RSA-whakamunatanga. Whakamārama me te whakatinanatanga o te hātepe RSA

RSA-whakamunatanga ko tetahi o te cryptosystems mahi tuatahi tūmatanui-matua Kei te whānui e whakamahia mō te tuku raraunga haumaru. Ko tōna rerekētanga matua i ngā ratonga rite ko e he tuwhera, me te rerekē i te kī wetemunatanga, puritia nei te ngaro te kī whakamunatanga. Te hangarau RSA , tenei karawhiti hāngai te i runga i te uaua mahi o Factoring te anō o rua tau pirimia nui (te raruraru o te Factoring).

History o hanga

RSA ngā o nga reta tuatahi o te ingoa whānau Rivest, Hamiri ko Adleman te ingoa - te pūtaiao e tuatahi nuitia fakamatala'i enei hātepe whakamunatanga i roto i 1977. Klifford Koks, he mathematician Ingarihi, nei mahi hoki ratonga maramarama Ingarangi, ki te tuatahi whakawhanake i tētahi pūnaha ōrite i roto i 1973, engari kihai i Declassified reira tae noa ki 1997

Hangaia RSA kaiwhakamahi, me te ka kaikauwhau i te kī tūmatanui e hāngai ana i runga i rua tau nui pirimia tahi me te uara pŭpŭ tauturu. tau Prime kia puritia ngaro. Ka taea e te tangata te whakamahi i te kī tūmatanui ki te whakamuna i te karere, engari ki te he te reira nui nui, ka anake te tangata ki te matauranga o tau pirimia taea te wetewaehere te karere. mohiotia RSA whakamunatanga whākinga te rite te raruraru matua tenei ra ko te kōrero tuwhera e pā ana ki te āhua o te huarahi pono.

Ko ngā puhoi RSA hātepe papatono, hoki nei take e kore te mea rite whānui whakamahia ki tika whakamuna te kaiwhakamahi. I roto i te nuinga o te wā, kei te whakamahia tenei tikanga mo te tuku i roto i te kī ngā whakamunatia mo te kī whakamunatanga hangarite, e i roto i te tahuri taea te mahi i ngā mahi whakamunatanga nuinga, me te wetemunatanga i te tere nui teitei.

A, no te reira i te cryptosystem i roto i tona ahua reira?

Ko te whakaaro o te matua cryptographic hangarite pēnei ki Diffie ko Hellman, e whakaputaina te ariā i roto i 1976, te whakauru waitohu mamati, ka ngana ana ki te tono i te ariā o ngā tau. whakamahi ratou waihanga he kī ngaro ngā hangaia i te tetahi maha o taupūtanga modulo he maha pirimia. Heoi, mahue ratou te whakatuwhera i te take o te whakatutukitanga o tenei mahi, mai kore i matau pai te mau parau tumu o te Factoring i te wa.

Rivest, Adi Hamiri, ko Adleman i MIT kua hanga e rave rahi nganatanga ki runga i te tau ki te hanga i tētahi mahi kotahi-ara e he uaua ki te Pūwhiwhi. Rivest ko Hamiri (rite kaiputaiao rorohiko) kua whakaarohia maha mahi pea, i Adleman (rite pāngarau) ki te rapu mō "ngā ngoikore" o te hātepe. whakamahia ratou he rota o huarahi, me te pae hopea te whakawhanake i tētahi pūnaha whakamutunga, e mohiotia nei rite RSA i April 1977.

waitohu Electronic me te kī tūmatanui

waitohu mamati waitohu hiko ranei, ko te wāhi o te momo tuhinga hiko. Kei te hanga e te reira i te tetahi huringa raraunga cryptographic. Ki te taea tenei huanga ki te tirohia i te tapatahi o te tuhinga, ki tona matatapu, me te whakatau ko wai nona te reira. I roto i te meka, he rerekē ki te tohu paerewa noa.

Tenei cryptosystem (RSA-whakamuna) tuku te kī tūmatanui, pērā hangarite. Ko tōna parau tumu o te mahi ko e e whakamahia nga mau taviri e rua rerekē - katia (whakamuna) me waho. Kei te whakamahia te tuatahi ki te whakaputa i te waitohu mamati, me te ka taea ki te wetemuna te kuputuhi. Tuarua - mo te whakamunatanga tūturu me waitohu hiko.

Mā te waitohu ki te mahino pai te whakamunatanga RSA, he tauira o e taea te heke rite te ngaro tonu "katia i prying kanohi," te tuhinga.

He aha te mea te hātepe?

ngā RSA hātepe o wha hikoinga: whakatupuranga matua, tohatoha, whakamunatanga me te wetemunatanga. Ka rite ki kua whakahuatia, RSA-whakamunatanga ngā te kī tūmatanui, me te kī tūmataiti. Ka taea te mohiotia Outdoor ki katoa me te whakamahia ki te whakamuna karere. takoto Ko tōna ngako i roto i te meka e taea anake te wetemuna karere whakamuna ki te kī tūmatanui i roto i te wā i homai o te wā mā te whakamahi i te kī ngaro.

No te take haumaru, ki te tau tōpu kia whiriwhiria i tupurangi, me te kia ōrite i roto i te rahi, engari rerekē i roto i te roa e te torutoru tau ki te hanga Factoring uaua atu. Ka taea te tōtika kitea tau taua Same e te whakamātautau i roto i te kuwaretanga ratou, pera me tika kia faingataa te whakamunatanga o ngā mōhiohio.

Kei te kī tūmatanui o te uara tawhiti, me te taupū tūmatanui. kōwae o roto, me te ngā o te tauira tūmataiti, e kia puritia ngaro.

RSA whakamunatanga o ngā kōnae me mau paruparu

Heoi, i reira e he maha o hacking tikanga RSA ohie. A, no te whakamuna ki uara iti, me te iti o te tau waehere e taea te ngāwari whakatuwheratia, ki te te ciphertext huri pakiaka ki runga ki te tau tōpu.

Mai te RSA-whakamunatanga ko te hātepe deterministic (arā, e kore wāhanga tupurangi), pai e taea te hoariri whakarewa te whakaeke tuwhera kuputuhi tīpakohia ki te cryptosystem mā te whakamuna plaintexts pea i raro i te kī tūmatanui me arowhai i runga i ranei he ratou rite ciphertext. Semantically i huaina cryptosystem haumaru i roto i te kaupapa e kore e taea e te hoariri te wehewehe i waenganui i te whakamunatanga e rua i ia atu, ara, ki te mohio ia ki nga tuhinga e hāngai ana i roto i te puka whakawhānui. Ka rite ki whakaahuatia ana i runga, e kore te mea haumaru semantically RSA atu ratonga kahore purpuru.

hātepe atu mō te whakamunatanga, me te tiaki

Ki te karo i te raruraru i runga, i roto i te whakatinanatanga mahi o RSA e te nuinga o whakaurua ki etahi ahua o te hanganga, whakakī randomized i mua i whakamunatanga. Ka āta whakarite tēnei e kore e te ihirangi hinga i roto i te whānuitanga o plaintexts pāhekeheke, a e kore e taea te whakatika tenei karere i te kōwhiringa tupurangi.

Haumarutanga RSA cryptosystem me whakamunatanga i runga i rua raruraru pāngarau: te raruraru o Factoring tau nui me te raruraru RSA tūturu. whakaaro whākinga tonu o te ciphertext me waitohu i roto i te RSA te inadmissible i runga i te whakaaro e kore e taea te whakatau i rua o enei raruraru ngātahi.

Heoi, me te kaha ki te whakahoki mai ngā āhuatanga pirimia, he hoariri taea tātai i te taupū ngaro o te kī tūmatanui, me te ka wetemuna kuputuhi mā te whakamahi i te tukanga paerewa. Ahakoa te meka e kore e taea e kitea i tenei ra kahore tikanga ngā mō te Factoring tau tōpu nui i runga i te rorohiko puāwaitanga, e kore nei te reira i kï e kore e tīari ia.

aunoatanga

Te taputapu, ka karanga Yafu, taea te whakamahi ki te arotau i te tukanga. Aunoatanga i roto i te YAFU ko te āhuatanga matatau e fakatahai hātepe factorization i roto i te tikanga hinengaro, me te urutau e whakaiti te wa ki te kitea te āhuatanga o ngā tau tāuru te noho. Te nuinga o implementations multithreaded hātepe tuku Yafu tonu whakamahi o orua ranei maha pūtukatuka maha-matua (tae atu SNFS, SIQS ko ECM). Tuatahi o te katoa, kua whakahaeretia ai e te taputapu rārangi-whakahau. Ko te wa pau rapu mō tauwehe whakamunatanga Yafu te whakamahi i te rorohiko tikanga, kia heke ai ki hēkona 103,1746. tukanga i te taputapu te -rua kaha o 320 paraire atu ranei. Ko te pūmanawa rawa matatini e titau te nui etahi o ngā pūkenga hangarau ki te tāuta me te whirihora tenei. Ko te kupu, kia RSA-whakamunatanga whakaraerae C.

Hacking nganatanga i roto i nga wa tata

I roto i te 2009, Bendzhamin Mudi te whakamahi i RSA-512 kī moka i te mahi i runga i deciphering kriptoteksta mo 73 ra, te whakamahi i te pūmanawa anake pai-mohiotia (GGNFS) me te papamahi toharite (rua-matua Athlon64 i 1900 MHz). Ka rite ki whakaaturia e te wheako, e hiahiatia paku iti iho i te 5 GB o kōpae, me te e pā ana ki te 2.5 gigabytes o mahara mo te tukanga o "Tātarihia."

Ka rite ki o 2010, ngä te tokomaha rawa i RSA 768 paraire roa (232 mati ira, ranei RSA-768). ta tona whākinga e rua nga tau i runga i te maha rau rorohiko i kotahi.

I roto i te mahi, e roa i te mau taviri RSA - te nuinga i 1024 ki te 4096 paraire. Ētahi tohunga whakapono e kia riro i te mau taviri moka-1024 tinihanga i roto i te heke mai tata noa roa taea te ngatata hoariri rawa pai-pūtea ranei. Heoi, e torutoru tautohe e hoki ai kia whākina taviri moka-4096 i roto i te heke mai e tata ana.

opuaraa

Na reira, ka rite ki te tikanga, kua riro te reira e RSA he haumaru ki te he nui nui nga tau. Ki te taea te decomposed te maha turanga o 300 paraire poto ranei, me te waitohu mamati ciphertext i roto i te torutoru haora i runga i te rorohiko whaiaro whakamahi pūmanawa e wātea ana kē i roto i te rohe whānui. He kī te roa 512 paraire, rite whakaaturia, e taea te whakatuwheratia rite wawe rite 1999, ki te whakamahi o te torutoru rau rorohiko. I tčnei wā ko reira taea i roto i te wiki torutoru te whakamahi i te pūmārō wātea nuitia. Ko te kupu, ko reira taea e i roto i te buduschembudet ngāwari whakakitea RSA-whakamuna i runga i nga maihao, a ka riro te pūnaha tūnga tawhito.

Mana i roto i te 2003, i huaina ki te pātai te haumaru o te mau taviri moka-1024. I tēnei wā, e tūtohu ana ki te whai i te roa iti o 2048 paraire.