
doshaala kii maarpiditoe ring learning

guudha lipi saastramlo, public kii exchange algorithm anedi oka guudha lipi shaastra algorithm, idhi rendu paarteelanu oka rahasya keeni srushtinchadaaniki mariyu panchukoovadaaniki anumatistundi, dheenini vaaru tama madhya sandeshaalanu gupteekarinchadaaniki upayoginchavacchu. errors kii exchange (rlwe-kex) thoo ring learning anedi quantum computernu kaligi unna pratyarthi nundi surakshitamgaa undela roopondinchabadina public kii exchange algarithamla yokka kotta taragatilo okati. idhi mukhyamainadi endukante atuvanti computerlanu amalu chesthe nedu upayogamlo unna konni public kii algorithamlu quantum computer dwara sulabhamgaa vichchinnam cheyabadataayi. jaalakaalato kuudina konni ganita samasyalanu parishkarinchadamlo ibbandi meeda aadhaarapadina post-quantum cryptographic algorithamla samitilo rlwe-kex okati. paatha jaalaka aadhaarita guudha lipi shaastra algorithamla maadirigaa kakunda, rlwe-kex jalakalalo telisina kathinamaina samasyaku niroopinchadagina vidhamgaa tagginchabadutundi.
nepathyam.
1980la nundi internet dwara guudha lipi shaastra kii marpidi mariyu digital santakaala bhadrata pradhanamgaa takkuva sankhyalo public kii algorithamlapai aadharapadi undhi. eee algorithamla bhadrata shaastreeya computinglo adevidhamgaa takkuva sankhyalo gananaparamgaa kathinamaina samasyalapai aadharapadi untundi. jagrattagaa enchukunna rendu pradhana sankhyala gunakaranni kaarakaparachadamlo ibbandi, jagrattagaa enchukunna parimita kshetramlo vivikta samvargamaanaalanu lekkinchadamlo ibbandi mariyu jagrattagaa enchukunna deerghavruttaakaara vakra samuuhamloo vivikta samvargamaanaalanu lekkinchadamlo ibbandi eee samasyalu. eee samasyalanu shaastreeya computerlo parishkarinchadam chaalaa kashtam (1940la nundi neti varaku prapanchaaniki telisina computer rakam) conny saapekshamgaa chinna quantum computer dwara 5 nundi 10 vaela bits memarini matrame upayoginchi sulabhamgaa parishkarinchavacchu. 2030 natiki pedda ettuna quantum computerlu andubaatulo untaayani computer parisramalo aasaavaadam undhi. taginanta parimaanamlo quantum computernu nirmiste, eee moodu saastriiyamgaa kathinamaina samasyala aadhaaramgaa anni public kii algorithamlu asurakshitamgaa untaayi. eee public kii guudha lipi shaastram nedu internet websitelanu bhadraparachadaaniki, computer lagin samacharanni rakshinchadaaniki mariyu haanikaramaina softwarenu angeekarinchakundaa mana computerlanu nirodhinchadaaniki upayoginchabadutundi.
quantum computer daadi cheyaleni guudha lipi saastraanni quantum saphe ledhaa post-quantum guudha lipi shaastram anie pilustaaru. quantum nirodhaka guudha lipi shaastra kramasuutraala yokka oka taragati 2005loe oded regev pravesapettina "lopalatho neerchukoevadam" anae bhaavanapai aadharapadi untundi. lopalatho kuudina abhyasam yokka pratyeka roopam parimita kshetrampai bahupadaala valayamlo panichestundi. eee pratyeka roopaanni ring learning vith errors ledhaa rlve antaaru.
rlve namuunaanu upayoginchi panichese vividha rakaala cryptographic algorithamlu unnaayi. eee vyaasamlo samarpinchina public kii, kii exchange algorithamtho paatu public-kii encryption algorithamlu, homomorphic encryption algorithamlu mariyu rlve digital signature algorithamlu unnaayi.
kii exchange algorithm anedi oka rakamaina public kii algorithm, idhi communications linkpai iddaru communicatorla madhya shared secret keeni erpaatu chestundi. kii exchange yokka uttama udaaharana defy-hellman kii exchange. eee maarpidilo line yokka oka chivara nundi oka prasaram mariyu link yokka maroka chivara nundi oka prasaram untundi. defy-hellman mariyu elliptic karv defy-hellman anevi rendu atyanta prachuryam pondina kii exchange algorithamlu.
viswasaneeyata laeni communication chaanellapai rahasya keelanu bhadraparachadaaniki upayoginche vistrutamgaa upayoginche defy-hellman mariyu elliptic karv defy-hellman kii exchangeelaku "quantum saphe" pratyamnaayamgaa rlve kii exchange roopondinchabadindi. defy-hellman mariyu elliptic karv defy-hellman maadirigaane, ring-lway kii exchange "forward secressy" anae guudha lipi shaastra lakshanaanni andistundi; dheeni lakshyam saamuuhika nigha kaaryakramaala prabhavanni tagginchadam mariyu bhaarii decryption praarambhinchae deerghakaalika rahasya keelu rajipadavani nirdhaarinchadam.
parichayam.
oka pradhana puurnaamkam q thoo praarambhinchi, ring-lway kii marpidi bahupadula valayamlo panichestundi, idhi bahupadi suutram _ 1, puurnaamkaalu maad q (i) kshetramloni gunakaalato panichestundi.ii. ring suutram _ 2). gunakaaram mariyu bahupadula jodimpu anedi gunakaaram tagginchina mode suutram _ 1 phalitaalato saadhaarana paddhatiloo panichestundi.
kii exchange kosam lway mariyu ring lvenu upayoginchaalane aalochananu modata 2011loe sinkinnati vishwavidhyaalayamlo gintoy ding pratipaadinchaaru mariyu daakhalu chesaaru. eee aalochana maatrika gunakaala anubandhata nundi vastundi, mariyu lopaalu bhadratanu andinchadaaniki upayoginchabadataayi. 2012loe taatkaalika patent darakhaastu daakhalu chesina taruvaata 2012loe eee patram kanipinchindi. ell. doubleu. eee samasyanu parishkarinche kaatinyam aadhaaramgaa protocol yokka bhadrata niroopinchabadindi.
2014loe, peakert ding yokka adhe praathamika aalochananu anusarinchi kii-ravana pathakaanni samarpinchaaru, ikkada ding nirmaanamloo rounding kosam adanapu 1-bitt signalnu pampe kotta aalochana kooda upayoginchabadutundi.
google yokka post-quantum prayogam kosam empika chesina "kotta aasha" amalu, lopam pampinheelo vaividhyamtho peakert yokka pathakaanni upayogistundi.
128 bits kante kontha ekkuva bhadrata kosam, singh peakert pathakam kosam 6956-bitt public keelanu kaligi unna paaraamitula samitini andistundi. sambandhita private kii sumaru 14,000 bits untundi. defy-hellman kii exchange yokka classic enqv roopaantaram yokka rlve samskarananu taruvaata jhang mariyu itarulu prachurinchaaru. 2014 loe. rendu keelaka marpidi yokka bhadrata anedi aadarsha jaalakamlo sumaru chinna vaahakaalanu kanugone samasyatho neerugaa sambandham kaligi untundi. eee vyaasam "lopaala samasyatho kuudina abhyasam aadhaaramgaa saralamaina niroopinchadagina surakshitamaina kii marpidi pathakam" loe ding yokka rlve panini nisitamgaa anusaristundi. eee pradarsana kosam oka vilakshanhamaina bahupadi ilaa vyakteekarinchabadutundi
eee bahupadi yokka gunakaala suutram _ 5 puurnaamkaalu mode "q". bahupadi suutram _ 1 cyclotomic bahupadi avutundi. n" anedi 2 yokka shakti ayithe suutram _ 7
rlwe-kex "ananta pramaanam" anie piluvabade kolataku sambandhinchi "chinnadi" gaa pariganinchabade bahupadaalanu upayogistundi."bahupadaaniki ananta pramaanam anedi bahupadi yokka atipedda gunakam yokka viluva, gunakaalanu suutram _ 8 (i) kante z loe puurnaamkaalugaa pariganinchinappudu.ii.samiti nundi {− ("q" −1)/2.., 0,... ("q" −1)/2}). algorithm yokka bhadrata ananta pramaanaaniki sambandhinchi chinna yaadruchchika bahupadaalanu utpatti chese saamardhyampai aadharapadi untundi. idhi kevalam bahupadi (sn-1,) kosam yaadrucchikamgaa gunakaalanu utpatti cheyadam dwara jarugutundi..., s0) ivi haamii ivvabadataayi ledhaa chinnaviga unde avakaasam undhi. deenni cheyadaaniki rendu saadhaarana margalu unnaih
eee vyaasam yokka migilina bhaagamlo, yaadruchchika chinna bahupadaalu kevalam d gaa perkonna pampinhee prakaram namuunaa cheyabadataayi. q anedi 1 mode 4 mariyu 1 mode 2n kii samanamga unde besi prime avutundi. q mariyu n kosam itara kesulu "ring-lway guudha lipi shaastram kosam oka sadhanam" loe mariyu singh yokka "jaalaka guudha lipi saastraanni upayoginchi internet kosam marinta aacharanaatmaka kii maarpidilo" puurtigaa charchinchabaddaayi."mariyu singh raasina maroka kaagitam. network yokka viniyogadaarulandaruu panchukune sthiramaina public bahupadi, a (x). idhi cryptographicga surakshitamaina muulam nundi nirnayaatmakamgaa utpatti cheyabadutundi.
perkonna vidhamgaa "a" ("x") ichinatlayithe, public kii exchangelo "private kii" gaa chinna bahupadaalu "s" ("x") mariyu "e" ("x") lanu yaadrucchikamgaa enchukovachhu. sambandhita public kii bahupadi "p" ("x") = "a" ("x") "s" ("x") + 2 "e" ("x") avutundi.
keelaka marpidi.
rendu parikaraala madhya keelaka marpidi jarugutundi. (i) gaa niyaminchabadina kii exchange kosam oka prarambhakudu mariyu (r) gaa niyaminchabadina prativaadi untaaru. i mariyu r rendintikee "q", "n", "a" ("x") telusu, mariyu parameter formula _ 10 thoo pampinhee formula _ 9 prakaram chinna bahupadaalanu utpatti cheyagala saamarthyam kaligi untundi. pampinhee formula _ 9 saadhaaranamgaa ring formula _ 12 paie vivikta gassian pampinhee. eee krindi vivaranalo link yokka rendu chivarlalo oke keeni enduku kii marpidi chestundi anedaaniki etuvanti vivarana undadu. badulugaa, idhi teesukovalasina charyalanu kluptamgaa perkontundi. kii marpidi prarambhakudu mariyu pratispandakudu oke keeni enduku kaligi untaarane daanipai samagra avagahana kosam, paatakudu ding mariyu itarula dwara suuchimchina panini chuudaali.
praarambhakarta (i) eee krindi vaatini cheyadamtho kii marpidi praarambhamavutundih
praarambham
pratispandanah
mugimpu
paie kii maarpidilo, suutram _ 26 anedi krinda nirvachinchina signal function
suutram _ 45 yokka upasamiti suutram _ 44 nii nirvachinchandi. ikkada, suutram _ 46 mariyu suutram _ 47 varusaga naela mariyu roundingnu sameepa puurnaamkaaniki suuchistaayi.
function formula _ 26 anedi e yokka compliment yokka lakshana function.
suutram _ 49: suutram _ 50
suutram _ 51 anedi eee krindi vidhamgaa nirvachinchina dosha nibandhanalanu tolaginchadaaniki mode 2 operation suutram _ 52
suutram _ 42 mariyu suutram _ 29 yokka viluvalu daadaapu samanamga matrame unnayani gamaninchandi. eee sumaru samaana viluvalanu upayoginchi shared keeni velikiteese kramamlo, signal function anie kooda piluvabade sayodhya function upayoginchabadutundi. eee function suutram _ 56 looni bahupadi suutram _ 55 yokka prati gunakam unna praantaanni suuchistumdi mariyu suutram _ 29 mariyu suutram _ 42 looni dosha padaalu ververu mode q operationlaku daariteeyavani nirdhaarinchukovadaaniki sahaayapadutundi.
sayodhya mariyu kii string generation paddhatulu prashnaarthakamaina nirdishta rlwe-kex pathakampai aadharapadi untaayi. konni paddhatulu modular ankaganitampai aadharapadi untaayi, marikonni adhika-parimaana jyaamitipai aadharapadi undavacchu.
kii marpidi sarigga panichesthe, praarambhakarta yokka string mariyu prativaadi yokka string okela untaayi.
enchukunna paaraamitula pratyaekatalanu batti, eee kii marpidi adhe keeni utpatti cheyadamlo viphalamayye chaalaa takkuva sambhaavyata undhi. kii exchange loe vaiphalyam sambhaavyatanu chaalaa takkuvagaa cheyadaaniki kii exchange kosam paaraamitulanu enchukovachhu; gurtinchaleni garbles ledhaa parikara vaiphalyala sambhaavyata kante chaalaa takkuva.
paramiti empikalu.
paina samarpinchina rlwe-kx marpidi "n" −1 ledhaa anthakante takkuva sthaayi bahupada suutram _ 1 yokka bahupadula valayamlo panichesindi. pradarsana n anedi 2 yokka shakti anie mariyu q anedi 1 (maad 2n) kii samanamga unde prime anie bhaavinchindi. peakert paperlo icchina maargadarsakatvaanni anusarinchi, singh rlv-kex kosam rendu setla paaraamitulanu suuchimchaaru.
128 bitla bhadrata kosam, "n" = 512, "q" = 25601, mariyu suutram _ 60
256 bits bhadrata kosam, "n" = 1024, "q" = 40961, mariyu suutram _ 61
kii exchange yaadruchchika sampling mariyu sthira sarihaddulanu upayogistundi kabatti kii exchange prarambhakudu mariyu pratispandakudiki adhe keeni utpatti cheyadamlo viphalamayye chinna sambhaavyata undhi. gassian paramiti "σ" suutram _ 62 mariyu ekareeti sampling bound ("b") = 5 (singh chudandi) anie manam anukunte, appudu 128-bitt surakshita paaraamitulaku kii aggrement vaiphalyam sambhaavyata 2−71 kante takkuvagaa mariyu 256-bitt surakshita paaraamitulaku 2−91 kante takkuvagaa untundi.
vaari november 2015 paperlo, alkim, ducas, poppelman mariyu shwabe eee krindi paaraamitulanu n = 1024, q = 12289, mariyu suutram _ 1 = x1024 + 1 nuu sifaarsu chesaaru. idhi singh yokka n = 1024 paaraamitulapai public kii parimaanamlo 70 saatam taggudalanu suuchistumdi, mariyu newhope paerutoe nist yokka post-quantum cryptography praamaaneekarana prajectuku samarpinchabadindi.
vaari november 2015 kaagitamlo, alkim, ducas, poppelman mariyu shwabe kii exchange (paina a (x)) kosam bays polynamial empikanu prati exchange kosam surakshita yaadruchchika sankhya generator nundi yaadrucchikamgaa utpatti cheyaalani ledhaa "naa sleeve paiki aemee ledhu" ledhaa sankhyala saanketikatanu upayoginchi dhruveekarinchadagina paddhatiloo srushtinchaalani sifaarsu chestaaru. eee vidhamgaa utpatti cheyabadina paaraamitulaku udaaharana internet kii marpidi (rfc 2409) kosam pradhana sankhyalu, ivi ganita sthiraamkam paie yokka ankelanu pradhana sankhya yokka digital praatinidhyamlo ponduparachutaayi. vaari modati paddhati aneka keelaka maarpidullo daadi kharchula runa vimochananu nirodhistundi, idhi nist elliptic vakrarekhalaku vyatiraekamgaa daan bernstein vivarinchina vidhamgaa daachina daadi yokka avakaasaanni terichi unche pramaadam undhi. sankhyala vidhanam runa vimochanaku terichi untundi, ayithe paie mariyu ii vanti saadhaarana ganita sthiraamkaalanu matrame upayoginchinatlayithe saadhaaranamgaa bernstein daadini nivaaristundi.
kii marpidi bhadrata.
eee kii exchange yokka bhadrata anedi ring learning yokka antarleena kaatinyampai aadharapadi untundi, idhi lopaala samasyatho kuudinadi, idhi aadarsha jaalakamlo atichinna vector samasya (ess. vii. pii) kii chettha parishkaram vale katinamainadigaa niroopinchabadindi. icchina jaalaka paaraamitula samiti yokka aacharanaatmaka bhadratanu anchanaa vaeyadaaniki uttama paddhati bkz 2. jaalaka taggimpu algorithm. bkz 2 algorithm prakaram paina jabita cheyabadina keelaka marpidi paaraamitulu varusaga 128 ledhaa 256 bitla kante ekkuva bhadratanu andistaayi.
amalu.
2014loe douglus stebila open sl 1.0.1f kosam oka pyaachnu roopondinchindi. athani pani mariyu itarula aadhaaramgaa "post-quantum kii exchange pharr dhi tls protocol frum dhi ring learning vith errors problem" loe prachurinchabadindi."singh panini amalu chese software githablo chudavachuhu// github.com/vscrypto/ringlwe.
itara vidhanalu.
paina vivarinchina vidhanam yokka oka roopaantaram vaari kaagitamlo jhang, jhang, ding, snook mariyu dogdelen yokka paniloo dhruveekarinchabadina samskarana, "aadarsha jaalikala nundi post quantum praamaaneekarinchabadina kii marpidi."sayodhya functiontho jaalakaalanu upayoginchi defy-hellman lanty kii exchange anie pilavabadedaanni srushtinche bhavananu french parisoedhakulu aguilar, gaborit, lacarme, shrek mariyu jemore vaari taaklo pqcrypto 2010 loe pradarsinchinatlu telustondi," "shabda defy-hellman protocols."
november 2015loe, alkim, ducas, poppelman mariyu shwabe peakert yokka munupati pani meeda nirminchaaru mariyu paaraamitulanu sifaarsu cheyadaaniki jaalaka daadula yokka marinta sampradaayabaddhamaina kharchu anie vaaru vishwasinche vaatini upayoginchaaru. alkim, ducas, poppelman mariyu shwabe rachanala aadhaaramgaa roopondinchina software, githablo, HTTPS:// Githubloe kanipistundi.com/tpoeppelmann/newhop

