Kalifornijas Universit\u0101tes San Diego p\u0113tnieki ir izstr\u0101d\u0101ju\u0161i uzlabotu uzbrukuma tehniku RSA algoritmam, kas \u013cauj vilto digit\u0101l\u0101s parakstus bez nepiecie\u0161am\u012bbas faktoriz\u0113t pamat\u0101 eso\u0161os RSA pirmskait\u013cus un atjaunot sl\u0113pto atsl\u0113gu. Resursi, kas vajadz\u012bgi uzbrukuma veik\u0161anai pret 1024 bitu RSA atsl\u0113gu, tiek nov\u0113rt\u0113ti k\u0101 1380 gadu skait\u013co\u0161anas uz vienu procesora kodolu, kas universit\u0101tes klaster\u012b \u013c\u0101va 5 m\u0113ne\u0161u laik\u0101 noteikt parametrus, kas nepiecie\u0161ami viltotu RSA parakstu izveido\u0161anai (eksperiment\u0101 netika izmantoti AI pa\u0101trin\u0101t\u0101ji un GPU, un to izmanto\u0161ana var\u0113tu b\u016btiski samazin\u0101t skait\u013co\u0161anas laiku). Sal\u012bdzin\u0101jumam, klasisk\u0101 faktoriz\u0101cijas metode prasa atjaunot RSA-1024 sl\u0113pto atsl\u0113gu no 500 t\u016bksto\u0161iem l\u012bdz miljonam gadu skait\u013co\u0161anas uz vienu procesora kodolu. <\/p>\n
Uz uzbrukuma \u012bsteno\u0161anu ir nepiecie\u0161ama iesp\u0113ja atk\u0101rtoti nos\u016bt\u012bt piepras\u012bjumus par parakstu, veidojot uzbruc\u0113ja datus, piem\u0113ram, piek\u013c\u016bstot autoriz\u0101cijas servisiem vai HSM-modu\u013ciem. Lai noteiktu RSA-1024 parametrus, pietiek nos\u016bt\u012bt 232 l\u012bdz\u012bgus piepras\u012bjumus, bet uzbrukumam uz RSA-2048 atsl\u0113g\u0101m, kas tiek izmantotas Privacy Pass protokol\u0101, b\u016bs nepiecie\u0161ami 243. Ieg\u016bstot parakst\u012btu datu mas\u012bvu, tiek uzs\u0101kts ilgs parametru apr\u0113\u0137in\u0101\u0161anas process (RSA-1024 gad\u012bjum\u0101 apm\u0113ram 265 oper\u0101cijas), p\u0113c kuru sa\u0146em\u0161anas uzbruc\u0113js var izveidot viltus parakstus jebkuriem datiem, t\u0113r\u0113jot apm\u0113ram 180 stundas apr\u0113\u0137inu uz vienu kodolu katram parakstam. <\/p>\n
Metode ir piem\u0113rojama tikai RSA parakstiem, kur nav izmantota format\u0113\u0161ana un papildus aizpild\u012b\u0161ana pirms \u0161ifr\u0113\u0161anas (padding). Uzbrukumam ir pak\u013cautas akl\u0101s parakst\u012b\u0161anas realiz\u0101cijas, tostarp t\u0101s, kas tiek izmantotas Privacy Pass protokol\u0101. Liel\u0101k\u0101 da\u013ca ikdien\u0101 lietoto RSA realiz\u0101ciju, tostarp PKCS#1v1.5 un RSA-PSS (kas tiek izmantoti TLS un SSH), izmanto papildus aizpild\u012b\u0161anu un nav pak\u013cautas uzbrukumam. <\/p>\n
RSA \u0161ifr\u0113\u0161anas pamats balst\u0101s uz liel\u0101 skait\u013ca k\u0101p\u0161anas oper\u0101cij\u0101m p\u0113c modu\u013ca. Atv\u0113rtaj\u0101 atsl\u0113g\u0101 ir modulis un eksponents. Modulis tiek veidots, pamatojoties uz diviem nejau\u0161iem prim\u0101rajiem skait\u013ciem, kas ir zin\u0101mi tikai sl\u0113pt\u0101s atsl\u0113gas \u012bpa\u0161niekam. Pied\u0101v\u0101t\u0101 metode ir balst\u012bta uz 2007. gad\u0101 public\u0113tu p\u0113t\u012bjumu, kas pier\u0101d\u012bja, ka saknes izvilk\u0161ana no \u0161ifr\u0113t\u0101 zi\u0146ojuma ar nor\u0101d\u012btu atv\u0113rtaj\u0101 atsl\u0113g\u0101 eksponentu bez inform\u0101cijas par slepenajiem reizin\u0101t\u0101jiem ir maz\u0101k resursu pras\u012bga oper\u0101cija nek\u0101 pa\u0161u reizin\u0101t\u0101ju faktoriz\u0101cija. <\/p>\n
Izmantojot \u012bpa\u0161u skait\u013cu lauka sietu metodi (SNFS), p\u0113tniekiem izdev\u0101s samazin\u0101t RSA-1024 atsl\u0113gu kompromit\u0101cijas sare\u017e\u0123\u012bt\u012bbu l\u012bdz 265 oper\u0101cij\u0101m, kas \u013cauj veikt praktiskas uzbrukumus m\u016bsdienu klasteros. RSA 2048 bitu atsl\u0113gu uzbrukuma sare\u017e\u0123\u012bt\u012bba tiek nov\u0113rt\u0113ta k\u0101 290, kas teor\u0113tiski ir iesp\u0113jams liel\u0101m korpor\u0101cij\u0101m vai specdienestiem. RSA 4096 bitu atsl\u0113g\u0101m uzbrukuma sare\u017e\u0123\u012bt\u012bba ir 2119 oper\u0101cijas, kas praks\u0113 joproj\u0101m ir neizpild\u0101ma, bet ir zem minim\u0101l\u0101 2128, ko ieteikusi NSA, Nacion\u0101lais standartu un tehnolo\u0123iju instit\u016bts, un Eiropas T\u012bklu un inform\u0101cijas dro\u0161\u012bbas a\u0123ent\u016bra. \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\udd47Uzbrukuma metode, kas iev\u0113rojami samazina resursus RSA digit\u0101lo parakstu vilto\u0161anai | ProHoster","description":"Kalifornijas Universit\u0101tes San Dieg\u0101 p\u0113tnieki ir izstr\u0101d\u0101ju\u0161i uzlabotu uzbrukuma tehniku RSA algoritmam, kas \u013cauj vilto digit\u0101l\u0101s parakstus bez RSA pamat\u0101 eso\u0161o prim\u0101ro skait\u013cu faktoriz\u0101cijas.","canonical_url":"https:\/\/prohoster.info\/lv\/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":"lv_LV","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\/lv\/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\/lv\/wp-json\/wp\/v2\/posts\/183509","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/prohoster.info\/lv\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/prohoster.info\/lv\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/prohoster.info\/lv\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/prohoster.info\/lv\/wp-json\/wp\/v2\/comments?post=183509"}],"version-history":[{"count":1,"href":"https:\/\/prohoster.info\/lv\/wp-json\/wp\/v2\/posts\/183509\/revisions"}],"predecessor-version":[{"id":183510,"href":"https:\/\/prohoster.info\/lv\/wp-json\/wp\/v2\/posts\/183509\/revisions\/183510"}],"wp:attachment":[{"href":"https:\/\/prohoster.info\/lv\/wp-json\/wp\/v2\/media?parent=183509"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/prohoster.info\/lv\/wp-json\/wp\/v2\/categories?post=183509"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/prohoster.info\/lv\/wp-json\/wp\/v2\/tags?post=183509"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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Avots: opennet.lv<\/a> <\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"