RSA-encryption. Description uye Implementation of RSA algorithm

RSA-encryption mumwe wokutanga inoshanda ruzhinji-anokosha cryptosystems kuti zvikuru kushandiswa yakachengeteka date hutachiwana. Its musiyano mukuru kubva mabasa akafanana ndezvokuti encryption kiyi yakazaruka uye rakasiyana Decryption kiyi, icho chakavanzika. The RSA ano , asymmetry ichi inobva inoshanda kuoma factoring ari playback makuru wehurumende nhamba mbiri (chinetso factoring).

History chokusika

RSA The zita ine kutanga mutsamba surnames Rivest, Shamiri uye Adleman - masayendisiti uyo akatanga kurondedzera pachena izvi encryption algorithms muna 1977. Klifford Koks, imwe nyanzvi yemasvomhu Chirungu, uyo akashanda British utikitivha, wokutanga kuva noenderana wemuTesitamende 1973, asi harina declassified kusvikira 1997

RSA mushandisi anosika uye ipapo rinobudisa kiyi yavose kwakavakirwa huru wehurumende nhamba mbiri pamwe upiyona ukoshi. Prime nhamba dzinofanira kuchengetwa muchivande. Munhu anogona kushandisa vanhu kiyi encrypt shoko, asi kana zviri yakakura zvakakwana, ipapo chete mumwe nokuziva inonyanya nhamba anogona bata shoko. RSA encryption kuburitsa anozivikanwa sezvo huru dambudziko nhasi bwakashama hurukuro pamusoro sei yakavimbika mashandiro.

RSA algorithm achiri kunonoka, nokuda kwechikonzero hazvina kufanana zvikuru kushandiswa zvakananga encrypt inodzidzisa. Kazhinji, nzira iri kushandiswa Kupfuudzwa ari vaiita kiyi encrypted kuti symmetric encryption kiyi, izvo zvinozoita anogona kuvhiya hombe encryption uye Decryption pane imwe yepamusoro zvikuru nokukurumidza.

Kana paiva cryptosystem waro aripo chimiro?

Pfungwa asymmetric cryptographic kiyi anonzi akataurwa Diffie uye Hellman, uyo akabudisa pfungwa muna 1976, Pakusuma digitaalinen vakasaina, uye kuedza kushandisa dzidziso nhamba. Pfungwa dzavo anoshandisa vaiita kiyi zvakavanzika yakawanikwa kubva imwe nhamba Exponentiation modulo chikuru nhamba. Zvisinei, vakasiya kuzarura nyaya kuitika basa iri, sezvo misimboti factoring haana zvakanaka kunzwisiswa panguva.

Rivest, Adi Shamiri, uye Adleman pana with kunge vakaedza kakawanda mumakore kusika munhu-nzira basa kuti chinonetsa nzwisisa. Rivest uye Shamiri (sezvo masayendisiti kombiyuta) kunge aronga dzakawanda zvinogona kushanda, apo Adleman (akaita masvomhu) kutsvaga "simba pfungwa" yacho algorithm. Vakashandisa yakawanda nzira uye pakupedzisira kuva wokupedzisira gadziriro, yava kuzivikanwa RSA muna April 1977.

Electronic siginicha uye veruzhinji kiyi

Digital siginicha kana yemagetsi siginicha, chinhu chinokosha pamusoro yemagetsi gwaro mhando. It achiumbwa pane imwe cryptographic mashoko kuchinja. With ichi chizenga zvichibvira kuongorora kuvimbika gwaro, zvakavanzika wayo, uyewo kuona muridzi izvozvo. Kutaura zvazviri, imwe nzira kune kwachaisvika siginicha.

cryptosystem ichi (RSA-encrypted) inopa veruzhinji kiyi, kusiyana symmetric. musimboti Its kushanda ndechokuti zviviri zvakasiyana kiyi anoshandiswa - kuvharwa (encrypted) uye Outdoor. Chokutanga chinoshandiswa kuti vaunze mashoko digitaalinen siginicha uye kukwanisa decrypt acho. Chechipiri - nokuti chaiwo encryption uye zvemagetsi siginicha.

Kushandisa vakasaina kunzwisisa zviri nani RSA encryption, muenzaniso iyo inogona kuderedzwa sezvo zvisingatomboiti chakavanzika "warega yokunzvera maziso," gwaro racho.

Chii algorithm?

RSA algorithm ine matanho mana: anokosha chizvarwa, kuparadzirwa, encryption uye Decryption. Sezvambotaurwa, RSA-encryption unosanganisira paruzhinji kiyi uye private kiyi. Outdoor zvingazivikanwa vose uye inoshandiswa encrypt mashoko. Chaizvoizvo Its iri pakuti mashoko encrypted pamwe yavose kiyi inogona chete decrypted munguva nguva vachishandisa pakavanda kiyi.

Nokuti vakachengeteka zvikonzero, kuti integers kusarudzwa pavaidira uye kuva akafanana pakukura, asi vakasiyana pakureba navashoma nhamba kuti factoring kwakamuomera. Same nhamba iyoyo inogona zvinobudirira akawanikwa pabvunzo havo saka encryption mashoko anofanira hazvo kuva kwakaoma.

The paruzhinji kiyi kuchibva modulus uye voruzhinji exponent. Indoor chikwata uye rine private nechipi, izvo zvinofanira akavanzwa.

RSA encryption kuti mafaira uye utera

Zvisinei, pane vakawanda nyore kugura RSA zvigadziriswe. Kana encrypting pamwe yakaderera uye diki tsika remitemo nhamba hunogona kungoparara akazarura, kana Sarudza mudzi ciphertext pamusoro integers.

Sezvo RSA-encryption chinhu deterministic algorithm (kureva, haana anongoitika zvinoriumba), imwe chibharo anogona kubudirira kumhanya rwaakasarudza Plaintext kurwiswa kwakaitwa cryptosystem kuburikidza encrypting zvichida plaintexts pasi kuruzhinji kiyi uye kuongororwa panyaya kana vari ciphertext vakaenzana. Semantically yakachengeteka cryptosystem ichinzi iri chiitiko kuti vavashungurudza havagoni musiyano maviri encryption kubva mumwe, kunyange kana anoziva kuMudzidzisi magwaro ari rakawedzerwa muchimiro. Sezvinotsanangurwa pamusoro, RSA mamwe mabasa pasina padding hakusi semantically yakachengeteka.

Zvimwe algorithms nokuti encryption uye kudzivirirwa

Kuti vadzivise pamusoro matambudziko, mune anobatsira Implementation pamusoro RSA anowanzoshandurwa rakapinzwa rwakati muronga, randomized zvekupfakira pamberi encryption. Izvi zvinoita kuti tigutsikane harwuwire mukati kuwanda kuchengeteka plaintexts, uye kuti shoko iri hazvigoni kugadziriswa vakasarudzwa zvisina kurongwa.

Security RSA cryptosystem uye encryption kunobva matambudziko maviri kwemasvomhu: chinetso factoring vazhinji uye chaiwoiwo RSA dambudziko. Full Kuziviswa pamusoro ciphertext uye siginicha muna RSA anonzi inadmissible ari kubvuma kuti matambudziko aya hazvigoni kugadziriswa pamwe.

Zvisinei, tichikwanisa wokugadzirisa chikuru zvinhu, imwe chibharo anogona ngaaverenge chakavanzika exponent evoruzhinji kiyi uye ipapo decrypt rugwaro uchishandisa mureza muitiro. Pasinei chokwadi kuti nhasi hapana aivapo nzira factoring integers hombe pamusoro dzekare kombiyuta haagoni kuwanikwa, haruna kupomberwa vakaratidza kuti haako.

kushandisa michina

The mudziyo, rinonzi Yafu, zvinogona kushandiswa optimize muitiro. Kushandisa michina iri YAFU chinhu yepamusoro chine kuti rinobatanidza factorization algorithms mune pfungwa uye adaptive nzira kuti waanodzikisira nguva kuwana zvinhu zviri zvemasanga chiyamuro nhamba. implementations Most multithreaded algorithm kubvumira Yafu zvizere kushandisa multi- kana vazhinji multi-Musimboti processors (kusanganisira SNFS, SIQS uye ECM). Chokutanga, hazvina inotongwa murayiro-mutsetse chokushandisa. Nguva yakapedzerwa kutsvaka encryption Yafu chinhu vachishandisa kwakajairika kombiyuta, anogona kuderedzwa kuti masekonzi 103,1746. The chishandiso kurongedza mashoko binary anokwanisa 320 matomu kana kupfuura. Uyu-software chaizvo kunzwisisa kuti inoda imwe mari unyanzvi unyanzvi kuisa uye kugadzira. Saka, RSA-encryption kungava nyore C.

Kugura kuedza achangopfuura

Muna 2009, Bendzhamin Mudi vachishandisa RSA-512 ikakuruma kiyi akanga achishandisa achiongorora zvaive kriptoteksta kwemazuva 73, achishandisa chete rinozivikanwa Software (GGNFS) uye avhareji pakombiyuta (hunyambiri-Musimboti Athlon64 pa 1900 MHz). Sezvinoratidzwa nezvakaitika, chinodikanwa zvishoma zvishoma pane 5 GB pamusoro dhisiki uye vanenge 2,5 gigabytes okuyeuka kuti muitiro "kusefa."

Muna 2010, nhamba huru isati akanga factored RSA 768 matomu refu (232 grade digits, kana RSA-768). kuburitsa ake kwakatora makore maviri ari akawanda zana makombiyuta kamwe.

In tsika, kuti RSA kiyi vari refu - yemanyorero kubva 1024 kusvika 4096 matomu. Dzimwe nyanzvi dzinodavira kuti 1024-ikakuruma makiyi vangava vasingavimbiki munguva yemberi iri pedyo kana akatowanda inogona wakatsemuka kwazvo-mari nemhomho. Zvisinei, vashoma vangati 4096-ikakuruma makiyi zvinogona kutaurwa ramangwana.

tarisiro

Naizvozvo, sezvo mutemo zvinofungirwa kuti RSA yakachengeteka kana nhamba yakakura zvakakwana. Kana mujinga nhamba 300 matomu kana mupfupi, uye ciphertext digitaalinen siginicha inogona yaora mumaawa mashomanana ari oga kombiyuta uchishandisa Software zvinowanikwa kare munzvimbo soumambo. Chinhu chikuru kureba 512 matomu, sezvinoratidzwa, zvinogona kushamisa kare 1999, pamwe nokushandiswa mashoma zana makombiyuta. Mazuva ano zvinoita mune shomanana vachishandisa pachena iripo Hardware. Saka, zvinokwanisika kuti buduschembudet nyore kuzivisa RSA-encrypted pamusoro minwe, uye hurongwa vachava tariro yechinyakare.

Pamutemo muna 2003, yainzi kupinda mubvunzo kuchengeteka 1024-ikakuruma kiyi. Pari, Zvinokurudzirwa kuti risingamboshandisi kureba 2048 matomu.