
goldwasser-mikeli guptapranali

goldwasser-mikeli (jee. emm.) guptalekhan pranali hii 1982 madhye shafee goldwasser aanee sylvio mikeli yanni vikasit keleli eka asamamit qee guptalekhan paddhat aahe. jee. emm. laa pahili sambhavya sarvajanik-qee guptalekhan yojana asalyache vaishishtya aahe jee pramanit guptalekhan gruhitkannusar khatrishirpane surakshit aahe. tathapi, hii eka karyaksham guptalekhan pranali nahee, kaaran seifertext prarambhik sadhya majkurachya kityekashe putt mothe asoo shakatat. guptapranaliche suraksha gunadharm siddha karnyasathi, goldwasser aanee mikali yanni shabdarth surakshechi mothya pramanat vaparali jaanari vyakhya prastavit kelee.
aadhar.
jee. emm. guptapranali hii dvighat avashishtata samasyechya gruheet naan lavnyavaril aadharit shabdarthadrushtya surakshit aahe, eka sammishra "aine" = "pii. kyu" jethe "pii, kyu" mothya avibhajya aahet. hii dharana sangate qee ("x", "n") dile tarr "x" heey eka dvighat avashesh modulo "n" (i) aahe qee nahee heey tharvane katheen aahe.eae.," x "=" y "2 modd" n "kahee" y "sathee), jevha" x "sathee jacoby chinh + 1 asate." n "chey gunank dile tarr varg avashisht samasya sahajpane sodavali jaate, tarr naveen varg avashesh konatyahi pakshadvare, yaa gunankanache dnyan asalyashivay dekhil tayar kele jaau shakatat. jee. emm. guptalekhan pranali yaa vishamatacha laabh vaiyaktik saada majkoor bits ektar yadruchchik varg avashesh kinwa gair-avashesh modulo "aine" mhanoon encrypt karoon ghete, serve varg avashesh chinh + 1 saha. praptakarte gupt killi mhanoon "aine" chey gunank vapartat aanee prapt jhalelya sanketik paath mulyanchya varg avasheshatechi chachani karoon sandesh decrypt karatat. 
kaaran goldwasser-mikali andaje aakarache moolya nirman karate ."aine". sadhya majkurachya pratyek bitala encrypt karnyasathi, jee. emm. encryptionmule mothya pramanat cyfertext vistar hoto. factorization halle talhanyasathi, ashee shifaras kelee jaate qee ."aine". kityekashe biit kinwa tyahoon adhik asoo dya. asha prakare, hii yojana pramukhyane sankalpanecha purava mhanoon kaam karate aanee tevhapasoon elgamalsarkhya adhik karyaksham-khatrishir-surakshit yojana vikasit kelya gelya aahet.
kaaran sambhavya algoridam vaparoon encryption kele jaate, pratyek velee jevha too encrypt keela jaato tevha dilela sadha majkoor khoop bhinn seifertext tayar karoo shakato. yache lakshaniy fayade aahet, kaaran heey shatrula dnyat sanketik aksharanchya shabdakoshasah tulana karoon avarodhit sandesh olakhanyapasun rokhate.
yojanechi vyakhya.
goldwasser-mikelimadhye teen algoridam asatatah eka sambhavya qee generation algoridam jeey sarvajanik aanee khajgi qee tayar karate, eka sambhavya encryption algoridam aanee eka nirdharak decryption algoridam.
n" chey gunank ("p", "q") dilelya dilelya "x" chey moolya vargakar modd "n" aahe qee nahee heey tharvanyavar yojana avalambun asate. khaleel prakriyecha vapar karoon heey sadhya kele jaau shakateh
pramukh pidhi.
jee. emm. encryptionmadhye vaparale jaanare modulus aar. ess. aii. cryptosystempramanech tayar kele jaate. (tapashilansathi aar. ess. aii., qee generation pahaa.)
sarvajanik killi" madhye ("x", "n") asate. gupt killi mhanje gunank ("pii", "kyu").
sandesh encryption.
samaja bobla elisala 'emm' sandesh pathvayacha aaheh
bobb sanketik akshar pathavato ("see" 1,..., see" aine ").
sandesh decryption.
elisala milate ("see" 1,..., see" aine "). tee khaleel prakriyecha vapar karoon 'emm' punarprapt karoo shakateh
ellis haah sandesh "m" = ("m" 1,..., emm" "aine").
suraksha malmatta.
yaa guptapranaliche vighatan karnyapasoon, jakobi chinh '+ 1' asalele yadruchchik moolya modulo 'aine' heey dvighat avashesh aahe qee nahee heey nirdharit karnyachya samasyeparyant eka sadhee ghat aahe. jarr 'aaa' haah algoridam cryptosystem modat asel,
tyanantar dilele moolya "x" heey eka dvighat avashesh modulo "n" aahe qee nahee heey nirdharit karnyasathi, teey sarvajanik killi mhanoon ("x", "n") vaparoon cryptosystem khandit karoo shakate qaa heey pahanyasathi aapan "a" chee chachani karato. jarr 'x' heey avashesh nasalele asel, tarr 'a' yogyaritya karya karel. tathapi, jarr 'x' heey avashesh asel, tarr pratyek 'sanketik paath' heey fakt yadruchchik dvighat avashesh asel, mhanoon
"aaa" ardhyahun adhik vela barobar asoo shakat nahee. shivay, hii samasya yadruchchik swayam-qamee karnyayogya aahe, jee hii sunishchit karate qee dilelya "aine" sathee, pratyek sarvajanik killi itar serve sarvajanik killipramanech surakshit aahe. 
jee. emm. cryptosystemadhye samaroop gunadharm aahet, yaa arthane qee jarr 'see' 0 ',' see '1' heey 'emm' 0 ',' emm '1' bitche encryption asel, tarr 'see' 0 'see' 1 modd 'aine' heey sootra _ 9 chey encryption asel. yaa karanastav, jee. emm. cryptosystem kadhikadhi adhik jatil cryptographic aadimmadhye vaparali jaate.