RSA-encryption. Inkcazelo kunye nokuphunyezwa algorithm RSA

RSA-ufihlo yenye esebenzayo cryptosystems yokuqala kawonke-isitshixo isetyenziswa ngokubanzi ukugqithisa data ekhuselekileyo. Umehluko yayo kwiinkonzo ezifanayo kukuba iqhosha elizinyelisiweyo ivuliwe yaye yahlukile isitshixo khowudi yasiwa kumbhalo, apho kugcinwa kuyimfihlo. Ithekhnoloji RSA , le asymmetry isekelwe phezu ubunzima eyenziwayo ukuyicazulula ukudlala yabo amanani amabini yinkulumbuso elikhulu (ingxaki kahle).

History of indalo

RSA Igama iqulathe oonobumba yokuqala iifani Rivest, eShamire kunye Adleman - neengcaphephe kuqala wachaza esidlangalaleni ezi algorithms ufihlo ngo-1977. Klifford Koks, i yezibalo IsiNgesi, owayesebenza iinkonzo zobuntlola yaseBritani, ngowokuqala ukuphuhlisa inkqubo elingana ngowe-1973, kodwa akazange declassified de 1997

umsebenzisi RSA idala kwaye ngoko ipapasha isitshixo sikawonke ngokususela kumanani amabini amakhulu prime kunye ixabiso abangabancedani. amanani Prime kufuneka zigcinwe ziyimfihlo. Nabani na usebenzise isitshixo sikawonke ikhowudi umyalezo, kodwa ukuba mkhulu ngokwaneleyo, ngoko umntu kuphela xa ulwazi amanani yinkulumbuso ungakwazi ukuguqula umyalezo. RSA encryption kuzibhengeza eyaziwa ngokuba le ngxaki iphambili namhlanje i ingxoxo malunga nendlela ziyindlela ethembekileyo.

algorithm RSA kade, kuba apho isizathu, andithethi nto nje ngokubanzi kusetyenziswa ngqo ikhowudi umsebenzisi. Kwiimeko ezininzi, le ndlela isetyenziswa ukuba ukudluliselwa isitshixo ekwabelwana ngokufihlisa iqhosha elizinyelisiweyo twatsa, nto leyo ukwenza imisebenzi encryption isambuku yaye yasiwa ngesantya esiphezulu kakhulu.

Xa kukho cryptosystem ngohlobo olulo ngoku?

Ingcamango yeqhosha yezi lokufihla wenziwa Diffie kunye Hellman, ngubani yapapasha ingqiqo ngo-1976, ukungenisa usayino lwedijithali, kunye nokuzama ukusebenzisa ngobhalo amanani. ekuqulunqeni kwabo isebenzisa wabelane isitshixo secret eyenziwe evela kwinani elithile exponentiation modulo linani lodidi lokuqala. Noko ke, bashiya ukuvula umba Ukuzaliseka msebenzi, ekubeni imigaqo kahle ayiqondwanga kakuhle ngelo xesha.

Rivest, Adi eShamire, kunye Adleman kwi MIT benze iinzame eziliqela kule minyaka ukwenza umsebenzi ngendlela enye ekunzima ukucazulula. Rivest kunye eShamire (njengoko izazinzulu computer) baye imisebenzi emininzi ezinokwenzeka, lo gama Adleman (ezifana nemathematika) ukufuna "ubuthathaka" le algorithm. Basebenzisa ezininzi iindlela yaye ekugqibeleni ukuphuhlisa inkqubo lokugqibela, ngoku eyaziwa ngokuba RSA ngo-Apreli 1977.

Utyikityo Electronic kwaye isitshixo sikawonke

usayino olungamanani okanye yogesi, yinxalenye ebalulekileyo yeentlobo xwebhu ngekhompyutha. It senziwa a utshintsho data lokufihla ezithile. Xa olu phawu kunokwenzeka ukukhangela ukuthembeka yoxwebhu, imfihlo yayo, kwakunye ukujonga ngubani ongumnini kuyo. Enyanisweni, enye ngakwisiginitsha eziqhelekileyo eqhelekileyo.

Le cryptosystem (RSA-zombhalo) inika isitshixo sikawonke, ngokungafaniyo twatsa. Umgaqo wakhe msebenzi kukuba izitshixo ezimbini ezahlukeneyo asetyenziswa - ivaliwe (zombhalo) nangaphandle. Eyokuqala isetyenziselwa ukwenza umsayino wedijithali uze ube nako ukubonakalisa okufihliweyo kokubhaliweyo. Second - kuba encryption kanye kunye yogesi.

Ukusebenzisa lweesignitsha ukuqonda ngcono encryption RSA, umzekelo apho kungancitshiswa njenge imfihlelo oluqhelekileyo "iyakuvingca prying emehlweni," uxwebhu.

Yintoni algorithm?

algorithm RSA iqulathe amanyathelo amane: sizukulwana ezingundoqo, ukwabiwa, encryption kubhalo. Njengoko sele kukhankanyiwe, RSA-ufihlo uquka umntu onesitshixo sakhe sikawonke kwaye isitshixo labucala. Zangaphandle kwazekayo bonke kwaye izakusebenziswa ukufihla imiyalezo. kubume bayo usendleleni yokuba imiyalezo ifihliwe enesitshixo zoluntu uguqulwa kuphela yothuba elithile sexesha usebenzisa isitshixo ngasese.

Ngenxa yezizathu zokhuseleko, i integers ku hlaseriwa ongayazi kufana twatse ubukhulu, kodwa zahluke ubude ngu amanani abambalwa ukwenza ukuyicazulula nzima ngakumbi. inani elifanayo efanayo inokufumaneka ngokufezekileyo uvavanyo eyeke umzimba, ngoko ke khowudi lolwazi kufuneka ukuba ibe nobucukubhede.

Isitshixo sikawonke ibandakanya modulus kunye exponent yoluntu. unit esendlwini kwaye iquka inani abucala, nekufuneka zigcinwe ziyimfihlo.

RSA khowudi iifayile kunye nobuthathaka

Nakuba kunjalo, kukho iqela ezilula uyamxhaxha mechanisms RSA. Xa kube lula kuvulwa uguqulela kunye neenqobo ephantsi amancinane nekhowudi amanani, ukuba op ingcambu eyimfihlo phezu integers.

Ekubeni RSA-khowudi algorithm deterministic (oko kukuthi, akukho icandelo random), ohlaselayo ingazisa ngempumelelo okubhaliweyo ukuhlasela okhethiweyo evulekileyo ngokuchasene cryptosystem ngokuthi zofihlo kusenokwenzeka plaintexts phantsi isitshixo karhulumente ziqwalasele ukuba ingaba eyimfihlo ngokulinganayo. Semantically cryptosystem ekhuselekileyo kuthiwa xa kunokwenzeka ukuba umhlaseli akakwazi ukwahlula phakathi ufihlo ezimbini enye kwenye, nokuba uyayazi izicatshulwa ezifanelekileyo ngeyona inde. Njengoko kuchaziwe ngentla, RSA ezinye iinkonzo ngaphandle izikhuseli ayikho semantically ekhuselekileyo.

ubuchule olongezelelweyo encryption nokhuseleko

Ukuze siphephe iingxaki ngasentla, ekuphunyezweni esebenzayo RSA zidla kufakwa kuhlobo oluthile yakhiwe, ukuzaliswa kokuhlola phambi encryption. Oku kuqinisekisa ukuba umxholo ayikho phantsi uluhlu plaintexts bengakhuselekanga, yaye ukuba lo myalezo ayikwazi ukuba kusonjululwe Ukukhetha ejikelezayo.

Ukhuseleko cryptosystem RSA kunye ufihlo ngokusekelwe iingxaki ezimbini zemathematika: ingxaki ukuyicazulula amanani amakhulu kunye ingxaki kanye RSA. ukuvezwa ezipheleleyo eyimfihlo kunye utyikityo kwi-RSA ithathwa azamkeleki kwingcinga yokuba zombini ezi ngxaki ayisombululeki ngokudibeneyo.

Nangona kunjalo, kunye ubuchule bokulungisa izinto inkulumbuso, ohlaselayo Ungabala isalathi ofihlakeleyo isitshixo sikawonke uze ukususa umbhalo usebenzisa inkqubo eqhelekileyo. Nangona into yokuba namhlanje akukho ndlela ekhoyo ukuze ukuyicazulula integers enkulu classical computer akafumaneki, ayiyi singqiniwe ukuba akakho.

isilawuli esizisebenzelayo

Isixhobo, ekuthiwa Yafu, ingasetyenziswa ukwandisa le nkqubo. Ukufunyanwa okuzenzekelayo in YAFU i inkalo enobuchwepheshe ngokudibanisa algorithms factorization kwindlela ngokwasengqondweni eyakuthi enciphisa ixesha ukufumana izinto amanani igalelo ngendlela engaqondakaliyo. Uninzi Ukusetyenziswa multithreaded algorithm ukuvumela Yafu ukusetyenziswa ngokupheleleyo abaninzi ezinochaso okanye iziqhubekisi multi-core (kubandakanywa SNFS, SIQS kunye ECM). Okokuqala, oko kulawulwa isixhobo zelayini yomyalelo. Ixesha elichithwa efuna encryption Yafu factor usebenzisa eqhelekileyo ikhompyutha, iya kuncitshiswa ukuba kwimizuzwana 103,1746. Isixhobo iinkqubo binary umthamo ziikhowudi-320 okanye ngaphezulu. Le software enzima kakhulu ukuba ufuna umlinganiselo othile izakhono zobugcisa ukufaka uze ulungiselele. Ngenxa yoko, RSA-ufihlo banokuziva bengakhuselekanga C.

Inkampani imizamo muva

Ngo-2009, Bendzhamin Mudi usebenzisa RSA-512 iqhosha bit wayesebenza kuyo yonke ezama kriptoteksta iintsuku 73, besebenzisa kuphela kakuhle eyaziwa-software (GGNFS) nakumndilili desktop (ezimbini-core Athlon64 kwi 1900 MHz). Njengoko kuboniswa ngamava, efunekayo ngaphantsi kancinane kwama-5 GB of diski kwaye malunga 2.5 gigabytes imemori inkqubo "ukuhluzwa."

Njengoko ka-2010, elona nani likhulu ke izinto RSA amasuntswana 768 ubude (232 amanani lokugqibela, okanye RSA-768). ukuxela kwakhe ubukho kangangeminyaka emibini kwiikhompyutha amakhulu ezininzi ngexesha elinye.

Ukuziqhelisa, izitshixo RSA elide - ngokuqhelekileyo ukususela 1024 ukuya 4096 ziintanda. Ezinye iingcali zikholelwa ukuba bit-1024 kumakhi babe ongathembekanga kwixa elizayo okanye ngaphezulu abe aqhekekileyo abahlaseli kakhulu ngemali kakuhle. Noko ke, bambalwa abantu bathi ukuba bit-4096 kumakhi ngokunjalo zibhengezwe kwixa elizayo.

amathuba

Ngoko ke, njengokuba umthetho, loo nto ixela ukuba RSA lukhuselekile ukuba amanani makhulu ngokwaneleyo. Ukuba inombolo isiseko ziikhowudi 300 okanye elifutshane, kwaye umsayino wedijithali eyimfihlo kuba ibolile kwisithuba iiyure ezimbalwa kwi computer siqu usebenzisa software ekhoyo sele kuwonke-wonke. Eyona ubude 512 amasuntswana, njengoko kubonisiwe, iya kuvulwa kwangethuba 1999, kunye nokusetyenziswa iikhompyutha ezilikhulu ambalwa. Kule mihla oko kuyenzeka apha kwiiveki ezimbalwa usebenzisa iintsimbi ezikhoyo esidlangalaleni. Ngaloo ndlela, kunokwenzeka ukuba buduschembudet lula kudizwe RSA-fihlwanga kwi kweminwe, yaye le nkqubo iza kuba akaziva lixesha.

Ngokusemthethweni ngo-2003, wabizelwa umbuzo ukhuseleko bit-1024 izitshixo. Okwangoku, kucetyiswa ukuba ubude ubuncinane 2048 ziintanda.