RSA-encryption. Description a me ka manaʻo o ka RSA algorithm

RSA-encryption o kekahi o ka mua he mea hiki lehulehu-ki cryptosystems i ua hoʻomano hoʻohana no ka maluhiaʻikepili EYI. Kona papa kuhikuhiE koena unuhi mai like lawelawe nei i ka encryption ki mea hamama, a okoa mai ka decryption kī, a ua mālama malu. Ke RSA enehana , keia asymmetry ua ma muli o ka mea hiki pilikia o factoring ka hōʻike hou o nā nui Kuhina Nui helu (i ka pilikia o ka factoring).

Mōʻaukala o ka hanaia'na

RSA ka inoa ninoieo o ka loiloi mua palapala o na kapaia Rivest,ʻo Samira, a Adleman - nā kānakaʻepekema i mua akea hōʻike i kēia mau encryption algorithms i ka makahiki 1977. Klifford Koks, he English mathematician, ka mea i hana no ka Pelekāne manao lawelawe, o ka mea mua, e kūkulu i ka hua'ōlelo'ōnaehana i ka 1973, akā, ka mea i ole declassified a hiki i 1997

RSA mea hoʻohana hana, a laila, publishes ka lehulehu ki ma muli o nā nui Kuhina Nui helu pu me ke kākoʻo cia. Kuhina Nui helu e e mālama malu. O ka mea hiki ke hoʻohana 'ia i ka lehulehu ki e encrypt i ka olelo, akā, inā e mea nui kupono, laila wale nō kekahi me ka ike o ke Kuhina Nui loa ke decode ka memo. RSA encryption 'aelike' ike e like me ka papa kuhikuhi pilikia keia mea he hamama kūkākūkā e pili ana pehea ka ike loeaʻano papa hana.

RSA algorithm, kŘpa a lohi, no i ke kumu ka mea, ua ole i hoʻomano hoʻohana 'ia' ana encrypt i ka mea hoʻohana. Ma ka hapanui o hoopii, keia iaoia ua hoʻohana 'ia no ka EYI i loko o ka mea i kaʻana like ki hoʻopā'āluaʻia no ka symmetric encryption kī, a ma ka huli e hana ana bulk encryption a me ka decryption ma ka mämä holo nui kiʻekiʻe.

I ka ua he cryptosystem i loko o kona keia ano?

Ka manaʻo o asymmetric cryptographic kī wahi i Diffie a me Hellman, ka mea i paʻiʻia ka manaʻo i loko o ka makahiki 1976, i hoʻolaunaʻia ma kikohoʻe inoa, a me ka imi e pili ana i ka kumumanaʻo o ka helu. Lākou hoʻomanaʻo hoʻohana i kaʻana malu kī ua loaʻa mai i kekahi helu o ka exponentiation modulo he Kuhina Nui helu. Eia naʻe, haʻalele wehe i ke kahe o ke kō o kēia kuleana pili i ka mea, no ka mea, ua i maopopo i nā loina o ka factoring i ka manawa.

Rivest, Adi Samira, a me Adleman ma mit ua i kekahi mau hoao ana ma luna o nā makahiki, e hana i kekahi i kekahi-ala kuleana pili i ka pilikia e decode. Rivest a Samira (me kamepiulaʻepekema) ua manaoia he nui Loaʻaʻia oihana, oiai Adleman (e like makemakika) e huli no ka "nawaliwali heluʻai" o ka algorithm. Ka mea, hoʻohana i kekahi lihi iki o ke hoʻokokoke mai, a ho'ōla kūkulu i ka hope loa'ōnaehana, eʻikeʻia me RSA ma April 1977.

Electronic inoa, a me ka lehulehu kī

Digital inoa a lolouila inoa, o ka integral hapa o ka lolouila palapalaʻAno. Ua Ua hanaʻia ma ka kekahi cryptographic ikepili loli. Me keia kaila hiki i ka nānā i ka pono o ka palapala, kona hūnā 'ia', e like me ka hoʻoholo 'ana ka mea nona ia. I ka mea, i kekahi koho i ka maʻamau maʻamau inoa.

Kēia cryptosystem (RSA-hoʻopā'āluaʻia) e kaumaha ana i ka lehulehu kī, e like symmetric. Kona rula o ka hana o ia ka mea okoa ki elua i hoʻohana - paa (hoʻopā'āluaʻia) a me ka foxmike. Ua ka mua hoʻohana hiki paha ke i ka mīkini inoa, a laila, e hiki ke decrypt i ke kikokikona. Lua - no ka mea maoli encryption a me ka uila inoa.

E ho ohana i inoa e pono maopopo i ka RSA encryption, he laʻana o ka i hiki hoemi e like me ka maʻamau huna "Hoopaa iho la, mai prying mau maka," i ka palapala.

He aha ka ke algorithm?

RSA algorithm ninoieo o eha mauʻanuʻu: kī hanauna, o ka makana, a me ka encryption decryption. E like me ua oleloia, RSA-encryption ka loaʻa o ka lehulehu kī a me ka ponoi kī. Foxmike hiki keʻikeʻia ai i nā mea a pau, a ua hoʻohana 'ia e encrypt memo. Kona o Mānoa, ke moe ia ma ka mea i memo hoʻopā'āluaʻia me ka lehulehu ki hiki wale ke decrypted i loko o ka hāʻawi au o ka manawa ka hoʻohana 'ana i ka malu kī.

No ka maluhia kumu, na integers e e koho i huikau a e'ālike ma ka nui, akā, oko ka lōʻihi ma kekahi mau huahelu, e hana factoring oi pilikia. Ia e like me ka helu hiki ke ka pono i loaʻa ma ka hoao i loko o kā lākou naaupo wale, no laila, ke encryption o ka 'ike pono pono e huikau.

Ka lehulehu kī ninoieo o ka modulus a me ka lehulehu exponent. I loko o ka mokuna a he o ke kula huahelu, a e e mālama malu.

RSA encryption o AEIU a me ka nawaliwali

Eia naʻe, loaʻa nō i ka helu o ka poe noonoo ole hacking RSA maomeka. encrypting me ka haʻahaʻa a me ka uuku aiee o kuhi helu hiki ke hoopuni wehe i ka wa, ina o kaʻohiʻana i kumu ciphertext ma luna o nā integers.

Mai ka RSA-encryption mea he deterministic algorithm ( 'o ia hoʻi,ʻaʻohe kaulele ke keʻena), he attacker hiki ana e holo aku au i ka wae plaintext hoouka aku i ka cryptosystem ma ka encrypting paha plaintexts ma lalo o ka lehulehu ki, a loaʻa, e kaha i ke kumuhana o ka ina ole paha ka mea, e like ciphertext. Semantically ua kapaia kona i hoopaa ia cryptosystem i loko o ka hanana i ka attacker hiki ole maopopo ma waena o nā mau encryption mai kekahi i kekahi, a hiki ina oia i ike i ka pili ölelo Pelekänia i loko o ka hoomaka palapala. I ho'ākāka 'ia ma luna, RSA' ē aʻe lawelawe me ka nenelu loa mea ole semantically ka puali.

Additional algorithms no ka encryption a me ka palekana

E pale i ka luna pilikia, ma ka mea hiki manaʻo o RSA e ana hookomo i loko o kekahi 'ano o ka mea kūkulu, randomized iie mua encryption. Kēia e hōʻoiaʻiʻo ana i ka maʻiʻo, aole ia i haule i loko o ka laulā o insecure plaintexts, a me ka mea i kēia memo hiki ke ole Wehewehe i nā hāʻina ma kaulele koho.

Maluhia RSA cryptosystem a me ka encryption ma muli o nā makemakika pilikia: ka pilikia o factoring nui loa, a me ka maoli RSA pilikia. Full 'ana o ka ciphertext a me ka inoa i loko o ka RSA ua noʻonoʻo inadmissible ma luna o ka mea mahuʻi i nā o kēia mau pilikia hiki ole ke hoʻonā' ia collectively.

Naʻe, a me ka hiki, e loaa Kuhina Nui aʻe, he attacker ke ho omaulia i ka malu exponent o ka lehulehu ki, a laila decrypt kikokikona ka hoʻohana 'ana i ka maʻamau ina hana. I loko nō o ka mea i keia la i na papa hana no ka factoring nui integers ma ka panina kamepiula hiki ole ke ike, ka mea, i ole, ua maopopo ia ia, aole ia e nei.

hana nona iho

Ke koʻi lipi, i kapaʻia Yafu, hiki ke hoʻohana 'e hoʻoikaika i ka kaʻina. Hana nona iho ma ka YAFU mea he holomua hiʻona e hiehie factorization algorithms ma ka 'imi naʻauao a me ka adaptive hoʻomanaʻo i minimizes ka manawa e loaʻa i nā kumumea o ākeʻakeʻa kumu hoʻokomo o helu. Ka hapanui o implementations multithreaded algorithm hele 'ana o Yafu piha ana o ka multi- a he nui nunui-kāna mau' ōlelo nā unu lawelawe (a me SNFS, SIQS a me ECM). Mua o nā mea a pau, ka mea, ua hoi malalo o ko kauoha-laina kila. , Ka mea hiki ke hoemi i ka kekona 103.1746 ka manawa hoolilo ia hulina, no ka encryption Yafu ololi ka hoʻohana 'ana i kaʻike mau kamepiula. Ke koʻi lipi ma keʻano o ka hanaʻana i ka aeaie nona iho a 320'āpana a oi. Kēia mea he nui loa luna 'lako polokalamu e pono i kekahi dala o oaoieei-nā mākau e hoʻouka, a kele pūnaewele. Penei, RSA-encryption paha e kūlana C.

Hacking ho'āʻo i loko o nā manawa

I ka 2009, Bendzhamin Mudi ka hoʻohana 'ana RSA-512 iki ki i hana ma deciphering kriptoteksta no 73 lā, ka hoʻohana' ana wale loa-ike lako polokalamu (GGNFS) a me ka awelikaʻoneki (pālua-kāna mau 'ōlelo Athlon64 ma 1900 MHz). E like me ka hoike ma ka ho'āʻoʻana, koi iki emi o 5 GB o ka pā hōkū, a ma kahi o 2,5 gigabytes o iaiyoe no ke kaʻina hana o ka "sifting."

Like mai o ka makahiki 2010, i ka nui helu i ho ololi RSA 768'āpana lōʻihi (232 kekimala huahelu, a RSA-768). Ke kaikoeke mau ae la ia mau makahiki ma kekahi mau haneri kamepiula 'ē aʻe ma kahi hoʻokahi.

Ma ka hana pono, i ka RSA ki i lōʻihi - nō kāu, mai 1024 a hiki i 4096'āpana. Kekahi poe akamai i manaoio i ka 1024-iki ki i lilo unreliable i loko o ka wā e hiki mai kokoke paha hoi hou hiki ke Hi ohia loa maikaʻi-hoʻolako 'attackers. Eia naʻe, mau makemake hoʻopaʻapaʻa ana i 4096-iki ki i e hōʻike pū 'ia ma ka wā e hiki mai ma kahi o.

ka manaʻolana 'ia

Nolaila, e like me ka rula, ka mea, ua hilahila ia RSA mea ai ina ka helu i nui kupono. Inā ke kumu helu o 300'āpana a pōkole, a me ka ciphertext kikohoʻe inoa hiki ke decomposed i loko o kekahi mau hola ma kekahi 'aoʻao pilikino kamepiula hoʻohana lako polokalamu i loaʻa ia i loko o ka lehulehu kikowaena. A ki lōʻihi 512'āpana, e like me ka hōʻike, hiki ke wehe i kakahiaka nui me ka makahiki 1999, a me ka hoʻohana 'ana o kekahi mau haneri kamepiula' ē aʻe. Kēia manawa ka ia mea hiki i loko o kekahi mau pule hoʻohana i ke akea i loaʻa Lako. Penei, he mea hiki i ka buduschembudet hoopuni hōʻike RSA-hoʻopā'āluaʻia ma luna o ka manamana, a me ka nenoaia, e lilo hopelessly OOAOAaXUEE.

Kauoha aku i ka 2003, i kapaʻia i loko o ninau i ka maluhia o ka 1024-iki ki. Currently, ka mea, ua waiho ia i ka palena iki lōʻihi o 2048'āpana.