{"id":625,"date":"2017-10-01T16:41:53","date_gmt":"2017-10-01T15:41:53","guid":{"rendered":"http:\/\/gjimnazi-perla.edu.al\/?p=625"},"modified":"2018-02-04T21:15:25","modified_gmt":"2018-02-04T20:15:25","slug":"matane-tik-11-arti-sekretet-e-kriptografise","status":"publish","type":"post","link":"http:\/\/gjimnazi-perla.edu.al\/?p=625","title":{"rendered":"Matan\u00eb TIK 11 – Arti & sekretet e kriptografis\u00eb"},"content":{"rendered":"

Sekretet e kriptografis\u00eb nga egjiptian\u00ebt e lasht\u00eb tek interneti i sot\u00ebm, mekanika kuantike dhe e ardhmja e komunikimit t\u00eb fsheht\u00eb<\/strong>
\nQ\u00eb nga agimi i historis\u00eb, njeriu ka patur nevoj\u00eb t\u00eb mbroj\u00eb dokumentet dhe komunikimet nga syt\u00eb dhe vesh\u00ebt e kund\u00ebrshtar\u00ebve apo armiqve. Q\u00eb n\u00eb vitin 1900 P.E.S, faraon\u00ebt p\u00ebrdornin hieroglife t\u00eb ndryshme nga ato standarde p\u00ebr t\u00eb komunikuar me gjeneral\u00ebt e tyre dhe 4000 vjet m\u00eb von\u00eb amerikan\u00ebt gjat\u00eb Luft\u00ebs s\u00eb Dyt\u00eb Bot\u00ebrore, rekrutuan qindra indian\u00eb Navajos si operator\u00eb n\u00eb komunikimet radiofonkie, t\u00eb cl\u00ebt fal\u00eb gjuh\u00ebs s\u00eb tyre t\u00eb pakuptueshme i b\u00ebnin t\u00eb sigurta komunikimet ushtarake n\u00eb rastin e p\u00ebrgjimit nga ana e japonez\u00ebve.
\nHistoria dhe e ardhmja<\/strong>
\nSot kriptografia, ose aft\u00ebsia p\u00ebr ta b\u00ebr\u00eb nj\u00eb mesazh t\u00eb pakuptuesh\u00ebm p\u00ebr t\u00eb gjith\u00eb me p\u00ebrjashtim t\u00eb marr\u00ebsit legjitim, \u00ebsht\u00eb nj\u00eb shkenc\u00eb e v\u00ebrtet\u00eb. M\u00eb posht\u00eb po paraqesim nj\u00eb udh\u00ebtim t\u00eb shkurt\u00ebr n\u00ebp\u00ebr histori t\u00eb emigmave, matematik\u00ebs dhe spiunazhit, p\u00ebr t\u00eb zbuluar se si krijohet nj\u00eb sistem kriptimi dhe si p\u00ebrdoret ai, cilat jan\u00eb sistemet m\u00eb t\u00eb sigurta, dhe si kontributi i nj\u00eb matematikani t\u00eb panjohur polak qe p\u00ebrcaktues n\u00eb fatet e Luft\u00ebs s\u00eb Dyt\u00eb Bot\u00ebrore. Por mos harroni se p\u00ebr t\u00eb zbuluar di\u00e7ka shum\u00eb private, nuk \u00ebsht\u00eb p\u00ebrher\u00eb e nevojshme t\u00eb kesh akses n\u00eb nj\u00eb kompjuter apo tek ndonj\u00eb sistem i avancuar kriptimi:ndonj\u00ebher\u00eb mjafton t\u00eb vini n\u00eb pun\u00eb zgjuarsin\u00eb dhe mir\u00ebbesimin\u2026
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\nKuptoj dhe nuk kuptoj<\/strong>
\nMiliona mesazhe p\u00ebrshkojn\u00eb \u00e7do dit\u00eb rrjetet e telekomunikacionit:\u00e7do dit\u00eb d\u00ebrgohen mbi 150 miliard\u00eb e-maile dhe 400 milion\u00eb mesazhe n\u00eb t\u00ebeeter (shih p\u00ebr kuriozitet statistikat e worldometers). Jan\u00eb e-maile dhe mesazhe, por edhe transaksione bankare, thirrje telefonike dhe madje edhe fakse (ende), p\u00ebrmbajtja e t\u00eb cilave shpesh duhet t\u00eb mbrohet nga p\u00ebrgjimet e paautorizuara: nga numri i kartave t\u00eb kreditit tek bisedat midis politikan\u00ebve.
\nMbrojtja e k\u00ebtyre komunikimeve i \u00ebsht\u00eb besuar nj\u00eb teknike t\u00eb ve\u00e7ant\u00eb t\u00eb quajtur kriptografi. Termi rrjedh nga greqishtja, nga bashkimi i fjal\u00ebve kriptos (i fshehur) dhe gramma (shkrim), dometh\u00ebn\u00eb shkrim i fsheht\u00eb. Kriptografia \u00ebsht\u00eb arti i d\u00ebrgimit t\u00eb mesazheve (dhe jo vet\u00ebm me shkrim) t\u00eb kuptueshme vet\u00ebm p\u00ebr marr\u00ebsit e duhur.
\n\u00c7el\u00ebsat e par\u00eb<\/strong>
\nRreth vitit 400 P.E.S komunikimet e \u201cndjeshme\u201d kodoheshin me metod\u00ebn skitale, nj\u00eb sistem i thjesht\u00eb dhe efektiv q\u00eb p\u00ebr her\u00eb t\u00eb par\u00eb futi konceptin e \u00e7el\u00ebsit t\u00eb dekriptimit. Mesazhi shkruhej nga e majta n\u00eb t\u00eb djatht\u00eb n\u00eb nj\u00eb rrip l\u00ebkure t\u00eb mb\u00ebshtjell\u00eb rreth nj\u00eb shkopi (skitale, gjuh\u00ebn e lasht\u00eb greke), n\u00eb m\u00ebnyr\u00eb q\u00eb \u00e7do radh\u00eb e brezit t\u00eb p\u00ebrmbante vet\u00ebm nj\u00eb g\u00ebrme:n\u00ebse rrotulla hapej, g\u00ebrmat riorganizoheshin dhe mesazhi nuk qe m\u00eb i lexuesh\u00ebm.
\nVet\u00ebm p\u00ebrdorimi i nj\u00eb shkopi identik me at\u00eb t\u00eb d\u00ebrguesit (\u00e7el\u00ebsi), do t\u2019i mund\u00ebsonte marr\u00ebsit t\u00eb rind\u00ebrtonte tekstin e mesazhit. N\u00eb Spart\u00eb ky system u p\u00ebrdor q\u00eb n\u00eb vitin 400 P.E.S. \u00cbsht\u00eb ndoshta metoda m\u00eb e vjet\u00ebr e njohur e kriptografis\u00eb p\u00ebrmes transpozimit. Me ndryshime t\u00eb vogla, kjo metod\u00eb mbijetoi p\u00ebr shum\u00eb shekuj krah p\u00ebr krah me sistemet m\u00eb naive, p\u00ebr shembull z\u00ebvend\u00ebsimin ose p\u00ebrzierjen e shkronjave t\u00eb b\u00ebra n\u00eb baz\u00eb t\u00eb rregullave jo shum\u00eb komplekse, n\u00eb m\u00ebnyr\u00eb q\u00eb edhe vet\u00eb marr\u00ebsi t\u00eb qe n\u00eb gjendje t\u00eb dekriptonte mesazhin.<\/p>\n

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Enigma b\u00ebhet art<\/strong>
\nSistemet e kriptimit t\u00eb bazuara tek z\u00ebvend\u00ebsimin e g\u00ebrmave, ishin shum\u00eb pak t\u00eb sigurta. N\u00eb fillim t\u00eb viteve \u201930 t\u00eb shekullit XX-t\u00eb, inteligjenca gjermane krijoi makinerin\u00eb elektro-mekanike t\u00eb kriptimit t\u00eb quajtur Enigma. Ajo ishte nj\u00eb makin\u00eb shkrimi e ve\u00e7ant\u00eb e pajisur me tri rrota t\u00eb ndryshme, secila prej t\u00eb cilave rendiste shkronjat e alfabetit n\u00eb nj\u00eb m\u00ebnyr\u00eb t\u00eb paracaktuar, dhe t\u00eb ndryshme nga ajo standarde.
\nRrota e par\u00eb lidhej me tastat e makin\u00ebs s\u00eb shkrimit, dhe riprodhonte tekstin duke \u00a0e koduar at\u00eb thjesht p\u00ebrmes z\u00ebvend\u00ebsimit t\u00eb \u00e7el\u00ebsit t\u00eb paracaktuar. Teksti i koduar rikodifikohej nga rrota e dyt\u00eb me nj\u00eb \u00e7el\u00ebs t\u00eb ndrysh\u00ebm, dhe pastaj s\u00ebrish nga i treti. Mekanizma shtes\u00eb mund t\u00eb nd\u00ebrhynin m\u00eb pas kodifikime t\u00eb tjera. P\u00ebr t\u00eb dekriptuar nj\u00eb tekst t\u00eb koduar nga Enigma, ishte e domosdoshme pasja e nj\u00eb tjet\u00ebr makinerie Enigma t\u00eb konfiguruar sakt\u00ebsisht si e para:dhe k\u00ebto t\u00eb fundit ishin parazgjedhur p\u00ebrpara shp\u00ebrndarjes s\u00eb makinave.
\nKy qe nj\u00eb sistem tmerr\u00ebsisht kompleks mekanik, i cili funksiononte n\u00eb nj\u00eb loj\u00eb po aq t\u00eb nd\u00ebrlikuar t\u00eb spiunazhit dhe kund\u00ebr-spiunazhit:sistemi u thye p\u00ebr her\u00eb t\u00eb par\u00eb n\u00eb vitin 1932 nga matematikani polak Marian Rejevski, pik\u00ebrisht n\u00eb saj\u00eb t\u00eb ndihm\u00ebs s\u00eb sh\u00ebrbimeve sekrete franceze dhe polake. Gjerman\u00ebt u kund\u00ebrp\u00ebrgjigj\u00ebn duke e b\u00ebr\u00eb m\u00eb kompleks mekanizmin e sistemit, por edhe ky evoluim i Enigm\u00ebs m\u00eb n\u00eb fund u thye nga Alan Turing.
\n\u00c7el\u00ebsi i dyfisht\u00eb<\/strong>
\nEdhe pse k\u00ebto sisteme kriptimi mbik\u00ebqyren nga algoritme komplekse, ato jan\u00eb t\u00eb destinuara p\u00ebr t\u2019u thyer, me kushtin q\u00eb t\u00eb kihet n\u00eb dispozicion kapaciteti i llogaritjeve dhe koha:nj\u00eb kompjuter modern mund t\u00eb deshifroj\u00eb pa shum\u00eb v\u00ebshtir\u00ebsi nj\u00eb mesazh t\u00eb koduar nga Enigma thjesht duke u p\u00ebrpjekur t\u00eb zb\u00ebrthej\u00eb nj\u00eb nga nj\u00eb t\u00eb gjith\u00eb \u00e7el\u00ebsat e mundsh\u00ebm:n\u00eb disa jav\u00eb do t\u00eb shfyt\u00ebzonte t\u00eb gjitha opsionet duke ia dal\u00eb t\u00eb zhbllokoj\u00eb kodin.
\nP\u00ebr k\u00ebt\u00eb arsye nga mesi i viteve \u201870, Uajtfilld Difi dhe Martin Helman, dy studiues amerikan\u00eb, nd\u00ebrtuan nj\u00eb sistem kriptimit bazuar n\u00eb p\u00ebrdorimin e dy \u00e7el\u00ebsave t\u00eb ndryshme, t\u00eb krijuar n\u00eb m\u00ebnyr\u00eb t\u00eb till\u00eb q\u00eb t\u00eb vareshin nga nj\u00ebri-tjetri. Dy kodet jan\u00eb t\u00eb njohur me emrat e \u00e7el\u00ebsit publik dhe tij privat:i pari p\u00ebrdoret p\u00ebr t\u00eb kriptuar, i dyti p\u00ebr t\u00eb dekriptuar.
\nKush ka nevoj\u00eb t\u00eb komunikoj\u00eb n\u00eb fsheht\u00ebsi, mjaftohet me kriptimin e mesazhit me \u00e7el\u00ebsin publik t\u00eb marr\u00ebsit. Ky i fundit mundet m\u00eb pas t\u00eb dekriptoj\u00eb mesazhin duke p\u00ebrdorur \u00e7el\u00ebsin e vet privat. Secili duhet pra t\u2019ia shp\u00ebrndaj\u00eb \u00e7el\u00ebsin e vet publik t\u00eb gjith\u00eb njer\u00ebzve nga t\u00eb cil\u00ebt duhet t\u00eb marr\u00eb komunikime t\u00eb koduara, pa u shqet\u00ebsuar p\u00ebr fshet\u00ebsin\u00eb e tij, p\u00ebrderisa leximi \u00ebsht\u00eb i mundur vet\u00ebm p\u00ebrmes kriptimit t\u00eb mesazheve.<\/p>\n

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Algoritmi RSA<\/strong>
\nEvolucioni i sistemit me \u00e7el\u00ebs t\u00eb dyfisht\u00eb ndodhi n\u00eb vitin 1978, kur matematikan\u00ebt dhe kriptograf\u00ebt amerikan\u00eb Ron Rivest dhe Leonard Adleman dhe izraeliti Adi Shamir nd\u00ebrtuan nj\u00eb algorit\u00ebm matematikor p\u00ebr t\u00eb gjeneruar dy \u00e7el\u00ebsa t\u00eb pavarur nga nj\u00ebri-tjetri. Sistemi i quajtur RSA sipas g\u00ebrmave t\u00eb para t\u00eb emrave t\u00eb 3 studiuesve, konsiderohet ende i pathyesh\u00ebm:n\u00eb vitin 1994, 600 grupeve k\u00ebrkimore nga 25 vende t\u00eb bot\u00ebs iu desh\u00ebn plot 8 muaj p\u00ebr t\u00eb thyer nj\u00eb \u00e7el\u00ebs RSA me 129 shifra, duke p\u00ebrdorur m\u00eb shum\u00eb se 1.600 kompjuter\u00eb t\u00eb lidhur paralel me an\u00eb t\u00eb internetit. Programet e kriptimit m\u00eb t\u00eb p\u00ebrhapura sot p\u00ebrdorin \u00e7el\u00ebsa me 2048 shifra:koha e nevojshme p\u00ebr t\u2019i thyer ato me mjetet statistikore dhe kompjuterat m\u00eb t\u00eb fuqish\u00ebm q\u00eb jan\u00eb aktualisht n\u00eb dispozicion, \u00ebsht\u00eb n\u00eb teori e barabart\u00eb me qindra vjet.
\nKu p\u00ebrdoren sistemet e kriptimit<\/strong>
\nAktualisht sistemet e kriptimit p\u00ebrdoren kryesisht n\u00eb mbrojtjen e dokumenteve t\u00eb transmetuara n\u00eb formatin dixhital. Sinjali q\u00eb duhet koduar, qoft\u00eb kjo nj\u00eb fotografi, nj\u00eb telefonat\u00eb apo nj\u00eb ndeshje futbolli, ndahet n\u00eb copa t\u00eb vogla t\u00eb quajtura paket\u00ebza, kodohen me nj\u00eb algorit\u00ebm t\u00eb ndryshuesh\u00ebm n\u00eb baz\u00eb t\u00eb nivelit t\u00eb siguris\u00eb s\u00eb k\u00ebrkuar, dhe postohen n\u00eb rrjetin e telekomunikacionit.
\nN\u00eb stacionin prit\u00ebs, aparati i marr\u00ebsit t\u00eb autorizuar deshifron dhe riorganizon paketat individuale n\u00eb nj\u00eb sinjal t\u00eb qart\u00eb. Kartat smart t\u00eb televizioneve me pages\u00eb, kartat e telefonave celular\u00eb dhe programet e ve\u00e7anta kompjuterike sh\u00ebrbejn\u00eb pik\u00ebrisht p\u00ebr k\u00ebt\u00eb:v\u00ebrtetojn\u00eb kredencialet e marr\u00ebsit (p\u00ebr shembull pagesat p\u00ebr t\u00eb shikuar ndeshjen), dhe autorizojn\u00eb dekriptimin e sinjalit.
\nN\u00ebnshkrimi dixhital<\/strong>
\nEvolucioni i sistemeve kriptografike ka qen\u00eb p\u00ebrcaktues n\u00eb zhvillimin e n\u00ebnshkrimit dixhital, sistemi i par\u00eb dhe i vet\u00ebm p\u00ebr v\u00ebrtetimin e origjin\u00ebs s\u00eb dokumenteve elektronike dhe autenticitetit t\u00eb tyre. Sistemi i n\u00ebnshkrimit dixhital p\u00ebrdor parimin e \u00e7el\u00ebsit t\u00eb dyfisht\u00eb, por n\u00eb kahun e kund\u00ebrt:\u00e7do dokumentet i koduar me \u00e7el\u00ebsin privat t\u00eb nj\u00eb individi, mund t\u00eb lexohet nga t\u00eb gjitha ata q\u00eb zot\u00ebrojn\u00eb \u00e7el\u00ebsin e tij publik.
\nT\u00eb arrish t\u00eb lexosh nj\u00eb mesazh me nj\u00eb \u00e7el\u00ebs t\u00eb ve\u00e7ant\u00eb publik, n\u00ebnkupton identifikimin unik t\u00eb d\u00ebrguesit. N\u00ebnshkrimi dixhital ka filluar t\u00eb p\u00ebrdoret gjer\u00ebsisht n\u00eb Itali n\u00eb vitin 2003, kur mij\u00ebra kompani paraqit\u00ebn pasqyrat e tyre financiare n\u00eb m\u00ebnyr\u00eb elektronike, duke v\u00ebrtetuar autenticitetin e k\u00ebtij aplikimi.
\nKufiri i fundit: Drita<\/strong>
\nE ardhmja e protokolleve t\u00eb kriptimit \u00ebsht\u00eb megjithat\u00eb e shk\u00ebputur nga algoritmet dhe funksionet matematikore: rritja e shpejt\u00ebsis\u00eb s\u00eb p\u00ebrpunimit nga ana e kompjuterve do t\u00eb lejoj\u00eb zhvillimin e formulave shum\u00eb m\u00eb komplekse, por gjithashtu do t\u00eb mund\u00ebsoj\u00eb zhvillimin e sistemeve gjithnj\u00eb e m\u00eb efektive q\u00eb sh\u00ebrbejn\u00eb p\u00ebr thyerjen e kodeve.
\nSistemi i vet\u00ebm i kriptimit aktualisht i pathyesh\u00ebm duket t\u00eb jet\u00eb i bazuar n\u00eb vetit\u00eb e materies, dhe n\u00eb ve\u00e7anti tek sjellja e kuanteve t\u00eb drit\u00ebs, ose fotoneve, grimca elementare pa asnj\u00eb ngarkes\u00eb elektrike q\u00eb udh\u00ebtojn\u00eb me shpejt\u00ebsin\u00eb e drit\u00ebs. \u00cbsht\u00eb kriptimi kuantik, n\u00eb baz\u00eb t\u00eb parimit t\u00eb pap\u00ebrcaktueshm\u00ebris\u00eb s\u00eb Hajzenbergut (nuk \u00ebsht\u00eb e mundur t\u00eb njihen n\u00eb t\u00eb nj\u00ebjt\u00ebn koh\u00eb dhe m\u00eb sakt\u00ebsi disa karakteristika themelore t\u00eb nj\u00eb objekti n\u00eb kuantike, si pozicioni dhe shpejt\u00ebsia), dhe mbi zbatimin e k\u00ebtij parimi tek fotonet.
\nSipas ligjeve t\u00eb mekanik\u00ebs kuantike, \u00ebsht\u00eb n\u00eb fakt e pamundur t\u00eb v\u00ebzhgohet nj\u00eb grimc\u00eb elementare pa e \u201cshqet\u00ebsuar\u201d at\u00eb: \u00e7do p\u00ebrpjekje p\u00ebr nd\u00ebrhyrje l\u00eb gjurm\u00eb t\u00eb pashlyeshme dhe t\u00eb p\u00ebrhershme. N\u00eb sistemet e kriptimit kuantik, informacioni ruhet n\u00eb fotone individuale: p\u00ebrpjekja p\u00ebr t\u00eb thyer nj\u00eb \u00e7el\u00ebs kuantik, nuk do t\u00eb shkaktonte gj\u00eb tjet\u00ebr ve\u00e7se ndryshimin e p\u00ebrhersh\u00ebm t\u00eb vet\u00eb \u00e7el\u00ebsit, q\u00eb p\u00ebr k\u00ebt\u00eb arsye do t\u00eb b\u00ebhej i padobish\u00ebm, dhe si d\u00ebrguesi ashtu edhe marr\u00ebsi i mesazhit do t\u00eb zbulonin menj\u00ebher\u00eb p\u00ebrpjekjen p\u00ebr t\u00eb nd\u00ebrhyr\u00eb. shkeputur nga Focus \u2013\u00a0Bota.al<\/p>\n","protected":false},"excerpt":{"rendered":"

Sekretet e kriptografis\u00eb nga egjiptian\u00ebt e lasht\u00eb tek interneti i sot\u00ebm, mekanika kuantike dhe e ardhmja e komunikimit t\u00eb fsheht\u00eb Q\u00eb nga agimi i historis\u00eb, njeriu ka patur nevoj\u00eb t\u00eb mbroj\u00eb dokumentet dhe komunikimet nga syt\u00eb dhe vesh\u00ebt e kund\u00ebrshtar\u00ebve apo armiqve. Q\u00eb n\u00eb vitin 1900 P.E.S, faraon\u00ebt p\u00ebrdornin hieroglife t\u00eb ndryshme nga ato standarde […]<\/p>\n","protected":false},"author":1,"featured_media":653,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,5,1,9],"tags":[12],"class_list":["post-625","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9-vjecare","category-e-mesme","category-e-pergjithshme","category-informacione-te-tjera","tag-tik-11"],"_links":{"self":[{"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=\/wp\/v2\/posts\/625","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=625"}],"version-history":[{"count":1,"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=\/wp\/v2\/posts\/625\/revisions"}],"predecessor-version":[{"id":626,"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=\/wp\/v2\/posts\/625\/revisions\/626"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=\/wp\/v2\/media\/653"}],"wp:attachment":[{"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=625"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/gjimnazi-perla.edu.al\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}