RSA-ukubethela. Incazelo nokusentshenziswa kwe-algorithm RSA

RSA-ukubethela ingenye esisebenzayo cryptosystems yenengi yokuthoma-ukhiye kabanzi ephephile ukudluliswa kwedatha. umehluko Its main kusukela izinkonzo ezifanayo liwukuthi isihluthulelo ukubethela ivuliwe futhi ihluke ukhiye ukuqaqwa, okuyinto kugcinwa kuyimfihlo. Ubuchwepheshe RSA , lokhu asymmetry isekelwe nobunzima esiwusizo sokuba nezinto eziqondile kahle ukudlala izinombolo ezimbili ezinkulu prime (inkinga ka kahle).

Umlando sokudalwa

RSA Igama liqukethe izinhlamvu zokuqala izibongo Rivest, eShamiri futhi Adleman - ososayensi okunguyena owokuqala owachaza lesi lezi esidlangalaleni ukubethela algorithm ngo-1977. Klifford Koks, i sezibalo English, owayesebenza amasevisi intelligence British, owokuqala ukuthuthukisa uhlelo okulingana ngo-1973, kodwa sasingawohloki declassified kuze 1997

RSA umsebenzisi kudala bese ishicilela ukhiye womphakathi esekelwe izinombolo ezimbili ezinkulu prime kanye ukubaluleka asizayo. izinombolo Prime kufanele avalelwe. Noma ubani angasebenzisa ukhiye womphakathi ukufaka ikhowudi kwimininingo umlayezo, kodwa uma izwe libanzi inxa zombili, bese kuphela umuntu onolwazi izinombolo eziyinhloko kungaba ukuqopha umlayezo. RSA ukuvezwa is njengoba inkinga eyinhloko aziwayo namuhla nengxoxo evulekile ngendlela indlela enokwethenjelwa.

RSA algorithm kuqhathaniswa kancane, okwenza izazi it is hhayi njengoba kabanzi ngqo ngemfihlo umsebenzisi. Ezimweni eziningi, le ndlela isetshenziswa yokudlulisela e ukhiye wabelane ngekhodi okwesikhathi ukubethela ukhiye lesinesitfombe-sibuko, kona okungaholela imisebenzi ukubethela ngobuningi nencazelo ngejubane elingaphezulu kakhulu kwaleli.

Lapho kwakukhona cryptosystem injalo manje?

Umqondo ukhiye quin cryptographic isibaluli Diffie futhi Hellman, owakhipha umqondo ngo-1976, ethula nesignesha digital, nokuzama ukusebenzisa imfundiso yokuziphendukela izinombolo. ekwakhiweni yabo isebenzisa wabelane ukhiye secret abake inombolo ethile Exponentiation modulo inombolo esiyinhloko. Nokho, bahamba ukuvula le ndaba yokungaziphathi ukugcwaliseka lo msebenzi, njengoba izimiso ka kahle awuzange bawuqonda ngaleso sikhathi.

Rivest, Adi eShamiri, futhi Adleman eMIT wenze imizamo eminingana eminyakeni ukwakha umsebenzi ngendlela eyodwa ukuthi kunzima ukunquma. Rivest futhi eShamiri (njengoba ososayensi computer), baye bahlongoza imisebenzi eminingi engaba, kuyilapho Adleman (efana le-IiMbalo) ukucinga "ubuthakathaka" ye-algorithm. Babesebenzisa eziningi izindlela futhi ekugcineni ukuthuthukisa uhlelo lokugcina, manje eyaziwa ngokuthi i-RSA ngo-April 1977.

yogesi kanye ukhiye womphakathi

Isiginesha yedijithali noma yogesi, iyingxenye ye-mbhalo izinhlobo electronic. Kumiswa It is ngesikhathi esithile cryptographic izinguquko idatha. Nale ngemfanelo kungenzeka ukuhlola ubuqotho idokhumenti, ngaphandle kokugcinwa kuyimfihlo yayo, kanye ukuthi ngubani ongumnikazi ke. Eqinisweni, esikhundleni abavamile isignesha ejwayelekile.

Lokhu cryptosystem (RSA-ngekhodi) inikeza ukhiye womphakathi, ngokungafani lesinesitfombe-sibuko. isimiso sayo wokusebenza ukuthi izihluthulelo ezimbili ezahlukene ezisetshenziswa - ivaliwe (ngekhodi) futhi ongaphandle. Eyokuqala lisetshenziselwa ukukhiqiza isignisha yezinombolo bese bakwazi ukuqaqa umbhalo. Okwesibili - ukuze ukubethela langempela futhi yogesi.

Ukusebenzisa amasignisha ukuze uqonde kangcono ukuthi ukubethela RSA, isibonelo lapho zingancishiswa njengoba imfihlo evamile "ivaliwe kusukela prying amehlo," kusho amaphepha ahanjiswe.

Iyini i-algorithm?

RSA algorithm siqukethe izinyathelo ezine: ukhiye isizukulwane, ukusatshalaliswa, ukubethela nencazelo. Njengoba sekushiwo, RSA-ukubethela kufaka ukhiye womphakathi kanye ukhiye wangasese. Outdoor ingaziwa bonke futhi lisetshenziswa ukubethela imiyalezo. essence yayo itholakala iqiniso ukuthi izigijimi ezifihliwe nge ukhiye womphakathi kungenziwa kuphela uguqulwa esikhathini esinikeziwe isikhathi usebenzisa ukhiye eyimfihlo.

Ngenxa yezizathu zokuphepha, i-integers ukuba ukhethwa nomaphi futhi lifane ngobukhulu, kodwa kuhluke obuphelele ngumuntu izinombolo ambalwa ukwenza kahle nzima. inombolo efanayo Kungashiwo okufanayo ngempumelelo wathola sivivinyo bemsulwa, ngakho ukuvikelwa kokwaziswa kumelwe nakanjani kube nzima.

Ukhiye womphakathi siqukethe wemfihlo futhi okungekho umphakathi. iyunithi wasendlini siqukethe sibalo yangasese, okumele abe yimfihlo.

RSA amafayela kanye nobuthakathaka

Nokho, zikhona eziningana ezilula nokugenca RSA izindlela. Lapho ekufihleni amanani aphansi futhi elincane ikhodi izinombolo angavulwa kalula, uma yezinhlamvu Pick impande phezu integers.

Kusukela RSA-ukubethela algorithm deterministic (ie, ayinakho ingxenye okungahleliwe), umhlaseli ongaphumelela uqalise umbhalo okhethiwe kuhlasela evulekile ngokumelene cryptosystem ngokubhala ngekhodi Cishe plaintexts ngaphansi ukhiye womphakathi kanye amasheke ku kungakhathaliseki ukuthi yezinhlamvu alinganayo. Wokufihla cryptosystem evikelekile ibizwa ngokuthi uma kwenzeka ukuthi umhlaseli abakwazi ukuhlukanisa phakathi ukubethela amabili komunye nomunye, ngisho noma yena uyazazi imibhalo efanele efomini ukunwetshwa. Njengoba kuchazwe ngenhla, RSA namanye amasevisi we ngaphandle ukupheda lungavikelekile wokufihla.

algorithm engeziwe for ukubethela nokuvikeleka

Ukuze ugweme izinkinga ngenhla, e ukusebenza nokusebenzisa RSA kuvame ifakwe uhlobo oluthile olwakhiwe, ukugcwaliswa olwenziwa phambi ukubethela. Lokhu kuqinisekisa ukuthi okuqukethwe akuweli uhla plaintexts bengalondekile futhi ukuthi lo mlayezo ayikwazi ingaxazululwa ngokuthi Ukukhetha okungahleliwe.

Ezokuphepha RSA cryptosystem kanye ukubethela esekelwe izinkinga ezimbili zezibalo: inkinga ka kahle izinombolo ezinkulu futhi langempela inkinga RSA. ukuvezwa Esigcwele yezinhlamvu kanye nesiginesha e-RSA kubhekwa inadmissible ngoba kucatshangwa ukuthi zombili lezi zinkinga azinakuxazululwa bebonke.

Nokho, ne ikhono alulame eziyinhloko, umhlaseli angakwazi bala exponent imfihlo ukhiye womphakathi bese ukususa ukubhala umbhalo usebenzisa inqubo ejwayelekile. Naphezu kweqiniso lokuthi namuhla ayikho indlela ekhona ngoba kahle integers enkulu kukhompyutha classical ayikwazi ukutholwa, ayizange kungase kutholakale ukuthi akekho.

ezishintshayo

Ithuluzi, ngokuthi Yafu, ingasetshenziswa nokwandisa inqubo. Automation e YAFU isici esithuthukile ehlanganisa factorization algorithm endleleni nabanengqondo futhi oluhambelana enciphisa isikhathi ukuthola izici izinombolo okokufaka ngaphandle kokubonisana nomkayo. implementations Iningi multithreaded algorithm ngokuvumela Yafu ukusebenzisa ngokugcwele yehlukene noma eziningi izilimi multi-core (kuhlanganise SNFS, SIQS futhi ECM). Okokuqala, it is kulawulwa womyalelo ithuluzi. Isikhathi esichithwa ekufuneni ukubethela Yafu isici usebenzisa ikhompyutha ezivamile, kungase sehliselwe imizuzwana 103,1746. Ithuluzi IZINHLELO kanambambili umthamo izingcezu 320 noma ngaphezulu. Lena isofthiwe eziyinkimbinkimbi kakhulu okudinga ethile amakhono obuchwepheshe ukufaka futhi ulungiselele. Ngakho, RSA-ukubethela kungenzeka C. sengozini

Hacking imizamo ezikhathini zamuva

Ngo-2009, Bendzhamin Mudi usebenzisa RSA-512 ukhiye kancane ayelungisa sokuqonda kriptoteksta izinsuku 73, usebenzisa isofthiwe kuphela owaziwa (GGNFS) kanye ideski elivamile (ezimbili-core Athlon64 at 1900 MHz). Njengoba kuboniswa okuhlangenwe nakho, kudingeka kancane esingaphansi 5 GB disk futhi mayelana 2.5 gigabytes memory ngoba inqubo "nokuhlungwa."

Kusukela ngomhla ka-2010, inani elikhulu kunawo wonke waba factored RSA 768 izingcezu eside (232 idesimali kwamadijithi, noma RSA-768). ukuvezwa kwakhe eyathatha iminyaka emibili kumakhompyutha abangamakhulu amaningana ngesikhathi esisodwa.

Ekusebenteni, okhiye RSA made - ngokuvamile kusukela 1024 kuya 4096 izingcezu. Abanye ochwepheshe bakholelwa ukuthi okhiye 1024-bit ingavuthi alithembekile esikhathini esizayo esiseduze noma ngisho nangaphezulu kungenziwa aqhephukile abahlaseli kakhulu kahle uxhaso. Nokho, abambalwa bangase baphikise ngokuthi 4096-bit okhiye ingaphinda avezwe esikhathini esizayo esiseduze.

amathemba

Ngakho-ke, njengoba umthetho, kucatshangwa ukuthi RSA ivikeleke uma izinombolo inkulu ngokwanele. Uma inombolo base izingcezu 300 noma zibe mfushane, kanye yezinhlamvu Isiginesha yedijithali kungenziwa ukubola ngaphakathi kwamahora ambalwa kwikhompyutha siqu usebenzisa isofthiwe iyatholakala selusezandleni zomphakathi. Isihluthulelo obuphelele 512 izingcezu, njengoba kukhonjisiwe, angavulwa kudala njengoba 1999, nokusetshenziswa amakhompyutha ambalwa. Namuhla kungenzeka emasontweni ambalwa usebenzisa hardware etholakala esidlangalaleni. Ngakho, kungenzeka ukuthi buduschembudet kudalulwe kalula RSA-ngekhodi phezu iminwe, futhi uhlelo iyoba ngendlela engenathemba yisikhathi.

Ngokusemthethweni ngo-2003, bangatshazwa ukuphepha okhiye 1024-bit. Okwamanje, kutuswa ukuba abe obuphelele ubuncane 2048 izingcezu.