{"id":5918,"date":"2025-10-31T00:00:00","date_gmt":"2025-10-30T22:00:00","guid":{"rendered":"https:\/\/elmeistrai.lt\/?p=5918"},"modified":"2025-10-07T14:05:28","modified_gmt":"2025-10-07T11:05:28","slug":"elektroniniu-parasu-kriptografija","status":"publish","type":"post","link":"https:\/\/elmeistrai.lt\/pl\/elektroniniu-parasu-kriptografija\/","title":{"rendered":"Elektronini\u0173 para\u0161\u0173 kriptografija"},"content":{"rendered":"

Kod\u0117l elektroninis para\u0161as n\u0117ra tiesiog j\u016bs\u0173 pavard\u0117 kompiuteryje<\/h2>\n\n\n\n

Kai pirm\u0105 kart\u0105 susid\u016briau su elektroniniu para\u0161u, atvirai sakant, nesupratau, kod\u0117l negaliu tiesiog nusifotografuoti savo rankra\u0161tinio para\u0161o ir lipinti jo visur, kur reikia. Pasirodo, elektroninis para\u0161as \u2013 tai daug sud\u0117tingesnis dalykas, kurio pagrindas yra matematika ir kriptografija. Jei kada nors band\u0117te suprasti, kaip veikia elektronin\u0117 bankininkyst\u0117 ar kaip pasira\u0161ote dokumentus per valstybines sistemas, \u0161is straipsnis jums.<\/p>\n\n\n\n

Elektroninis para\u0161as i\u0161 esm\u0117s yra matematinis b\u016bdas \u012frodyti, kad dokument\u0105 pasira\u0161\u0117te b\u016btent j\u016bs, ir kad niekas jo nepakeit\u0117 po to, kai j\u012f pasira\u0161\u0117te. Tai tarsi antspaudas ir lak\u0161tas viename, tik daug saugesnis. Skirtingai nuo rankra\u0161tinio para\u0161o, kur\u012f galima nukopijuoti ar suklastoti, elektronin\u012f para\u0161\u0105 prakti\u0161kai ne\u012fmanoma suklastoti d\u0117l jo matematin\u0117s prigimties.<\/p>\n\n\n\n

Asimetrin\u0117 kriptografija \u2013 dviej\u0173 rakt\u0173 magija<\/h2>\n\n\n\n

Visa elektronini\u0173 para\u0161\u0173 sistema remiasi tuo, kas vadinama asimetrine arba vie\u0161ojo rakto kriptografija. Tai skamba sud\u0117tingai, bet principas gana paprastas. \u012esivaizduokite, kad turite dvi dalis \u2013 vien\u0105 rakt\u0105, kur\u012f rodote visiems (vie\u0161asis raktas), ir kit\u0105, kur\u012f saugote kaip akies vyzd\u012f (privatus raktas).<\/p>\n\n\n\n

\u0160tai kaip tai veikia praktikoje: kai pasira\u0161ote dokument\u0105 elektroniniu para\u0161u, j\u016bs\u0173 privatus raktas sukuria unikal\u0173 skaitmenin\u012f \u201eatspaud\u0105” tam konkre\u010diam dokumentui. Bet kas kitas, tur\u0117damas j\u016bs\u0173 vie\u0161\u0105j\u012f rakt\u0105, gali patikrinti, ar tas para\u0161as tikrai j\u016bs\u0173 ir ar dokumentas nebuvo pakeistas. Bet niekas negali sukurti j\u016bs\u0173 para\u0161o be privataus rakto.<\/p>\n\n\n\n

Matemati\u0161kai tai pagr\u012fsta labai sud\u0117tingomis problemomis, kurias lengva i\u0161spr\u0119sti viena kryptimi, bet beveik ne\u012fmanoma \u2013 kita. Pavyzd\u017eiui, lengva padauginti du didelius pirminius skai\u010dius, bet labai sunku suskaidyti j\u0173 sandaug\u0105 atgal \u012f tuos pirminius skai\u010dius. \u0160is principas vadinamas \u201evienakrypte funkcija”.<\/p>\n\n\n\n

Kaip tiksliai sukuriamas elektroninis para\u0161as<\/h2>\n\n\n\n

Dabar pa\u017evelkime \u012f proces\u0105 \u017eingsnis po \u017eingsnio. Kai spaud\u017eiate mygtuk\u0105 \u201ePasira\u0161yti” kokioje nors sistemoje, \u012fvyksta keletas dalyk\u0173, kuri\u0173 paprastai nematote.<\/p>\n\n\n\n

Pirma, j\u016bs\u0173 kompiuteris ar i\u0161manusis \u012frenginys paima dokument\u0105 ir praleid\u017eia j\u012f per vadinam\u0105j\u0105 mai\u0161os (hash) funkcij\u0105. Tai matematin\u0117 funkcija, kuri bet kokio dyd\u017eio dokument\u0105 paver\u010dia fiksuoto ilgio simboli\u0173 seka \u2013 tarsi dokumento \u201epir\u0161to atspaudu”. Net ma\u017eiausias pasikeitimas dokumente sukuria visi\u0161kai kitok\u012f mai\u0161os kod\u0105.<\/p>\n\n\n\n

Antras \u017eingsnis \u2013 j\u016bs\u0173 privatus raktas u\u017e\u0161ifruoja \u0161\u012f mai\u0161os kod\u0105. Tai ir yra pats elektroninis para\u0161as. Svarbu suprasti, kad \u0161ifruojamas ne visas dokumentas, o tik jo mai\u0161os kodas, tod\u0117l procesas vyksta greitai net su dideliais failais.<\/p>\n\n\n\n

Kai kas nors nori patikrinti j\u016bs\u0173 para\u0161\u0105, sistema paima j\u016bs\u0173 vie\u0161\u0105j\u012f rakt\u0105 ir i\u0161\u0161ifruoja elektronin\u012f para\u0161\u0105, gaudama original\u0173 mai\u0161os kod\u0105. Tada ji pati apskai\u010diuoja gautojo dokumento mai\u0161os kod\u0105 ir palygina abu. Jei jie sutampa \u2013 puiku, dokumentas autenti\u0161kas ir nepakeistas. Jei ne \u2013 ka\u017ekas negerai.<\/p>\n\n\n\n

RSA, DSA ir kiti kriptografiniai algoritmai<\/h2>\n\n\n\n

Elektroniniams para\u0161ams naudojami skirtingi kriptografiniai algoritmai, ir kiekvienas turi savo privalum\u0173. RSA (Rivest-Shamir-Adleman) yra vienas populiariausi\u0173 ir seniausi\u0173 \u2013 sukurtas dar 1977 metais. Jo saugumas remiasi min\u0117ta did\u017ei\u0173j\u0173 skai\u010di\u0173 faktorizacijos problema.<\/p>\n\n\n\n

DSA (Digital Signature Algorithm) buvo sukurtas specialiai skaitmeniniams para\u0161ams ir tapo JAV federaliniu standartu. Jis veikia \u0161iek tiek kitaip nei RSA \u2013 naudoja diskretinio logaritmo problem\u0105, kuri taip pat yra labai sunki i\u0161spr\u0119sti.<\/p>\n\n\n\n

Pastaraisiais metais vis populiaresni tampa elipsini\u0173 kreivi\u0173 algoritmai (ECDSA). Jie leid\u017eia pasiekti t\u0105 pat\u012f saugumo lyg\u012f naudojant gerokai trumpesnius raktus. Tai svarbu mobiliesiems \u012frenginiams ir sistemoms, kur skai\u010diavimo galia ar atmintis ribota. Pavyzd\u017eiui, Bitcoin naudoja b\u016btent ECDSA algoritm\u0105.<\/p>\n\n\n\n

Lietuvoje da\u017eniausiai sutinkamas RSA algoritmas su 2048 bit\u0173 raktais, nors jau dabar rekomenduojama pereiti prie 3072 ar net 4096 bit\u0173 rakt\u0173, kad b\u016bt\u0173 u\u017etikrintas saugumas ateityje.<\/p>\n\n\n\n

Sertifikatai ir pasitik\u0117jimo grandin\u0117<\/h2>\n\n\n\n

Vienas dalykas, kuris da\u017enai glumina \u017emones \u2013 kaip \u017einoti, kad tas vie\u0161asis raktas tikrai priklauso tam, kam tur\u0117t\u0173 priklausyti? \u010cia \u012f \u017eaidim\u0105 \u012fsijungia skaitmeniniai sertifikatai ir sertifikavimo centrai.<\/p>\n\n\n\n

Sertifikatas \u2013 tai tarsi elektroninis asmens dokumentas. Jame yra j\u016bs\u0173 vie\u0161asis raktas, j\u016bs\u0173 tapatyb\u0117s informacija ir patikimos tre\u010diosios \u0161alies (sertifikavimo centro) skaitmeninis para\u0161as, patvirtinantis, kad visa \u0161i informacija teisinga. Lietuvoje tokius sertifikatus i\u0161duoda \u012fvairios \u012fstaigos \u2013 nuo bank\u0173 iki specializuot\u0173 sertifikavimo centr\u0173.<\/p>\n\n\n\n

Pasitik\u0117jimo grandin\u0117 veikia taip: j\u016bs pasitikite sertifikavimo centru, sertifikavimo centras patikrina asmens tapatyb\u0119 ir i\u0161duoda jam sertifikat\u0105, o tada visi kiti gali pasitik\u0117ti tuo asmeniu per t\u0105 sertifikat\u0105. Tai primena notar\u0173 sistem\u0105, tik skaitmenin\u0117je erdv\u0117je.<\/p>\n\n\n\n

Kai atidarote pasira\u0161yt\u0105 dokument\u0105, programa automati\u0161kai tikrina ne tik pat\u012f para\u0161\u0105, bet ir ar sertifikatas galioja, ar nebuvo at\u0161auktas, ar sertifikavimo centras patikimas. Visa \u0161i patikra vyksta akimirksniu fone.<\/p>\n\n\n\n

Mai\u0161os funkcijos \u2013 dokument\u0173 pir\u0161t\u0173 atspaudai<\/h2>\n\n\n\n

Gr\u012f\u017ekime prie mai\u0161os funkcij\u0173, nes jos tikrai nusipelno daugiau d\u0117mesio. Gera mai\u0161os funkcija turi kelet\u0105 svarbi\u0173 savybi\u0173: ji turi b\u016bti greita skai\u010diuoti, bet ne\u012fmanoma atkurti originalaus dokumento i\u0161 mai\u0161os kodo, ir beveik ne\u012fmanoma rasti du skirtingus dokumentus, kurie tur\u0117t\u0173 t\u0105 pat\u012f mai\u0161os kod\u0105.<\/p>\n\n\n\n

Seniau populiarios buvo MD5 ir SHA-1 mai\u0161os funkcijos, bet jos jau neb\u0117ra laikomos saugiomis. \u0160iandien standartas yra SHA-256 (i\u0161 SHA-2 \u0161eimos) arba naujesn\u0117 SHA-3. Skai\u010dius 256 rei\u0161kia, kad mai\u0161os kodas yra 256 bit\u0173 ilgio \u2013 tai 2^256 galim\u0173 kombinacij\u0173, kas yra astronomi\u0161kai didelis skai\u010dius.<\/p>\n\n\n\n

Kad suvokti mast\u0105: jei tur\u0117tum\u0117te kompiuter\u012f, galint\u012f patikrinti milijard\u0105 mai\u0161os kod\u0173 per sekund\u0119, jums prireikt\u0173 daugiau laiko nei visatos am\u017eius, kad rastum\u0117te kolizijas SHA-256 funkcijai. \u0160tai kod\u0117l tai laikoma saugiu.<\/p>\n\n\n\n

Praktinis elektronini\u0173 para\u0161\u0173 naudojimas<\/h2>\n\n\n\n

Teorija teorija, bet kaip tai veikia realiame gyvenime? Lietuvoje elektroniniai para\u0161ai naudojami labai pla\u010diai \u2013 nuo mokes\u010di\u0173 deklaracij\u0173 pateikimo iki sutar\u010di\u0173 pasira\u0161ymo su bankais.<\/p>\n\n\n\n

Yra keletas b\u016bd\u0173, kaip galite pasira\u0161yti dokumentus elektroni\u0161kai. Pats populiariausias \u2013 per mobili\u0105j\u0105 aplikacij\u0105 su i\u0161maniuoju ID (Smart-ID) arba mobil\u0173j\u012f para\u0161\u0105. \u0160iuo atveju j\u016bs\u0173 privatus raktas saugomas saugioje telefono zonoje arba pas paslaugos teik\u0117j\u0105, o pasira\u0161yti galite \u012fved\u0119 PIN kod\u0105.<\/p>\n\n\n\n

Kitas b\u016bdas \u2013 naudoti ID kortel\u0119 su skaitytuvu. \u010cia privatus raktas yra pa\u010diame kortel\u0117s mikroscheme, ir j\u012f negalima i\u0161 ten i\u0161traukti. Tai labai saugus metodas, nors reikalauja papildomo \u012frangos.<\/p>\n\n\n\n

Versle da\u017enai naudojamos USB rakt\u0173 formos priemon\u0117s (token’ai), kuriuose saugomi sertifikatai. Jos patogios, nes galima ne\u0161iotis su savimi ir naudoti skirtinguose kompiuteriuose.<\/p>\n\n\n\n

Svarbu suprasti skirtum\u0105 tarp elektroninio para\u0161o tip\u0173. Paprastas elektroninis para\u0161as gali b\u016bti net tiesiog \u012fra\u0161ytas vardas el. lai\u0161ko pabaigoje. I\u0161pl\u0117stinis elektroninis para\u0161as jau turi b\u016bti unikaliai susietas su pasira\u0161an\u010diuoju. O kvalifikuotas elektroninis para\u0161as \u2013 tai auk\u0161\u010diausio lygio para\u0161as, teisi\u0161kai prilygintas rankra\u0161tiniam, ir jis turi atitikti grie\u017etus techninius reikalavimus.<\/p>\n\n\n\n

Saugumo i\u0161\u0161\u016bkiai ir ateities perspektyvos<\/h2>\n\n\n\n

Nors elektronini\u0173 para\u0161\u0173 kriptografija yra labai saugi, ji n\u0117ra ne\u012fveikiama. Did\u017eiausias pavojus paprastai kyla ne i\u0161 matematikos silpnumo, o i\u0161 \u017emogi\u0161kojo faktoriaus ar \u012fgyvendinimo klaid\u0173.<\/p>\n\n\n\n

Jei kas nors pavog\u0117 j\u016bs\u0173 privat\u0173 rakt\u0105 ir PIN kod\u0105, jis gali pasira\u0161in\u0117ti j\u016bs\u0173 vardu. Tod\u0117l labai svarbu saugoti savo slapta\u017eod\u017eius ir niekada ne\u012fvesti j\u0173 \u012ftartinose svetain\u0117se. Taip pat svarbu nedelsiant prane\u0161ti apie pametusi\u0105 ar pavogt\u0105 ID kortel\u0119.<\/p>\n\n\n\n

Kitas i\u0161\u0161\u016bkis \u2013 kvantiniai kompiuteriai. Teori\u0161kai pakankamai galingas kvantinis kompiuteris gal\u0117t\u0173 \u012fveikti dabartines kriptografines sistemas, nes jis gal\u0117t\u0173 efektyviai spr\u0119sti tas \u201esunkias” matematines problemas, ant kuri\u0173 visa sistema pagr\u012fsta. D\u0117l to jau dabar kuriami post-kvantiniai kriptografiniai algoritmai, kurie b\u016bt\u0173 atspar\u016bs ir kvantiniams kompiuteriams.<\/p>\n\n\n\n

Lietuvos institucijos ir tarptautin\u0117s organizacijos stebi \u0161iuos poky\u010dius ir ruo\u0161iasi palaipsniui pereiti prie nauj\u0173 standart\u0173. Tai ilgas procesas, nes reikia u\u017etikrinti suderinamum\u0105 su esamomis sistemomis.<\/p>\n\n\n\n

Kai matematika tampa kasdieniu \u012frankiu<\/h2>\n\n\n\n

Elektronini\u0173 para\u0161\u0173 kriptografija \u2013 puikus pavyzdys, kaip sud\u0117tinga matematika tampa kasdieniu \u012frankiu, kurio veikimo princip\u0173 net nereikia suprasti, kad juo naudotum\u0117t\u0117s. Ta\u010diau bent pavir\u0161utini\u0161kas supratimas, kas vyksta u\u017e mygtuko \u201ePasira\u0161yti”, padeda geriau \u012fvertinti \u0161ios technologijos patikimum\u0105 ir saugum\u0105.<\/p>\n\n\n\n

Svarbiausias dalykas, kur\u012f reikia \u012fsiminti: elektroninis para\u0161as n\u0117ra tik patogumas, tai yra matemati\u0161kai pagr\u012fstas b\u016bdas u\u017etikrinti dokument\u0173 autenti\u0161kum\u0105 ir vientisum\u0105. Kol saugote savo priva\u010dius raktus ir naudojate patikimas sistemas, elektroninis para\u0161as yra saugesnis u\u017e bet kok\u012f rankra\u0161tin\u012f.<\/p>\n\n\n\n

Technologija nuolat tobul\u0117ja, algoritmai stipr\u0117ja, o naudojimas tampa vis paprastesnis. Kas \u017eino, galb\u016bt ateityje elektroniniai para\u0161ai taps tokia savaime suprantama dalimi m\u016bs\u0173 gyvenimo, kad net negalvosime apie tai, kaip jie veikia \u2013 tiesiog pasira\u0161ysime ir tiek. Bet kol kas verta bent \u0161iek tiek suprasti t\u0105 matematin\u0119 magij\u0105, kuri leid\u017eia mums pasitik\u0117ti skaitmeniniais dokumentais taip pat, kaip kadaise pasitik\u0117jome ra\u0161alu ant popieriaus.<\/p>","protected":false},"excerpt":{"rendered":"

Kod\u0117l elektroninis para\u0161as n\u0117ra tiesiog j\u016bs\u0173 pavard\u0117 kompiuteryje Kai pirm\u0105 kart\u0105 susid\u016briau su elektroniniu para\u0161u, atvirai sakant, nesupratau, kod\u0117l negaliu…<\/p>","protected":false},"author":1,"featured_media":5972,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","footnotes":""},"categories":[15,17,16,7],"tags":[],"class_list":["post-5918","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kompiuteriu-remontas-kaune","category-kompiuteriu-remontas-klaipedoje","category-kompiuteriu-remontas-vilniuje","category-kompiuteriu-remontas-kompiuteriai-naujienos-patarimai","wpcat-15-id","wpcat-17-id","wpcat-16-id","wpcat-7-id"],"yoast_head":"\nElektronini\u0173 para\u0161\u0173 kriptografija<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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