,3778,3781],{},[602,3772,3773],{},"Le chiffrement asymétrique est lent."," RSA met typiquement 1000 à\n10 000 fois plus de temps qu'AES pour chiffrer la même quantité de\ndonnées. On ne l'utilise donc ",[602,3776,1650],{}," pour chiffrer le gros d'une\ncommunication — on s'en sert pour ",[602,3779,3780],{},"échanger une clé symétrique",", plus\ncourte, qui prend ensuite le relais. C'est le mécanisme central\nd'HTTPS, vu au cours suivant.",[3010,3783,3785,3790],{"correct":3012,"slug":3784},"chiffrement-asymetrique-c2",[3015,3786,3787],{"v-slot:question":2661},[598,3788,3789],{},"Si Alice veut envoyer un message confidentiel à Bob, elle chiffre avec…",[3015,3791,3792],{"v-slot:choices":2661},[646,3793,3794,3797,3800],{},[649,3795,3796],{},"sa propre clé privée",[649,3798,3799],{},"la clé publique de Bob",[649,3801,3802],{},"la clé privée de Bob",[593,3804,3806],{"id":3805},"activité-débranchée","Activité débranchée",[1625,3808,3809],{},[598,3810,3811,3814,3815,3818,3819,633],{},[602,3812,3813],{},"Activité débranchée — la boîte aux lettres",". Bob fabrique une boîte\nverrouillable avec une serrure dont ",[602,3816,3817],{},"lui seul"," a la clé. Il distribue à\ntoute la classe des cadenas ouverts qui ferment cette boîte. Alice écrit\nun message, le glisse dans la boîte, referme avec un cadenas. Elle remet\nla boîte à Bob (par main, par fil, par drone). Seul Bob peut ouvrir\n— même si la boîte transite par dix intermédiaires curieux. ",[602,3820,3821],{},"Le\ncadenas est la clé publique, la clé de la serrure est la clé privée",[593,3823,3825],{"id":3824},"pour-aller-plus-loin","Pour aller plus loin",[598,3827,3828,3829,3832,3833,3836,3837,633],{},"D'autres systèmes asymétriques existent : ",[602,3830,3831],{},"Diffie-Hellman"," (échange de\nclé), ",[602,3834,3835],{},"ECC"," (cryptographie sur courbes elliptiques, plus compacte que\nRSA à sécurité équivalente). RSA reste le plus enseigné parce qu'il\nillustre directement le rôle du modulo et de l'exponentiation — deux\nopérations que vous savez écrire en Python avec ",[2663,3838,3839],{},"pow(a, b, n)",[631,3841],{"code":588},[3843,3844,3845],"style",{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: 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possible.",null,"md",{},[3859,3863],{"slug":3013,"kind":3860,"question":3019,"choices":3861,"correct":3012,"multi":3862,"explanation":2661},"qcm",[3026,3029,3032],false,{"slug":3784,"kind":3860,"question":3789,"choices":3864,"correct":3012,"multi":3862,"explanation":2661},[3796,3799,3802],{"title":529,"description":3854},"lihEOe-dRnVlYR8ano-IiwHchxXKU4cEE8k8gcyAJMQ",{"id":3868,"title":3869,"bo":3870,"body":3871,"description":5830,"eval":3855,"extension":3856,"labo":3855,"meta":5831,"navigation":3862,"path":5832,"quizzes":5833,"readingTime":2668,"seo":5834,"stem":5835,"tp":3855,"__hash__":5836},"coursMemo\u002F2.nsi-tale\u002Ftc-archi-os-reseaux\u002F7.chiffrement-asymetrique.memo.md","Chiffrement asymétrique — l'essentiel",[588],{"type":590,"value":3872,"toc":5823},[3873,3877,4057,4061,5402,5406,5794,5798,5808,5812],[593,3874,3876],{"id":3875},"en-une-phrase","En une phrase",[598,3878,3879],{},[602,3880,3881,3882,3966,3967,4056],{},"Chaque personne a une paire de clés : la publique ",[657,3883,3885,3908],{"className":3884},[660],[657,3886,3888],{"className":3887},[664],[666,3889,3890],{"xmlns":668},[670,3891,3892,3906],{},[673,3893,3894],{},[676,3895,3896,3898],{},[679,3897,681],{},[673,3899,3900,3902,3904],{},[679,3901,598],{},[679,3903,688],{},[679,3905,691],{},[693,3907,696],{"encoding":695},[657,3909,3911],{"className":3910,"ariaHidden":701},[700],[657,3912,3914,3917],{"className":3913},[705],[657,3915],{"className":3916,"style":710},[709],[657,3918,3920,3923],{"className":3919},[714],[657,3921,681],{"className":3922,"style":719},[714,718],[657,3924,3926],{"className":3925},[723],[657,3927,3929,3958],{"className":3928},[727,728],[657,3930,3932,3955],{"className":3931},[732],[657,3933,3935],{"className":3934,"style":737},[736],[657,3936,3937,3940],{"style":740},[657,3938],{"className":3939,"style":745},[744],[657,3941,3943],{"className":3942},[749,750,751,752],[657,3944,3946,3949,3952],{"className":3945},[714,752],[657,3947,598],{"className":3948},[714,718,752],[657,3950,688],{"className":3951},[714,718,752],[657,3953,691],{"className":3954},[714,718,752],[657,3956,769],{"className":3957},[768],[657,3959,3961],{"className":3960},[732],[657,3962,3964],{"className":3963,"style":776},[736],[657,3965],{}," chiffre, la\nprivée ",[657,3968,3970,3995],{"className":3969},[660],[657,3971,3973],{"className":3972},[664],[666,3974,3975],{"xmlns":668},[670,3976,3977,3993],{},[673,3978,3979],{},[676,3980,3981,3983],{},[679,3982,681],{},[673,3984,3985,3987,3989,3991],{},[679,3986,598],{},[679,3988,811],{},[679,3990,814],{},[679,3992,817],{},[693,3994,820],{"encoding":695},[657,3996,3998],{"className":3997,"ariaHidden":701},[700],[657,3999,4001,4004],{"className":4000},[705],[657,4002],{"className":4003,"style":710},[709],[657,4005,4007,4010],{"className":4006},[714],[657,4008,681],{"className":4009,"style":719},[714,718],[657,4011,4013],{"className":4012},[723],[657,4014,4016,4048],{"className":4015},[727,728],[657,4017,4019,4045],{"className":4018},[732],[657,4020,4022],{"className":4021,"style":848},[736],[657,4023,4024,4027],{"style":740},[657,4025],{"className":4026,"style":745},[744],[657,4028,4030],{"className":4029},[749,750,751,752],[657,4031,4033,4036,4039,4042],{"className":4032},[714,752],[657,4034,598],{"className":4035},[714,718,752],[657,4037,811],{"className":4038,"style":866},[714,718,752],[657,4040,814],{"className":4041},[714,718,752],[657,4043,817],{"className":4044,"style":873},[714,718,752],[657,4046,769],{"className":4047},[768],[657,4049,4051],{"className":4050},[732],[657,4052,4054],{"className":4053,"style":776},[736],[657,4055],{}," déchiffre — RSA met en œuvre cette idée via le modulo\net l'exponentiation sur un produit de grands nombres premiers.",[593,4058,4060],{"id":4059},"à-mémoriser","À mémoriser",[646,4062,4063,4244,4585,4766,5152,5236,5390],{},[649,4064,4065,4068,4069,4153,4154,4243],{},[602,4066,4067],{},"Deux clés par personne"," : ",[657,4070,4072,4095],{"className":4071},[660],[657,4073,4075],{"className":4074},[664],[666,4076,4077],{"xmlns":668},[670,4078,4079,4093],{},[673,4080,4081],{},[676,4082,4083,4085],{},[679,4084,681],{},[673,4086,4087,4089,4091],{},[679,4088,598],{},[679,4090,688],{},[679,4092,691],{},[693,4094,696],{"encoding":695},[657,4096,4098],{"className":4097,"ariaHidden":701},[700],[657,4099,4101,4104],{"className":4100},[705],[657,4102],{"className":4103,"style":710},[709],[657,4105,4107,4110],{"className":4106},[714],[657,4108,681],{"className":4109,"style":719},[714,718],[657,4111,4113],{"className":4112},[723],[657,4114,4116,4145],{"className":4115},[727,728],[657,4117,4119,4142],{"className":4118},[732],[657,4120,4122],{"className":4121,"style":737},[736],[657,4123,4124,4127],{"style":740},[657,4125],{"className":4126,"style":745},[744],[657,4128,4130],{"className":4129},[749,750,751,752],[657,4131,4133,4136,4139],{"className":4132},[714,752],[657,4134,598],{"className":4135},[714,718,752],[657,4137,688],{"className":4138},[714,718,752],[657,4140,691],{"className":4141},[714,718,752],[657,4143,769],{"className":4144},[768],[657,4146,4148],{"className":4147},[732],[657,4149,4151],{"className":4150,"style":776},[736],[657,4152],{}," (publiable), ",[657,4155,4157,4182],{"className":4156},[660],[657,4158,4160],{"className":4159},[664],[666,4161,4162],{"xmlns":668},[670,4163,4164,4180],{},[673,4165,4166],{},[676,4167,4168,4170],{},[679,4169,681],{},[673,4171,4172,4174,4176,4178],{},[679,4173,598],{},[679,4175,811],{},[679,4177,814],{},[679,4179,817],{},[693,4181,820],{"encoding":695},[657,4183,4185],{"className":4184,"ariaHidden":701},[700],[657,4186,4188,4191],{"className":4187},[705],[657,4189],{"className":4190,"style":710},[709],[657,4192,4194,4197],{"className":4193},[714],[657,4195,681],{"className":4196,"style":719},[714,718],[657,4198,4200],{"className":4199},[723],[657,4201,4203,4235],{"className":4202},[727,728],[657,4204,4206,4232],{"className":4205},[732],[657,4207,4209],{"className":4208,"style":848},[736],[657,4210,4211,4214],{"style":740},[657,4212],{"className":4213,"style":745},[744],[657,4215,4217],{"className":4216},[749,750,751,752],[657,4218,4220,4223,4226,4229],{"className":4219},[714,752],[657,4221,598],{"className":4222},[714,718,752],[657,4224,811],{"className":4225,"style":866},[714,718,752],[657,4227,814],{"className":4228},[714,718,752],[657,4230,817],{"className":4231,"style":873},[714,718,752],[657,4233,769],{"className":4234},[768],[657,4236,4238],{"className":4237},[732],[657,4239,4241],{"className":4240,"style":776},[736],[657,4242],{}," (secrète).",[649,4245,4246,4412,4413,4584],{},[657,4247,4249,4287],{"className":4248},[660],[657,4250,4252],{"className":4251},[664],[666,4253,4254],{"xmlns":668},[670,4255,4256,4284],{},[673,4257,4258,4260,4262,4278,4280,4282],{},[679,4259,911],{},[913,4261,915],{},[676,4263,4264,4266],{},[679,4265,920],{},[676,4267,4268,4270],{},[679,4269,681],{},[673,4271,4272,4274,4276],{},[679,4273,598],{},[679,4275,688],{},[679,4277,691],{},[913,4279,936],{"stretchy":935},[679,4281,939],{},[913,4283,942],{"stretchy":935},[693,4285,4286],{"encoding":695},"C = E_{K_{pub}}(M)",[657,4288,4290,4308],{"className":4289,"ariaHidden":701},[700],[657,4291,4293,4296,4299,4302,4305],{"className":4292},[705],[657,4294],{"className":4295,"style":988},[709],[657,4297,911],{"className":4298,"style":719},[714,718],[657,4300],{"className":4301,"style":995},[944],[657,4303,915],{"className":4304},[999],[657,4306],{"className":4307,"style":995},[944],[657,4309,4311,4314,4403,4406,4409],{"className":4310},[705],[657,4312],{"className":4313,"style":1009},[709],[657,4315,4317,4320],{"className":4316},[714],[657,4318,920],{"className":4319,"style":1016},[714,718],[657,4321,4323],{"className":4322},[723],[657,4324,4326,4395],{"className":4325},[727,728],[657,4327,4329,4392],{"className":4328},[732],[657,4330,4332],{"className":4331,"style":1029},[736],[657,4333,4334,4337],{"style":1032},[657,4335],{"className":4336,"style":745},[744],[657,4338,4340],{"className":4339},[749,750,751,752],[657,4341,4343],{"className":4342},[714,752],[657,4344,4346,4349],{"className":4345},[714,752],[657,4347,681],{"className":4348,"style":719},[714,718,752],[657,4350,4352],{"className":4351},[723],[657,4353,4355,4384],{"className":4354},[727,728],[657,4356,4358,4381],{"className":4357},[732],[657,4359,4361],{"className":4360,"style":1060},[736],[657,4362,4363,4366],{"style":1063},[657,4364],{"className":4365,"style":1067},[744],[657,4367,4369],{"className":4368},[749,1071,1072,752],[657,4370,4372,4375,4378],{"className":4371},[714,752],[657,4373,598],{"className":4374},[714,718,752],[657,4376,688],{"className":4377},[714,718,752],[657,4379,691],{"className":4380},[714,718,752],[657,4382,769],{"className":4383},[768],[657,4385,4387],{"className":4386},[732],[657,4388,4390],{"className":4389,"style":1094},[736],[657,4391],{},[657,4393,769],{"className":4394},[768],[657,4396,4398],{"className":4397},[732],[657,4399,4401],{"className":4400,"style":1106},[736],[657,4402],{},[657,4404,936],{"className":4405},[1112],[657,4407,939],{"className":4408,"style":1116},[714,718],[657,4410,942],{"className":4411},[1120]," pour chiffrer, ",[657,4414,4416,4456],{"className":4415},[660],[657,4417,4419],{"className":4418},[664],[666,4420,4421],{"xmlns":668},[670,4422,4423,4453],{},[673,4424,4425,4427,4429,4447,4449,4451],{},[679,4426,939],{},[913,4428,915],{},[676,4430,4431,4433],{},[679,4432,955],{},[676,4434,4435,4437],{},[679,4436,681],{},[673,4438,4439,4441,4443,4445],{},[679,4440,598],{},[679,4442,811],{},[679,4444,814],{},[679,4446,817],{},[913,4448,936],{"stretchy":935},[679,4450,911],{},[913,4452,942],{"stretchy":935},[693,4454,4455],{"encoding":695},"M = D_{K_{priv}}(C)",[657,4457,4459,4477],{"className":4458,"ariaHidden":701},[700],[657,4460,4462,4465,4468,4471,4474],{"className":4461},[705],[657,4463],{"className":4464,"style":988},[709],[657,4466,939],{"className":4467,"style":1116},[714,718],[657,4469],{"className":4470,"style":995},[944],[657,4472,915],{"className":4473},[999],[657,4475],{"className":4476,"style":995},[944],[657,4478,4480,4483,4575,4578,4581],{"className":4479},[705],[657,4481],{"className":4482,"style":1143},[709],[657,4484,4486,4489],{"className":4485},[714],[657,4487,955],{"className":4488,"style":866},[714,718],[657,4490,4492],{"className":4491},[723],[657,4493,4495,4567],{"className":4494},[727,728],[657,4496,4498,4564],{"className":4497},[732],[657,4499,4501],{"className":4500,"style":1029},[736],[657,4502,4503,4506],{"style":1164},[657,4504],{"className":4505,"style":745},[744],[657,4507,4509],{"className":4508},[749,750,751,752],[657,4510,4512],{"className":4511},[714,752],[657,4513,4515,4518],{"className":4514},[714,752],[657,4516,681],{"className":4517,"style":719},[714,718,752],[657,4519,4521],{"className":4520},[723],[657,4522,4524,4556],{"className":4523},[727,728],[657,4525,4527,4553],{"className":4526},[732],[657,4528,4530],{"className":4529,"style":1192},[736],[657,4531,4532,4535],{"style":1195},[657,4533],{"className":4534,"style":1067},[744],[657,4536,4538],{"className":4537},[749,1071,1072,752],[657,4539,4541,4544,4547,4550],{"className":4540},[714,752],[657,4542,598],{"className":4543},[714,718,752],[657,4545,811],{"className":4546,"style":866},[714,718,752],[657,4548,814],{"className":4549},[714,718,752],[657,4551,817],{"className":4552,"style":873},[714,718,752],[657,4554,769],{"className":4555},[768],[657,4557,4559],{"className":4558},[732],[657,4560,4562],{"className":4561,"style":1226},[736],[657,4563],{},[657,4565,769],{"className":4566},[768],[657,4568,4570],{"className":4569},[732],[657,4571,4573],{"className":4572,"style":1238},[736],[657,4574],{},[657,4576,936],{"className":4577},[1112],[657,4579,911],{"className":4580,"style":719},[714,718],[657,4582,942],{"className":4583},[1120]," pour déchiffrer.",[649,4586,4587,4588,4591,4592,4681,4682,633],{},"Calculatoirement ",[602,4589,4590],{},"impossible"," de déduire 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expéditeur",[3068,5706,5707,5704],{},[657,5708,5710,5733],{"className":5709},[660],[657,5711,5713],{"className":5712},[664],[666,5714,5715],{"xmlns":668},[670,5716,5717,5731],{},[673,5718,5719],{},[676,5720,5721,5723],{},[679,5722,681],{},[673,5724,5725,5727,5729],{},[679,5726,598],{},[679,5728,688],{},[679,5730,691],{},[693,5732,696],{"encoding":695},[657,5734,5736],{"className":5735,"ariaHidden":701},[700],[657,5737,5739,5742],{"className":5738},[705],[657,5740],{"className":5741,"style":710},[709],[657,5743,5745,5748],{"className":5744},[714],[657,5746,681],{"className":5747,"style":719},[714,718],[657,5749,5751],{"className":5750},[723],[657,5752,5754,5783],{"className":5753},[727,728],[657,5755,5757,5780],{"className":5756},[732],[657,5758,5760],{"className":5759,"style":737},[736],[657,5761,5762,5765],{"style":740},[657,5763],{"className":5764,"style":745},[744],[657,5766,5768],{"className":5767},[749,750,751,752],[657,5769,5771,5774,5777],{"className":5770},[714,752],[657,5772,598],{"className":5773},[714,718,752],[657,5775,688],{"className":5776},[714,718,752],[657,5778,691],{"className":5779},[714,718,752],[657,5781,769],{"className":5782},[768],[657,5784,5786],{"className":5785},[732],[657,5787,5789],{"className":5788,"style":776},[736],[657,5790],{},[3068,5792,5793],{},"Preuve d'identité",[593,5795,5797],{"id":5796},"analogie","Analogie",[598,5799,5800,5803,5804,5807],{},[602,5801,5802],{},"Cadenas ouverts distribués par Bob"," = clés publiques. ",[602,5805,5806],{},"Clé de la\nserrure restée chez Bob"," = clé privée.",[593,5809,5811],{"id":5810},"pièges-courants","Pièges courants",[646,5813,5814,5817,5820],{},[649,5815,5816],{},"Croire que la clé qui chiffre est aussi celle qui déchiffre — non, ce\nserait symétrique.",[649,5818,5819],{},"Croire qu'on chiffre toute une communication HTTPS en asymétrique — non,\ntrop lent ; on s'en sert pour échanger une clé symétrique.",[649,5821,5822],{},"Inverser les rôles dans la signature.",{"title":2661,"searchDepth":2705,"depth":2705,"links":5824},[5825,5826,5827,5828,5829],{"id":3875,"depth":2705,"text":3876},{"id":4059,"depth":2705,"text":4060},{"id":5404,"depth":2705,"text":5405},{"id":5796,"depth":2705,"text":5797},{"id":5810,"depth":2705,"text":5811},"Mémo de révision sur la paire clé publique \u002F clé privée et l'idée de RSA.",{},"\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-asymetrique.memo",[],{"title":3869,"description":5830},"2.nsi-tale\u002Ftc-archi-os-reseaux\u002F7.chiffrement-asymetrique.memo","5ElPs4_DmTbiLaIOAxvWQgrDMrb8kKYu6-fqafDYu7o",{"id":5838,"title":5839,"body":5840,"description":7713,"extension":3856,"meta":7714,"navigation":3862,"path":7715,"seo":7716,"stem":7717,"__hash__":7718},"coursSlides\u002F2.nsi-tale\u002Ftc-archi-os-reseaux\u002F7.chiffrement-asymetrique.slides.md","Chiffrement asymétrique — diapositives",{"type":590,"value":5841,"toc":7711},[5842,5846,5849,5852,5856,5877,5879,5883,5886,6071,6391,6393,6397,6415,6417,6421,6915,6917,6921,7109,7111,7115,7175,7285,7287,7289,7670,7672,7676,7697,7699,7703,7708],[5843,5844,529],"h1",{"id":5845},"chiffrement-asymétrique",[598,5847,5848],{},"TC04 — Deux clés, l'une publique, l'autre privée.",[5850,5851],"hr",{},[5843,5853,5855],{"id":5854},"le-problème-du-symétrique","Le problème du symétrique",[646,5857,5858,5864,5867],{},[649,5859,5860,5861,633],{},"Le chiffrement symétrique demande une ",[602,5862,5863],{},"clé partagée",[649,5865,5866],{},"Comment l'échanger sur Internet sans interception ?",[649,5868,5869,5872,5873,5876],{},[602,5870,5871],{},"Idée 1976"," : et si chaque personne avait ",[602,5874,5875],{},"deux clés"," ?",[5850,5878],{},[5843,5880,5882],{"id":5881},"le-principe","Le principe",[598,5884,5885],{},"Chaque utilisateur possède :",[646,5887,5888,5977],{},[649,5889,651,5890,655,5892,5976],{},[602,5891,654],{},[657,5893,5895,5918],{"className":5894},[660],[657,5896,5898],{"className":5897},[664],[666,5899,5900],{"xmlns":668},[670,5901,5902,5916],{},[673,5903,5904],{},[676,5905,5906,5908],{},[679,5907,681],{},[673,5909,5910,5912,5914],{},[679,5911,598],{},[679,5913,688],{},[679,5915,691],{},[693,5917,696],{"encoding":695},[657,5919,5921],{"className":5920,"ariaHidden":701},[700],[657,5922,5924,5927],{"className":5923},[705],[657,5925],{"className":5926,"style":710},[709],[657,5928,5930,5933],{"className":5929},[714],[657,5931,681],{"className":5932,"style":719},[714,718],[657,5934,5936],{"className":5935},[723],[657,5937,5939,5968],{"className":5938},[727,728],[657,5940,5942,5965],{"className":5941},[732],[657,5943,5945],{"className":5944,"style":737},[736],[657,5946,5947,5950],{"style":740},[657,5948],{"className":5949,"style":745},[744],[657,5951,5953],{"className":5952},[749,750,751,752],[657,5954,5956,5959,5962],{"className":5955},[714,752],[657,5957,598],{"className":5958},[714,718,752],[657,5960,688],{"className":5961},[714,718,752],[657,5963,691],{"className":5964},[714,718,752],[657,5966,769],{"className":5967},[768],[657,5969,5971],{"className":5970},[732],[657,5972,5974],{"className":5973,"style":776},[736],[657,5975],{},", distribuable librement,",[649,5978,651,5979,655,5981,6070],{},[602,5980,788],{},[657,5982,5984,6009],{"className":5983},[660],[657,5985,5987],{"className":5986},[664],[666,5988,5989],{"xmlns":668},[670,5990,5991,6007],{},[673,5992,5993],{},[676,5994,5995,5997],{},[679,5996,681],{},[673,5998,5999,6001,6003,6005],{},[679,6000,598],{},[679,6002,811],{},[679,6004,814],{},[679,6006,817],{},[693,6008,820],{"encoding":695},[657,6010,6012],{"className":6011,"ariaHidden":701},[700],[657,6013,6015,6018],{"className":6014},[705],[657,6016],{"className":6017,"style":710},[709],[657,6019,6021,6024],{"className":6020},[714],[657,6022,681],{"className":6023,"style":719},[714,718],[657,6025,6027],{"className":6026},[723],[657,6028,6030,6062],{"className":6029},[727,728],[657,6031,6033,6059],{"className":6032},[732],[657,6034,6036],{"className":6035,"style":848},[736],[657,6037,6038,6041],{"style":740},[657,6039],{"className":6040,"style":745},[744],[657,6042,6044],{"className":6043},[749,750,751,752],[657,6045,6047,6050,6053,6056],{"className":6046},[714,752],[657,6048,598],{"className":6049},[714,718,752],[657,6051,811],{"className":6052,"style":866},[714,718,752],[657,6054,814],{"className":6055},[714,718,752],[657,6057,817],{"className":6058,"style":873},[714,718,752],[657,6060,769],{"className":6061},[768],[657,6063,6065],{"className":6064},[732],[657,6066,6068],{"className":6067,"style":776},[736],[657,6069],{},", gardée secrète.",[657,6072,6074],{"className":6073},[895],[657,6075,6077,6144],{"className":6076},[660],[657,6078,6080],{"className":6079},[664],[666,6081,6082],{"xmlns":668,"display":904},[670,6083,6084,6142],{},[673,6085,6086,6088,6090,6106,6108,6110,6112,6114,6116,6118,6136,6138,6140],{},[679,6087,911],{},[913,6089,915],{},[676,6091,6092,6094],{},[679,6093,920],{},[676,6095,6096,6098],{},[679,6097,681],{},[673,6099,6100,6102,6104],{},[679,6101,598],{},[679,6103,688],{},[679,6105,691],{},[913,6107,936],{"stretchy":935},[679,6109,939],{},[913,6111,942],{"stretchy":935},[944,6113],{"width":946},[679,6115,939],{},[913,6117,915],{},[676,6119,6120,6122],{},[679,6121,955],{},[676,6123,6124,6126],{},[679,6125,681],{},[673,6127,6128,6130,6132,6134],{},[679,6129,598],{},[679,6131,811],{},[679,6133,814],{},[679,6135,817],{},[913,6137,936],{"stretchy":935},[679,6139,911],{},[913,6141,942],{"stretchy":935},[693,6143,978],{"encoding":695},[657,6145,6147,6165,6284],{"className":6146,"ariaHidden":701},[700],[657,6148,6150,6153,6156,6159,6162],{"className":6149},[705],[657,6151],{"className":6152,"style":988},[709],[657,6154,911],{"className":6155,"style":719},[714,718],[657,6157],{"className":6158,"style":995},[944],[657,6160,915],{"className":6161},[999],[657,6163],{"className":6164,"style":995},[944],[657,6166,6168,6171,6260,6263,6266,6269,6272,6275,6278,6281],{"className":6167},[705],[657,6169],{"className":6170,"style":1009},[709],[657,6172,6174,6177],{"className":6173},[714],[657,6175,920],{"className":6176,"style":1016},[714,718],[657,6178,6180],{"className":6179},[723],[657,6181,6183,6252],{"className":6182},[727,728],[657,6184,6186,6249],{"className":6185},[732],[657,6187,6189],{"className":6188,"style":1029},[736],[657,6190,6191,6194],{"style":1032},[657,6192],{"className":6193,"style":745},[744],[657,6195,6197],{"className":6196},[749,750,751,752],[657,6198,6200],{"className":6199},[714,752],[657,6201,6203,6206],{"className":6202},[714,752],[657,6204,681],{"className":6205,"style":719},[714,718,752],[657,6207,6209],{"className":6208},[723],[657,6210,6212,6241],{"className":6211},[727,728],[657,6213,6215,6238],{"className":6214},[732],[657,6216,6218],{"className":6217,"style":1060},[736],[657,6219,6220,6223],{"style":1063},[657,6221],{"className":6222,"style":1067},[744],[657,6224,6226],{"className":6225},[749,1071,1072,752],[657,6227,6229,6232,6235],{"className":6228},[714,752],[657,6230,598],{"className":6231},[714,718,752],[657,6233,688],{"className":6234},[714,718,752],[657,6236,691],{"className":6237},[714,718,752],[657,6239,769],{"className":6240},[768],[657,6242,6244],{"className":6243},[732],[657,6245,6247],{"className":6246,"style":1094},[736],[657,6248],{},[657,6250,769],{"className":6251},[768],[657,6253,6255],{"className":6254},[732],[657,6256,6258],{"className":6257,"style":1106},[736],[657,6259],{},[657,6261,936],{"className":6262},[1112],[657,6264,939],{"className":6265,"style":1116},[714,718],[657,6267,942],{"className":6268},[1120],[657,6270],{"className":6271,"style":1124},[944],[657,6273,939],{"className":6274,"style":1116},[714,718],[657,6276],{"className":6277,"style":995},[944],[657,6279,915],{"className":6280},[999],[657,6282],{"className":6283,"style":995},[944],[657,6285,6287,6290,6382,6385,6388],{"className":6286},[705],[657,6288],{"className":6289,"style":1143},[709],[657,6291,6293,6296],{"className":6292},[714],[657,6294,955],{"className":6295,"style":866},[714,718],[657,6297,6299],{"className":6298},[723],[657,6300,6302,6374],{"className":6301},[727,728],[657,6303,6305,6371],{"className":6304},[732],[657,6306,6308],{"className":6307,"style":1029},[736],[657,6309,6310,6313],{"style":1164},[657,6311],{"className":6312,"style":745},[744],[657,6314,6316],{"className":6315},[749,750,751,752],[657,6317,6319],{"className":6318},[714,752],[657,6320,6322,6325],{"className":6321},[714,752],[657,6323,681],{"className":6324,"style":719},[714,718,752],[657,6326,6328],{"className":6327},[723],[657,6329,6331,6363],{"className":6330},[727,728],[657,6332,6334,6360],{"className":6333},[732],[657,6335,6337],{"className":6336,"style":1192},[736],[657,6338,6339,6342],{"style":1195},[657,6340],{"className":6341,"style":1067},[744],[657,6343,6345],{"className":6344},[749,1071,1072,752],[657,6346,6348,6351,6354,6357],{"className":6347},[714,752],[657,6349,598],{"className":6350},[714,718,752],[657,6352,811],{"className":6353,"style":866},[714,718,752],[657,6355,814],{"className":6356},[714,718,752],[657,6358,817],{"className":6359,"style":873},[714,718,752],[657,6361,769],{"className":6362},[768],[657,6364,6366],{"className":6365},[732],[657,6367,6369],{"className":6368,"style":1226},[736],[657,6370],{},[657,6372,769],{"className":6373},[768],[657,6375,6377],{"className":6376},[732],[657,6378,6380],{"className":6379,"style":1238},[736],[657,6381],{},[657,6383,936],{"className":6384},[1112],[657,6386,911],{"className":6387,"style":719},[714,718],[657,6389,942],{"className":6390},[1120],[5850,6392],{},[5843,6394,6396],{"id":6395},"analogie-du-cadenas","Analogie du cadenas",[646,6398,6399,6405,6408],{},[649,6400,6401,6402,6404],{},"Bob distribue des ",[602,6403,1635],{}," (clé publique).",[649,6406,6407],{},"N'importe qui peut fermer une boîte avec.",[649,6409,6410,6411,6414],{},"Seul Bob, avec sa ",[602,6412,6413],{},"clé"," (clé privée), peut rouvrir.",[5850,6416],{},[5843,6418,6420],{"id":6419},"lidée-de-rsa","L'idée de RSA",[1667,6422,6423,6468,6544,6657,6786],{},[649,6424,6425,6426,633],{},"Choisir deux grands premiers ",[657,6427,6429,6447],{"className":6428},[660],[657,6430,6432],{"className":6431},[664],[666,6433,6434],{"xmlns":668},[670,6435,6436,6444],{},[673,6437,6438,6440,6442],{},[679,6439,598],{},[913,6441,1947],{"separator":701},[679,6443,1716],{},[693,6445,6446],{"encoding":695},"p, q",[657,6448,6450],{"className":6449,"ariaHidden":701},[700],[657,6451,6453,6456,6459,6462,6465],{"className":6452},[705],[657,6454],{"className":6455,"style":1697},[709],[657,6457,598],{"className":6458},[714,718],[657,6460,1947],{"className":6461},[1975],[657,6463],{"className":6464,"style":1979},[944],[657,6466,1716],{"className":6467,"style":873},[714,718],[649,6469,6470,6471,6543],{},"Calculer ",[657,6472,6474,6495],{"className":6473},[660],[657,6475,6477],{"className":6476},[664],[666,6478,6479],{"xmlns":668},[670,6480,6481,6493],{},[673,6482,6483,6485,6487,6489,6491],{},[679,6484,1746],{},[913,6486,915],{},[679,6488,598],{},[913,6490,1753],{},[679,6492,1716],{},[693,6494,1758],{"encoding":695},[657,6496,6498,6516,6534],{"className":6497,"ariaHidden":701},[700],[657,6499,6501,6504,6507,6510,6513],{"className":6500},[705],[657,6502],{"className":6503,"style":1768},[709],[657,6505,1746],{"className":6506},[714,718],[657,6508],{"className":6509,"style":995},[944],[657,6511,915],{"className":6512},[999],[657,6514],{"className":6515,"style":995},[944],[657,6517,6519,6522,6525,6528,6531],{"className":6518},[705],[657,6520],{"className":6521,"style":1787},[709],[657,6523,598],{"className":6524},[714,718],[657,6526],{"className":6527,"style":1794},[944],[657,6529,1753],{"className":6530},[1798],[657,6532],{"className":6533,"style":1794},[944],[657,6535,6537,6540],{"className":6536},[705],[657,6538],{"className":6539,"style":1697},[709],[657,6541,1716],{"className":6542,"style":873},[714,718]," — public.",[649,6545,6546,6547,6598,6599,6627,6628,6656],{},"Produire deux exposants ",[657,6548,6550,6571],{"className":6549},[660],[657,6551,6553],{"className":6552},[664],[666,6554,6555],{"xmlns":668},[670,6556,6557,6569],{},[673,6558,6559,6561,6563,6565,6567],{},[913,6560,936],{"stretchy":935},[679,6562,1944],{},[913,6564,1947],{"separator":701},[679,6566,1950],{},[913,6568,942],{"stretchy":935},[693,6570,1955],{"encoding":695},[657,6572,6574],{"className":6573,"ariaHidden":701},[700],[657,6575,6577,6580,6583,6586,6589,6592,6595],{"className":6576},[705],[657,6578],{"className":6579,"style":1965},[709],[657,6581,936],{"className":6582},[1112],[657,6584,1944],{"className":6585},[714,718],[657,6587,1947],{"className":6588},[1975],[657,6590],{"className":6591,"style":1979},[944],[657,6593,1950],{"className":6594},[714,718],[657,6596,942],{"className":6597},[1120]," — ",[657,6600,6602,6615],{"className":6601},[660],[657,6603,6605],{"className":6604},[664],[666,6606,6607],{"xmlns":668},[670,6608,6609,6613],{},[673,6610,6611],{},[679,6612,1944],{},[693,6614,1944],{"encoding":695},[657,6616,6618],{"className":6617,"ariaHidden":701},[700],[657,6619,6621,6624],{"className":6620},[705],[657,6622],{"className":6623,"style":1768},[709],[657,6625,1944],{"className":6626},[714,718]," public, ",[657,6629,6631,6644],{"className":6630},[660],[657,6632,6634],{"className":6633},[664],[666,6635,6636],{"xmlns":668},[670,6637,6638,6642],{},[673,6639,6640],{},[679,6641,1950],{},[693,6643,1950],{"encoding":695},[657,6645,6647],{"className":6646,"ariaHidden":701},[700],[657,6648,6650,6653],{"className":6649},[705],[657,6651],{"className":6652,"style":2070},[709],[657,6654,1950],{"className":6655},[714,718]," privé.",[649,6658,6659,6660,633],{},"Chiffrer : ",[657,6661,6663,6700],{"className":6662},[660],[657,6664,6666],{"className":6665},[664],[666,6667,6668],{"xmlns":668},[670,6669,6670,6698],{},[673,6671,6672,6674,6676,6682,6684,6694,6696],{},[679,6673,911],{},[913,6675,915],{},[2127,6677,6678,6680],{},[679,6679,939],{},[679,6681,1944],{},[2134,6683,2136],{},[913,6685,6686],{"lspace":2139,"rspace":2139},[673,6687,6688,6690,6692],{},[679,6689,2145],{"mathvariant":2144},[679,6691,2148],{"mathvariant":2144},[679,6693,1950],{"mathvariant":2144},[2134,6695,2136],{},[679,6697,1746],{},[693,6699,4935],{"encoding":695},[657,6701,6703,6721,6777],{"className":6702,"ariaHidden":701},[700],[657,6704,6706,6709,6712,6715,6718],{"className":6705},[705],[657,6707],{"className":6708,"style":988},[709],[657,6710,911],{"className":6711,"style":719},[714,718],[657,6713],{"className":6714,"style":995},[944],[657,6716,915],{"className":6717},[999],[657,6719],{"className":6720,"style":995},[944],[657,6722,6724,6727,6756,6759,6762,6771,6774],{"className":6723},[705],[657,6725],{"className":6726,"style":2070},[709],[657,6728,6730,6733],{"className":6729},[714],[657,6731,939],{"className":6732,"style":1116},[714,718],[657,6734,6736],{"className":6735},[723],[657,6737,6739],{"className":6738},[727],[657,6740,6742],{"className":6741},[732],[657,6743,6745],{"className":6744,"style":4981},[736],[657,6746,6747,6750],{"style":2932},[657,6748],{"className":6749,"style":745},[744],[657,6751,6753],{"className":6752},[749,750,751,752],[657,6754,1944],{"className":6755},[714,718,752],[657,6757],{"className":6758,"style":2222},[944],[657,6760],{"className":6761,"style":1794},[944],[657,6763,6765],{"className":6764},[1798],[657,6766,6768],{"className":6767},[714],[657,6769,2236],{"className":6770},[714,2235],[657,6772],{"className":6773,"style":2222},[944],[657,6775],{"className":6776,"style":1794},[944],[657,6778,6780,6783],{"className":6779},[705],[657,6781],{"className":6782,"style":1768},[709],[657,6784,1746],{"className":6785},[714,718],[649,6787,6788,6789,633],{},"Déchiffrer : ",[657,6790,6792,6829],{"className":6791},[660],[657,6793,6795],{"className":6794},[664],[666,6796,6797],{"xmlns":668},[670,6798,6799,6827],{},[673,6800,6801,6803,6805,6811,6813,6823,6825],{},[679,6802,939],{},[913,6804,915],{},[2127,6806,6807,6809],{},[679,6808,911],{},[679,6810,1950],{},[2134,6812,2136],{},[913,6814,6815],{"lspace":2139,"rspace":2139},[673,6816,6817,6819,6821],{},[679,6818,2145],{"mathvariant":2144},[679,6820,2148],{"mathvariant":2144},[679,6822,1950],{"mathvariant":2144},[2134,6824,2136],{},[679,6826,1746],{},[693,6828,5064],{"encoding":695},[657,6830,6832,6850,6906],{"className":6831,"ariaHidden":701},[700],[657,6833,6835,6838,6841,6844,6847],{"className":6834},[705],[657,6836],{"className":6837,"style":988},[709],[657,6839,939],{"className":6840,"style":1116},[714,718],[657,6842],{"className":6843,"style":995},[944],[657,6845,915],{"className":6846},[999],[657,6848],{"className":6849,"style":995},[944],[657,6851,6853,6856,6885,6888,6891,6900,6903],{"className":6852},[705],[657,6854],{"className":6855,"style":5092},[709],[657,6857,6859,6862],{"className":6858},[714],[657,6860,911],{"className":6861,"style":719},[714,718],[657,6863,6865],{"className":6864},[723],[657,6866,6868],{"className":6867},[727],[657,6869,6871],{"className":6870},[732],[657,6872,6874],{"className":6873,"style":5092},[736],[657,6875,6876,6879],{"style":2932},[657,6877],{"className":6878,"style":745},[744],[657,6880,6882],{"className":6881},[749,750,751,752],[657,6883,1950],{"className":6884},[714,718,752],[657,6886],{"className":6887,"style":2222},[944],[657,6889],{"className":6890,"style":1794},[944],[657,6892,6894],{"className":6893},[1798],[657,6895,6897],{"className":6896},[714],[657,6898,2236],{"className":6899},[714,2235],[657,6901],{"className":6902,"style":2222},[944],[657,6904],{"className":6905,"style":1794},[944],[657,6907,6909,6912],{"className":6908},[705],[657,6910],{"className":6911,"style":1768},[709],[657,6913,1746],{"className":6914},[714,718],[5850,6916],{},[5843,6918,6920],{"id":6919},"pourquoi-cest-sûr","Pourquoi c'est sûr",[646,6922,6923,6983,7060],{},[649,6924,6925,6926,6954,6955,633],{},"Connaître ",[657,6927,6929,6942],{"className":6928},[660],[657,6930,6932],{"className":6931},[664],[666,6933,6934],{"xmlns":668},[670,6935,6936,6940],{},[673,6937,6938],{},[679,6939,1746],{},[693,6941,1746],{"encoding":695},[657,6943,6945],{"className":6944,"ariaHidden":701},[700],[657,6946,6948,6951],{"className":6947},[705],[657,6949],{"className":6950,"style":1768},[709],[657,6952,1746],{"className":6953},[714,718]," ne suffit pas pour retrouver ",[657,6956,6958,6971],{"className":6957},[660],[657,6959,6961],{"className":6960},[664],[666,6962,6963],{"xmlns":668},[670,6964,6965,6969],{},[673,6966,6967],{},[679,6968,1950],{},[693,6970,1950],{"encoding":695},[657,6972,6974],{"className":6973,"ariaHidden":701},[700],[657,6975,6977,6980],{"className":6976},[705],[657,6978],{"className":6979,"style":2070},[709],[657,6981,1950],{"className":6982},[714,718],[649,6984,6985,6986,655,6988,633],{},"Il faut ",[602,6987,5157],{},[657,6989,6991,7012],{"className":6990},[660],[657,6992,6994],{"className":6993},[664],[666,6995,6996],{"xmlns":668},[670,6997,6998,7010],{},[673,6999,7000,7002,7004,7006,7008],{},[679,7001,1746],{},[913,7003,915],{},[679,7005,598],{},[913,7007,1753],{},[679,7009,1716],{},[693,7011,1758],{"encoding":695},[657,7013,7015,7033,7051],{"className":7014,"ariaHidden":701},[700],[657,7016,7018,7021,7024,7027,7030],{"className":7017},[705],[657,7019],{"className":7020,"style":1768},[709],[657,7022,1746],{"className":7023},[714,718],[657,7025],{"className":7026,"style":995},[944],[657,7028,915],{"className":7029},[999],[657,7031],{"className":7032,"style":995},[944],[657,7034,7036,7039,7042,7045,7048],{"className":7035},[705],[657,7037],{"className":7038,"style":1787},[709],[657,7040,598],{"className":7041},[714,718],[657,7043],{"className":7044,"style":1794},[944],[657,7046,1753],{"className":7047},[1798],[657,7049],{"className":7050,"style":1794},[944],[657,7052,7054,7057],{"className":7053},[705],[657,7055],{"className":7056,"style":1697},[709],[657,7058,1716],{"className":7059,"style":873},[714,718],[649,7061,7062,7063,7104,7105,7108],{},"Avec ",[657,7064,7066,7083],{"className":7065},[660],[657,7067,7069],{"className":7068},[664],[666,7070,7071],{"xmlns":668},[670,7072,7073,7081],{},[673,7074,7075,7077,7079],{},[679,7076,598],{},[913,7078,1947],{"separator":701},[679,7080,1716],{},[693,7082,6446],{"encoding":695},[657,7084,7086],{"className":7085,"ariaHidden":701},[700],[657,7087,7089,7092,7095,7098,7101],{"className":7088},[705],[657,7090],{"className":7091,"style":1697},[709],[657,7093,598],{"className":7094},[714,718],[657,7096,1947],{"className":7097},[1975],[657,7099],{"className":7100,"style":1979},[944],[657,7102,1716],{"className":7103,"style":873},[714,718]," de 1024 bits : ",[602,7106,7107],{},"infaisable"," en temps raisonnable.",[5850,7110],{},[5843,7112,7114],{"id":7113},"en-python","En Python",[2656,7116,7118],{"className":2658,"code":7117,"language":2660,"meta":2661,"style":2661},"n, e, d = 143, 7, 103   # exemple jouet\nM = 42\nC = pow(M, e, n)        # 81\nM2 = pow(C, d, n)       # 42\n",[2663,7119,7120,7140,7148,7161],{"__ignoreMap":2661},[657,7121,7122,7124,7126,7128,7130,7132,7134,7137],{"class":2667,"line":2668},[657,7123,2741],{"class":2679},[657,7125,915],{"class":2671},[657,7127,2746],{"class":2683},[657,7129,2749],{"class":2679},[657,7131,2752],{"class":2683},[657,7133,2749],{"class":2679},[657,7135,7136],{"class":2683},"103",[657,7138,7139],{"class":2734},"   # exemple jouet\n",[657,7141,7142,7144,7146],{"class":2667,"line":2705},[657,7143,2763],{"class":2679},[657,7145,915],{"class":2671},[657,7147,2768],{"class":2683},[657,7149,7150,7152,7154,7156,7159],{"class":2667,"line":2712},[657,7151,2774],{"class":2679},[657,7153,915],{"class":2671},[657,7155,2718],{"class":2683},[657,7157,7158],{"class":2679},"(M, e, n)        ",[657,7160,2791],{"class":2734},[657,7162,7163,7166,7168,7170,7173],{"class":2667,"line":2724},[657,7164,7165],{"class":2679},"M2 ",[657,7167,915],{"class":2671},[657,7169,2718],{"class":2683},[657,7171,7172],{"class":2679},"(C, d, n)       ",[657,7174,2813],{"class":2734},[598,7176,7177,5242,7179,7284],{},[2663,7178,3839],{},[657,7180,7182,7216],{"className":7181},[660],[657,7183,7185],{"className":7184},[664],[666,7186,7187],{"xmlns":668},[670,7188,7189,7213],{},[673,7190,7191,7197,7199,7209,7211],{},[2127,7192,7193,7195],{},[679,7194,2837],{},[679,7196,691],{},[2134,7198,2136],{},[913,7200,7201],{"lspace":2139,"rspace":2139},[673,7202,7203,7205,7207],{},[679,7204,2145],{"mathvariant":2144},[679,7206,2148],{"mathvariant":2144},[679,7208,1950],{"mathvariant":2144},[2134,7210,2136],{},[679,7212,1746],{},[693,7214,7215],{"encoding":695},"a^b \\bmod n",[657,7217,7219,7275],{"className":7218,"ariaHidden":701},[700],[657,7220,7222,7225,7254,7257,7260,7269,7272],{"className":7221},[705],[657,7223],{"className":7224,"style":5092},[709],[657,7226,7228,7231],{"className":7227},[714],[657,7229,2837],{"className":7230},[714,718],[657,7232,7234],{"className":7233},[723],[657,7235,7237],{"className":7236},[727],[657,7238,7240],{"className":7239},[732],[657,7241,7243],{"className":7242,"style":5092},[736],[657,7244,7245,7248],{"style":2932},[657,7246],{"className":7247,"style":745},[744],[657,7249,7251],{"className":7250},[749,750,751,752],[657,7252,691],{"className":7253},[714,718,752],[657,7255],{"className":7256,"style":2222},[944],[657,7258],{"className":7259,"style":1794},[944],[657,7261,7263],{"className":7262},[1798],[657,7264,7266],{"className":7265},[714],[657,7267,2236],{"className":7268},[714,2235],[657,7270],{"className":7271,"style":2222},[944],[657,7273],{"className":7274,"style":1794},[944],[657,7276,7278,7281],{"className":7277},[705],[657,7279],{"className":7280,"style":1768},[709],[657,7282,1746],{"className":7283},[714,718]," efficacement.",[5850,7286],{},[5843,7288,5405],{"id":5404},[3041,7290,7291,7304],{},[3044,7292,7293],{},[3047,7294,7295,7298,7301],{},[3050,7296,7297],{},"Action",[3050,7299,7300],{},"Chiffrer avec",[3050,7302,7303],{},"Déchiffrer 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