RSA-encryption. Hauj lwm thiab kev siv ntawm cov RSA algorithm

RSA-encryption yog ib tug ntawm cov thawj cov tswv yim rau pej xeem tseem ceeb cryptosystems uas yog dav siv rau kev ruaj ntseg cov ntaub ntawv kis tau tus mob. Nws lub ntsiab sib txawv los ntawm zoo xws li cov kev pab yog hais tias lub encryption qhov tseem ceeb yog qhib thiab sib txawv ntawm cov decryption tseem ceeb, uas yog khaws zais cia. Lub RSA technology , qhov no asymmetry yog raws li nyob rau hauv lub tswv yim teeb meem ntawm factoring lub playback ntawm ob tug loj prime xov tooj (qhov teeb meem ntawm factoring).

Keeb kwm ntawm creation

RSA Lub npe muaj cov thawj tsiaj ntawv ntawm lub surnames Rivest, Shamir thiab Adleman - tus zaum uas thawj laj mej pej xeem piav cov encryption algorithms nyob rau hauv 1977. Klifford Koks, kev kawm lus Askiv mathematician, uas ua hauj lwm rau British txawj ntse cov kev pab cuam, cov thawj los tsim muaj kev sib npaug system nyob rau hauv 1973, tab sis nws twb tsis Declassified kom txog rau thaum 1997

RSA neeg siv tsim thiab ces luam tawm cov pej xeem tseem ceeb raws li ob tug loj prime xov tooj ua ke nrog lub koom haum pab nqi. Prime numbers yuav tsum tau khaws cia tsis pub leejtwg paub. Txhua tus yuav siv cov pej xeem tseem ceeb rau encrypt ib cov lus, tab sis yog hais tias nws yog loj txaus, ces tsuas ib tug neeg uas paub txog prime xov tooj yuav txiav suab ntawm cov lus. RSA encryption qhia tawm yog hu ua lub ntsiab teeb meem niaj hnub no yog ib qho qhib kev sib tham txog yuav ua li cas ib tug txhim khu kev qha mechanism.

RSA algorithm yog tus qeeb, rau cov uas yog vim li cas nws yog tsis raws li lug siv mus ncaj qha mus encrypt tus neeg siv. Nyob rau hauv Feem ntau, qhov no txoj kev yog siv rau kis tau tus mob nyob rau hauv lub qhia tseem ceeb encrypted rau ib yam encryption qhov tseem ceeb, uas nyob rau hauv lem yuav ua hauj lwm tej encryption thiab decryption ntawm ib tug ntau dua ceev.

Thaum muaj ib tug cryptosystem nyob rau hauv nws cov tam sim no daim ntawv no?

Lub tswv yim ntawm asymmetric cryptographic tseem ceeb ntaus nqi mus rau Diffie thiab Hellman, uas luam tawm lub tswvyim nyob rau hauv 1976, plaug cov kos npe, thiab sim mus thov cov kev tshawb xav ntawm cov zauv. Lawv formulation siv ib tug sib tsis pub leejtwg paub tseem ceeb generated los ntawm ib tug tej yam muaj pes tsawg tus ntawm exponentiation modulo ib tug prime xov tooj. Txawm li cas los, lawv tshuav qhib qhov teeb meem ntawm realization ntawm no muaj nuj nqi, txij thaum lub hauv paus ntsiab lus ntawm factoring twb tsis tau to taub thaum lub sij hawm.

Rivest, Adi Shamir, thiab Adleman ntawm MIT tau ua ob peb npaj siab nyob rau lub xyoo los ua ib tug ib tug-txoj kev muaj nuj nqi uas yog ib qhov nyuaj los txiav suab ntawm. Rivest thiab Shamir (raws li lub computer zaum) tau npaj ntau tej zaum zog, thaum Adleman (xws li kev kawm txog zauv) mus nrhiav rau "tsis muaj zog cov ntsiab lus" ntawm lub algorithm. Lawv siv ib tug ntau ntawm le caag thiab nws thiaj li tsim ib tug zaum kawg system, tam sim no lub npe hu ua RSA nyob rau hauv lub Plaub Hlis 1977.

Hauv kos npe thiab cov pej xeem tseem ceeb

Cov kos npe los yog hluav taws xob kos npe, yog ib feem ntawm lub tshuab hluav taws xob yam ntaub ntawv. Nws yog tsim nyob rau ntawm ib tug tej yam cryptographic cov ntaub ntawv hloov. Nrog rau qhov no attribute tau mus xyuas lub sam xeeb ntawm cov ntaub ntawv, nws pub leej twg paub, raws li zoo raws li los mus txiav txim uas yog tswv rau nws. Nyob rau hauv qhov tseeb, ib tug lwm txoj rau tib yam txuj kos npe.

Qhov no cryptosystem (RSA-encrypted) muaj cov pej xeem tseem ceeb, tsis zoo li yam. Nws paus ntsiab lus ntawm lub lag luam yog hais tias ob tug sib txawv tuav siv - kaw (encrypted) thiab sab nraum zoov. Tus thawj yog siv los ua kom cov npe thiab ces yuav tau decrypt cov ntawv nyeem. Ob - rau lub sij encryption thiab hluav taws xob kos npe.

Siv kos npe rau to taub zoo dua cov RSA encryption, ib qho piv txwv ntawm cov uas yuav txo tau raws li ib tug qub tsis pub leejtwg paub "kaw los ntawm prying ob lub qhov muag," cov ntaub ntawv.

Yuav ua li cas yog lub algorithm?

RSA algorithm muaj plaub kauj ruam: tseem ceeb tiam, tis, encryption thiab decryption. Raws li twb tau hais, RSA-encryption muaj xws li ib tug pej xeem tseem ceeb thiab ib tug lwm yam tseem ceeb. Sab nraum zoov yuav tsum paub tag nrho thiab yog siv los encrypt lus. Nws essence lies nyob rau hauv lub fact tias cov lus encrypted nrog cov pej xeem tseem ceeb muaj peev xwm nkaus xwb yuav decrypted nyob rau hauv ib tug muab lub sij hawm ntawm lub sij hawm siv ib daim card qhov tseem ceeb.

Muaj kev nyab xeeb yog vim li cas, lub zauv yuav tsum tau xaiv nyob random thiab yuav zoo tib yam nyob rau hauv loj, tiam sis txawv nyob rau hauv ntev los ntawm ib tug ob peb tus xov tooj yuav ua rau factoring nyuaj. Tib yam li tib tooj yuav zoo nyob los ntawm ib tug kuaj nyob rau hauv lawv cov simplicity, li ntawd, lub encryption ntawm cov ntaub ntawv yuav tsum tau yuav nyuab.

Cov pej xeem tseem ceeb muaj lub modulus thiab pej xeem exponent. Nyob sab hauv tsev chav tsev thiab muaj ib tug private daim duab, uas yuav tsum tau khaws cia tsis pub leejtwg paub.

RSA encryption ntawm cov ntaub ntawv thiab kev qaug zog

Txawm li cas los, muaj ib tug xov tooj ntawm tej yam yooj yim hacking RSA mechanisms. Thaum encrypting nrog tsawg tsawg thiab me me qhov tseem ceeb ntawm code xov tooj yuav muab tau yooj yim qhib, yog hais tias tus tuaj tos cov hauv paus hniav ciphertext tshaj lub zauv.

Txij li thaum lub RSA-encryption yog ib tug deterministic algorithm (ie, muaj tsis muaj random tivthaiv), ib tug attacker yuav ntse tso rau hauv lub xaiv ntawv nyeem qhib nres tiv thaiv lub cryptosystem los ntawm encrypting yuav plaintexts nyob rau hauv cov pej xeem tseem ceeb thiab cov tshev mis ntawm seb lawv yog muaj sib npaug ciphertext. Semantically ruaj ntseg cryptosystem yog hu ua nyob rau hauv cov kev tshwm sim hais tias ib tug attacker yuav tsis paub qhov txawv nruab nrab ntawm ob encryption los ntawm txhua lwm yam, txawm yog hais tias nws paub cov phau ntawv nyob rau hauv lub txhab rau daim ntawv. Raws li tau piav saum toj no, RSA lwm yam kev pab uas tsis muaj kev padding yog tsis semantically ruaj ntseg.

Ntxiv algorithms rau encryption thiab kev tiv thaiv

Yuav kom tsis txhob muaj cov saum toj no teeb meem, nyob rau hauv lub tswv yim siv ntawm RSA no feem ntau yog tso rau hauv ib co daim ntawv ntawm cob randomized filling ua ntej encryption. Qhov no kom hais tias cov ntsiab lus tsis poob nyob rau hauv lub ntau yam ntawm insecure plaintexts, thiab hais tias cov lus no yuav tsis tau daws tau los ntawm kev xaiv.

Security RSA cryptosystem thiab encryption raws li nyob rau hauv ob zauv teeb meem: qhov teeb meem ntawm factoring loj tus xov tooj thiab lub sij RSA teeb meem. Qhia tag nrho ntawm cov ciphertext thiab kos npe nyob rau hauv lub RSA yog suav tias yog inadmissible rau lub assumption tias ob cov teeb meem muab daws tsis tau collectively.

Txawm li cas los, uas muaj peev xwm rov qab prime yam, ib tug attacker yuav xam ntawm daim card exponent ntawm cov pej xeem tseem ceeb thiab ces decrypt ntawv nyeem uas siv tus qauv txheej txheem. Txawm tias muaj tseeb tias niaj hnub no tsis muaj uas twb muaj lawm txoj kev factoring loj zauv rau ib tug classical computer yuav tsis tau pom, nws tsis tau pov thawj hais tias nws tsis muaj nyob.

automation

Lub cuab tam, hu ua Yafu, yuav siv tau rau optimize tus txheej txheem. Automation nyob rau hauv YAFU yog ib tug txawm feature uas combines factorization algorithms nyob rau hauv kev txawj ntse thiab coj vib this hais tias minimizes lub sij hawm mus nrhiav cov yam tseem ceeb ntawm arbitrary zauv. Feem ntau cov implementations multithreaded algorithm uas Yafu tag nrho kev siv ntawm ntau los yog ntau tej tub ntxhais processors (xws li SNFS, SIQS thiab ECM). Ua ntej ntawm tag nrho cov, nws yog tshuaj los ntawm kev hais kom ua kab cuab tam. Lub sij hawm siv searching rau encryption Yafu tau siv ib tug pa computer, tej zaum nws yuav raug txo kom vib nas this 103,1746. Lub cuab tam dab lub binary peev xwm ntawm 320 khoom los yog ntau tshaj. Qhov no yog ib tug heev software uas yuav tsum tau ib qhov nqi ntawm kev txawj nruab thiab configure. Yog li, RSA-encryption tej zaum yuav lam tau lam ua C.

Hacking cov me nyuam nyob rau hauv tsis ntev los no lub sij hawm

Nyob rau hauv 2009, Bendzhamin Mudi siv RSA-512 ntsis tseem ceeb tau ua hauj lwm rau deciphering kriptoteksta rau 73 hnub, siv tsuas zoo-paub software (GGNFS) thiab qhov nruab nrab desktop (dual-core Athlon64 ntawm 1900 MHz). Raws li qhia los ntawm cov kev, yuav tsum tau me ntsis tsawg tshaj li 5 GB ntawm disk thiab hais txog 2.5 gigabytes ntawm lub cim xeeb rau tus txheej txheem ntawm "sifting."

Raws li ntawm 2010, qhov loj tshaj plaws pes tsawg tus twb factored RSA 768 khoom ntev (232 decimal tug lej tom qab, los yog RSA-768). Nws qhia tawm ntawd kub ntev li ob lub xyoos rau ob peb puas computers ib zaug.

Nyob rau hauv kev xyaum, cov RSA tuav cov ntev - feem ntau los ntawm 1024 mus 4096 khoom. Ib txhia kws txawj ntseeg tau hais tias lub 1024-ntsis hauv lub lag luam tej zaum yuav ua unreliable nyob rau hauv lub nyob ze yav tom ntej los txawm ntev yuav tawg zoo heev-nyiaj attackers. Txawm li cas los, ob peb yuav cam hais tias 4096-ntsis hauv lub lag luam tej zaum kuj yuav qhia tawm nyob rau hauv lub nyob ze yav tom ntej.

prospects

Yog li ntawd, raws li ib tug txoj cai, nws yog assumed tias RSA yog kev ruaj ntseg yog hais tias tus xov tooj yog loj txaus. Yog hais tias yog lub hauv paus xov tooj ntawm 300 khoom los yog luv luv, thiab cov ciphertext cov kos npe yuav tsum decomposed rau hauv ib ob peb teev nyob rau hauv ib tug tus kheej lub computer siv software muaj twb nyob rau hauv lub tsev sau. Ib tug tseem ceeb ntev 512 me me, raws li qhia, yuav tsum qhib raws li thaum ntxov raws li xyoo 1999, nrog rau cov kev siv ntawm ib tug ob peb puas computers. Niaj hnub no nws yog tau nyob rau hauv ib tug ob peb lub lis piam siv ib tug laj mej pej xeem muaj kev kho vajtse. Yog li, nws yog tau hais tias nyob rau hauv buduschembudet yooj yim qhia tawm RSA-encrypted rau cov ntiv tes, thiab lub kaw lus yuav ua hopelessly outdated.

Teb nyob rau hauv 2003, twb hu ua rau hauv lo lus nug kev ruaj ntseg ntawm cov 1024-ntsis hauv lub lag luam. Tam sim no, nws yog pom zoo kom muaj ib tug tsawg kawg nkaus ntev ntawm 2048 khoom.