V\u00fdzkumn\u00edci z Kalifornsk\u00e9 univerzity v San Diegu vyvinuli zlep\u0161enou techniku \u00fatoku na algoritmus RSA, kter\u00e1 umo\u017e\u0148uje fal\u0161ov\u00e1n\u00ed digit\u00e1ln\u00edch podpis\u016f bez faktorizace z\u00e1kladn\u00edch prvo\u010d\u00edsel RSA a bez nutnosti obnovit soukrom\u00fd kl\u00ed\u010d. Zdroje pot\u0159ebn\u00e9 k proveden\u00ed \u00fatoku na 1024bitov\u00fd kl\u00ed\u010d RSA jsou odhadov\u00e1ny na 1380 let v\u00fdpo\u010dt\u016f na jednom procesorov\u00e9m j\u00e1d\u0159e, co\u017e na dostupn\u00e9m univerzitn\u00edm clusteru umo\u017enilo za 5 m\u011bs\u00edc\u016f ur\u010dit parametry pot\u0159ebn\u00e9 pro vytvo\u0159en\u00ed fale\u0161n\u00e9ho RSA podpisu (v experimentu nebyly pou\u017eity urychlova\u010de AI a GPU, jejich\u017e pou\u017eit\u00edm by se v\u00fdpo\u010detn\u00ed \u010das mohl v\u00fdrazn\u011b zkr\u00e1tit). Pro srovn\u00e1n\u00ed, klasick\u00e1 metoda faktorizace vy\u017eaduje pro obnovu soukrom\u00e9ho kl\u00ed\u010de RSA-1024 mezi 500 tis\u00edci a\u017e milionem let v\u00fdpo\u010dt\u016f na jednom procesorov\u00e9m j\u00e1d\u0159e. <\/p>\n
K proveden\u00ed \u00fatoku je t\u0159eba m\u00edt mo\u017enost opakovan\u011b pos\u00edlat \u017e\u00e1dosti na podepisov\u00e1n\u00ed dat generovan\u00fdch \u00fato\u010dn\u00edkem, nap\u0159\u00edklad p\u0159i obracen\u00ed se na autentiza\u010dn\u00ed slu\u017ebu nebo HSM modul. K ur\u010den\u00ed parametr\u016f RSA-1024 sta\u010d\u00ed poslat 232 takov\u00fdch \u017e\u00e1dost\u00ed, a pro \u00fatok na kl\u00ed\u010de RSA-2048 pou\u017e\u00edvan\u00e9 v protokolu Privacy Pass \u2013 243. Po z\u00edsk\u00e1n\u00ed pole podepsan\u00fdch dat za\u010d\u00edn\u00e1 dlouh\u00fd proces v\u00fdpo\u010dtu parametr\u016f (pro RSA-1024 p\u0159ibli\u017en\u011b 265 operac\u00ed), po jejich\u017e z\u00edsk\u00e1n\u00ed m\u016f\u017ee \u00fato\u010dn\u00edk vytv\u00e1\u0159et fiktivn\u00ed podpisy pro jak\u00e1koliv data, p\u0159i\u010dem\u017e na ka\u017ed\u00fd podpis vynalo\u017e\u00ed p\u0159ibli\u017en\u011b 180 hodin v\u00fdpo\u010dt\u016f na jednom j\u00e1dru. <\/p>\n
Metoda je aplikovateln\u00e1 pouze pro RSA podpisy, ve kter\u00fdch se nepou\u017e\u00edv\u00e1 form\u00e1tov\u00e1n\u00ed a dodate\u010dn\u00e9 vypln\u011bn\u00ed p\u0159ed \u0161ifrov\u00e1n\u00edm (padding). \u00datoku podl\u00e9haj\u00ed implementace slep\u00e9 signatury, v\u010detn\u011b t\u011bch pou\u017e\u00edvan\u00fdch v protokolu Privacy Pass. V\u011bt\u0161ina b\u011b\u017en\u011b pou\u017e\u00edvan\u00fdch implementac\u00ed RSA, v\u010detn\u011b PKCS#1v1.5 a RSA-PSS (pou\u017e\u00edvan\u00e9 v TLS a SSH), pou\u017e\u00edvaj\u00ed dodate\u010dn\u00e9 vypln\u011bn\u00ed a nejsou \u00fatoku podrobeny. <\/p>\n
Z\u00e1kladem \u0161ifrov\u00e1n\u00ed RSA je operace umoc\u0148ov\u00e1n\u00ed modulo velk\u00e9ho \u010d\u00edsla. Ve ve\u0159ejn\u00e9m kl\u00ed\u010di se nach\u00e1z\u00ed modul a exponent. Modul je vytvo\u0159en na z\u00e1klad\u011b dvou n\u00e1hodn\u00fdch prvo\u010d\u00edsel, kter\u00e1 zn\u00e1 pouze majitel soukrom\u00e9ho kl\u00ed\u010de. Navrhovan\u00e1 metoda vych\u00e1z\u00ed z v\u00fdzkumu zve\u0159ejn\u011bn\u00e9ho v roce 2007, kter\u00fd prok\u00e1zal, \u017ee extrakce ko\u0159ene v exponentu uveden\u00e9m ve ve\u0159ejn\u00e9m kl\u00ed\u010di ze za\u0161ifrovan\u00e9 zpr\u00e1vy bez informac\u00ed o tajn\u00fdch faktorech je m\u00e9n\u011b n\u00e1ro\u010dn\u00e1 operace ne\u017e faktorizace samotn\u00fdch faktor\u016f. <\/p>\n
Pou\u017eit\u00edm speci\u00e1ln\u00ed metody s\u00edta \u010d\u00edseln\u00e9ho pole (SNFS) se v\u00fdzkumn\u00edk\u016fm poda\u0159ilo sn\u00ed\u017eit slo\u017eitost kompromitace kl\u00ed\u010d\u016f RSA-1024 na 265 operac\u00ed, co\u017e umo\u017e\u0148uje prov\u00e1d\u011bn\u00ed praktick\u00fdch \u00fatok\u016f na modern\u00edch klastrech. U 2048bitov\u00fdch kl\u00ed\u010d\u016f RSA je slo\u017eitost \u00fatoku odhadov\u00e1na na 290, co\u017e je teoreticky provediteln\u00e9 velk\u00fdmi korporacemi nebo tajn\u00fdmi slu\u017ebami. U 4096bitov\u00fdch kl\u00ed\u010d\u016f je slo\u017eitost \u00fatoku 2119 operac\u00ed, co\u017e je prozat\u00edm prakticky nedosa\u017eiteln\u00e9, ale je to pod minimem 2128 doporu\u010dovan\u00fdm NSA, N\u00e1rodn\u00edm \u00fa\u0159adem pro normy a technologie a Evropskou agenturou pro kybernetickou bezpe\u010dnost. \u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u0438 \u0438\u0437 \u041a\u0430\u043b\u0438\u0444\u043e\u0440\u043d\u0438\u0439\u0441\u043a\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430 \u0432 \u0421\u0430\u043d-\u0414\u0438\u0435\u0433\u043e \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0430\u043b\u0438 \u0443\u0441\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u043d\u0443\u044e \u0442\u0435\u0445\u043d\u0438\u043a\u0443 \u0430\u0442\u0430\u043a\u0438 \u043d\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c RSA, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0443\u044e \u043f\u043e\u0434\u0434\u0435\u043b\u044b\u0432\u0430\u0442\u044c \u0446\u0438\u0444\u0440\u043e\u0432\u044b\u0435 \u043f\u043e\u0434\u043f\u0438\u0441\u0438 \u0431\u0435\u0437 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u043b\u0435\u0436\u0430\u0449\u0438\u0445 \u0432 \u043e\u0441\u043d\u043e\u0432\u0435 RSA \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u0438 \u0431\u0435\u0437 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \u0432\u043e\u0441\u0441\u0442\u0430\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u044f \u0437\u0430\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430. \u0420\u0435\u0441\u0443\u0440\u0441\u044b, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0435 \u0434\u043b\u044f \u0441\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u044f \u0430\u0442\u0430\u043a\u0438 \u043d\u0430 1024-\u0440\u0430\u0437\u0440\u044f\u0434\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 RSA, \u043e\u0446\u0435\u043d\u0435\u043d\u044b \u0432 1380 \u043b\u0435\u0442 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0439 \u043d\u0430 \u043e\u0434\u043d\u043e\u043c \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u043e\u0440\u043e\u043c \u044f\u0434\u0440\u0435, \u0447\u0442\u043e \u043d\u0430 \u0438\u043c\u0435\u044e\u0449\u0435\u043c\u0441\u044f \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0441\u043a\u043e\u043c \u043a\u043b\u0430\u0441\u0442\u0435\u0440\u0435 \u043f\u043e\u0437\u0432\u043e\u043b\u0438\u043b\u043e […]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":10,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[702],"tags":[],"class_list":["post-183509","post","type-post","status-publish","format-standard","hentry","category-news"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\n","aioseo_head_json":{"title":"\ud83e\udd47Metoda \u00fatoku, kter\u00e1 v\u00fdrazn\u011b sni\u017euje n\u00e1roky na zdroje pro fal\u0161ov\u00e1n\u00ed digit\u00e1ln\u00edch podpis\u016f RSA | ProHoster","description":"V\u011bdci z Kalifornsk\u00e9 univerzity v San Diegu vyvinuli vylep\u0161enou techniku \u00fatoku na algoritmus RSA, kter\u00e1 umo\u017e\u0148uje fal\u0161ov\u00e1n\u00ed digit\u00e1ln\u00edch podpis\u016f bez faktorizace z\u00e1kladn\u00edch prvo\u010d\u00edsel RSA.","canonical_url":"https:\/\/prohoster.info\/cs\/blog\/news\/attack-method-that-significantly-reduces-the-resources-needed-to-forge-rsa-digital-signatures","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":null,"og:locale":"cs_CZ","og:site_name":"ProHoster | \u041a\u0443\u043f\u0438\u0442\u044c \u043d\u0430\u0434\u0435\u0436\u043d\u044b\u0439 \u0445\u043e\u0441\u0442\u0438\u043d\u0433 \u0434\u043b\u044f \u0441\u0430\u0439\u0442\u043e\u0432 \u0441 \u0437\u0430\u0449\u0438\u0442\u043e\u0439 \u043e\u0442 DDoS, VPS VDS \u0441\u0435\u0440\u0432\u0435\u0440\u044b","og:type":"article","og:title":"\ud83e\udd47\u041c\u0435\u0442\u043e\u0434 \u0430\u0442\u0430\u043a\u0438, \u0437\u043d\u0430\u0447\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0441\u043e\u043a\u0440\u0430\u0449\u0430\u044e\u0449\u0438\u0439 \u0440\u0435\u0441\u0443\u0440\u0441\u044b \u0434\u043b\u044f \u043f\u043e\u0434\u0434\u0435\u043b\u043a\u0438 \u0446\u0438\u0444\u0440\u043e\u0432\u044b\u0445 \u043f\u043e\u0434\u043f\u0438\u0441\u0435\u0439 RSA | ProHoster","og:description":"\u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u0438 \u0438\u0437 \u041a\u0430\u043b\u0438\u0444\u043e\u0440\u043d\u0438\u0439\u0441\u043a\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430 \u0432 \u0421\u0430\u043d-\u0414\u0438\u0435\u0433\u043e \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0430\u043b\u0438 \u0443\u0441\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u043d\u0443\u044e \u0442\u0435\u0445\u043d\u0438\u043a\u0443 \u0430\u0442\u0430\u043a\u0438 \u043d\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c RSA, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0443\u044e \u043f\u043e\u0434\u0434\u0435\u043b\u044b\u0432\u0430\u0442\u044c \u0446\u0438\u0444\u0440\u043e\u0432\u044b\u0435 \u043f\u043e\u0434\u043f\u0438\u0441\u0438 \u0431\u0435\u0437 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u043b\u0435\u0436\u0430\u0449\u0438\u0445 \u0432 \u043e\u0441\u043d\u043e\u0432\u0435 RSA \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u0438.","og:url":"https:\/\/prohoster.info\/cs\/blog\/news\/attack-method-that-significantly-reduces-the-resources-needed-to-forge-rsa-digital-signatures","og:image":"https:\/\/prohoster.info\/wp-content\/uploads\/2021\/11\/logo-350.jpg","og:image:secure_url":"https:\/\/prohoster.info\/wp-content\/uploads\/2021\/11\/logo-350.jpg","og:image:width":350,"og:image:height":350,"article:published_time":"2026-09-29T14:54:35+00:00","article:modified_time":"2026-09-29T14:54:41+00:00","article:publisher":"https:\/\/www.facebook.com\/prohoster"},"aioseo_meta_data":[],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/prohoster.info\/cs\/wp-json\/wp\/v2\/posts\/183509","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/prohoster.info\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/prohoster.info\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/prohoster.info\/cs\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/prohoster.info\/cs\/wp-json\/wp\/v2\/comments?post=183509"}],"version-history":[{"count":1,"href":"https:\/\/prohoster.info\/cs\/wp-json\/wp\/v2\/posts\/183509\/revisions"}],"predecessor-version":[{"id":183510,"href":"https:\/\/prohoster.info\/cs\/wp-json\/wp\/v2\/posts\/183509\/revisions\/183510"}],"wp:attachment":[{"href":"https:\/\/prohoster.info\/cs\/wp-json\/wp\/v2\/media?parent=183509"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/prohoster.info\/cs\/wp-json\/wp\/v2\/categories?post=183509"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/prohoster.info\/cs\/wp-json\/wp\/v2\/tags?post=183509"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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Zdroj: opennet.ru<\/a> <\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"