{"id":53444,"date":"2019-12-02T00:00:00","date_gmt":"2019-12-01T21:00:00","guid":{"rendered":"https:\/\/prohoster.info\/blog\/blog_prohoster\/shema-razdeleniya-sekreta-shamira"},"modified":"2020-02-18T14:01:21","modified_gmt":"2020-02-18T11:01:21","slug":"shema-razdeleniya-sekreta-shamira","status":"publish","type":"post","link":"https:\/\/prohoster.info\/et\/blog\/administrirovanie\/shema-razdeleniya-sekreta-shamira","title":{"rendered":"Shamira saladuse jagamise skeem","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p>Kujutame ette olukorda, kus on vajalik pangahoiustamise turvalisuse tagamine. Seda peetakse t\u00e4iesti ligip\u00e4\u00e4smatuks ilma v\u00f5tmeta, mille saate esimese t\u00f6\u00f6p\u00e4eva jooksul. Teie eesm\u00e4rk on v\u00f5ti turvaliselt hoida.<\/p>\n<p>Oletame, et otsustasite kogu aeg v\u00f5tme enda juures hoida, v\u00f5imaldades juurdep\u00e4\u00e4su hoiustamisele vajaduse korral. Kuid kiiresti m\u00f5istate, et selline lahendus ei toimi, kuna igaks hoiustamise avamiseks on vajalik teie f\u00fc\u00fcsiline kohalolu. Mis siis, kui soovite puhkusele minna? Veelgi rohkem h\u00e4irib teid k\u00fcsimus: mis juhtub, kui kaotate ainulaadse v\u00f5tme?<\/p>\n<p>M\u00f5eldes puhkusele, otsustasite teha v\u00f5tme koopia ja anda see usaldusv\u00e4\u00e4rsele kolleegile. Kuid m\u00f5istate, et see pole ka ideaalne lahendus. Kahe v\u00f5tme olemasolu kahekordistab ka v\u00f5tme varguse v\u00f5imalused.<\/p>\n<p>Meeleheite t\u00f5ttu h\u00e4vitate koopia ja otsustate jagada algse v\u00f5tme kahele osale. N\u00fc\u00fcd arvate, et kaks usaldusv\u00e4\u00e4rset isikut, kellel on v\u00f5tme fragmentide osad, peavad f\u00fc\u00fcsiliselt kohal olema, et koos kokku panna v\u00f5tmega ja avada ladu. See t\u00e4hendab, et vargal on vaja varastada kaks fragmenti, mis teeb selle varguse kaks korda raskemaks kui \u00fche v\u00f5tme varastamine. Siiski m\u00f5istate peagi, et see skeem ei ole palju parem kui lihtsalt \u00fcks v\u00f5ti, sest kui keegi kaotab poole v\u00f5tme, ei saa tervet v\u00f5tit taastada.<br \/>\n<noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><br \/>\nProbleemi saab lahendada t\u00e4iendavate v\u00f5tmete ja lukkude seeria abil, kuid sellise l\u00e4henemise korral on kiiresti vajalikud <i>palju<\/i> v\u00f5tmed ja lukud. Otsustate, et ideaalne skeem peaks v\u00f5tme jagama, et turvalisus ei s\u00f5ltuks t\u00e4ielikult \u00fchest inimesest. J\u00f5uate ka j\u00e4reldusele, et peab olema mingi minimaalne fragmentide arv, nii et \u00fche fragmendi kadumise korral (v\u00f5i kui inimene on puhkusele l\u00e4inud) j\u00e4\u00e4ks kogu v\u00f5ti funktsionaalseks.<\/p>\n<h1>Kuidas jagada saladust<\/h1>\n<p>\nSellise v\u00f5tmete haldamise skeemi m\u00f5tles v\u00e4lja Adi Shamir 1979. aastal, kui avaldas oma t\u00f6\u00f6 <noindex><a rel=\"nofollow\" href=\"https:\/\/cs.jhu.edu\/~sdoshi\/crypto\/papers\/shamirturing.pdf\">\u201eKuidas jagada saladust\u201c<\/a><\/noindex>. Artiklis selgitatakse l\u00fchidalt nii nimetatud <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/64d1d06429d10e2571b04ba756a9e44d.jpg\" style=\"display:block;margin: 0 auto;\" \/> efektiivne piiri\u00fclese jagamise skeem, et jagada salajane v\u00e4\u00e4rtus (n\u00e4iteks kr\u00fcptograafiline v\u00f5ti) <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/d2ecc715b363a149fefb4cc647a30e6e.jpg\" style=\"display:block;margin: 0 auto;\" \/> osadeks. Seej\u00e4rel, kui v\u00e4hemalt <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/7a3f94d0d7874387726d18ef0c5c4174.jpg\" style=\"display:block;margin: 0 auto;\" \/> kohast <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/83808316ecdccf2d3d1d05696c6d5507.jpg\" style=\"display:block;margin: 0 auto;\" \/> osakest on kogutud, saab salajase v\u00e4\u00e4rtuse lihtsalt taastada. <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/ec92794c36ed48497df201c55697e065.jpg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<p>Turvalisuse seisukohast on selle skeemi oluline omadus see, et kurjategija ei tohiks teada midagi, kui tal ei ole v\u00e4hemalt <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/49419db7a603359c9d7f2949263e0f7d.jpg\" style=\"display:block;margin: 0 auto;\" \/> osakest. Isegi <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/13aad9d68bc8f0729bf06fc49435b7dc.jpg\" style=\"display:block;margin: 0 auto;\" \/> osakese olemasolu ei tohi andma mingit teavet. Me nimetame seda omadust <i>semantiliseks turvalisuseks.<\/i>.<\/p>\n<h1>Pol\u00fcnoomiline interpolatsioon.<\/h1>\n<p>\nShamir'i piiri\u00fclese skeem <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/5bcbb5a7f61e4e37103c379964d49e63.jpg\" style=\"display:block;margin: 0 auto;\" \/> on \u00fcles ehitatud <b>pol\u00fcnoomilise interpolatsiooni kontseptsioonile<\/b>. Kui te pole selle kontseptsiooniga tuttav, on see tegelikult \u00fcsna lihtne. \u00dcldiselt, kui olete kunagi joonistanud punkte graafikule ja seej\u00e4rel neid joonte v\u00f5i k\u00f5veratega \u00fchendama hakanud, olete juba seda kasutanud!<\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/66d66cc226dde7af9d71ab1ad7f92eea.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Kaks punkti v\u00f5ivad l\u00e4bi minna piiramatu arvu teise astme pol\u00fcnoome. Nende seast ainulaadse valimiseks on vajalik kolmas punkt. Illustreerimiseks: <noindex><a rel=\"nofollow\" href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%A1%D1%85%D0%B5%D0%BC%D0%B0_%D1%80%D0%B0%D0%B7%D0%B4%D0%B5%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F_%D1%81%D0%B5%D0%BA%D1%80%D0%B5%D1%82%D0%B0_%D0%A8%D0%B0%D0%BC%D0%B8%D1%80%D0%B0#\/media\/File:3_polynomials_of_degree_2_through_2_points.svg\">Vikipeedia<\/a><\/noindex><\/i> <\/p>\n<p>Vaatame pol\u00fcnoomi, mille aste on \u00fcks, <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/479ff09339b6907cf7fd5420a6b66907.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Kui soovite seda funktsiooni graafikule joonistada, kui palju punkte teil vaja on? Noh, me teame, et see on lineaarne funktsioon, mis moodustab joone ja seet\u00f5ttu on vajalik v\u00e4hemalt kaks punkti. Edasi vaatame pol\u00fcnoomfunktsiooni astmega kaks, <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/bd6591a5e317fadba394b9f93c03f813.jpg\" style=\"display:block;margin: 0 auto;\" \/>. See on ruutfunktsioon, seega on graafiku joonistamiseks vajalik v\u00e4hemalt kolm punkti. Kuidas on kolmanda astme pol\u00fcnoomiga? V\u00e4hemalt neli punkti. Ja nii edasi ja nii edasi.<\/p>\n<p>T\u00f5eliselt lahe asi selle omaduse juures on see, et arvestades pol\u00fcnoomfunktsiooni astet ja v\u00e4hemalt <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/97d23bb431f561738675a8eecd78c8bd.jpg\" style=\"display:block;margin: 0 auto;\" \/> punkte, saame j\u00e4reldada t\u00e4iendavaid punkte selle pol\u00fcnoomfunktsiooni jaoks. T\u00e4iendavate punktide ekstrapoleerimist nimetame <i>pol\u00fcnoominterpoleerimiseks.<\/i>.<\/p>\n<h1>Saladuse koostamine.<\/h1>\n<p>\nV\u00f5ib-olla olete juba aru saanud, et siia astub m\u00e4ngu Shamir'i nutikas skeem. Oletame, et meie saladus <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/9f18d04feb91617cc6b17ee999f7621e.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u2014 see on <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/724e6fe3c0b6e8460207592d515dde4a.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Saame selle <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/e1bb80717e0e060d77dc3fa2bff5e396.jpg\" style=\"display:block;margin: 0 auto;\" \/> punktiks graafikul <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/d7291bf682131a3cd1dc9fb65c351a5d.jpg\" style=\"display:block;margin: 0 auto;\" \/> ja leiutada pol\u00fcnoomfunktsiooni astmega <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/c63b9a9efa9409f73baf5916cd77b8b5.jpg\" style=\"display:block;margin: 0 auto;\" \/>, mis rahuldab seda punkti. Kordan, et <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/4670e092c7dc86f70984a3d5e875ae7e.jpg\" style=\"display:block;margin: 0 auto;\" \/> see on meie n\u00f5utavate fragmentide l\u00e4vi, seega kui seame l\u00e4ve kolmeks fragmentideks, peame valima pol\u00fcnoomi, mille kraad on kaks.<\/p>\n<p>Meie pol\u00fcnoom on kujul <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/06e96a58093b9e00d7c37ad5f832a6f4.jpg\" style=\"display:block;margin: 0 auto;\" \/>, kus <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/fc9ce1b274e8224fcfee33290fee6455.jpg\" style=\"display:block;margin: 0 auto;\" \/> ja <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/ec120b09589c1ee882f1f93b47626c94.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u2014 juhuslikult valitud positiivsed t\u00e4isarvud. Ehitatakse lihtsalt pol\u00fcnoom, mille kraad on <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/ef10f07dfb8496cca70579246c1d9c48.jpg\" style=\"display:block;margin: 0 auto;\" \/>, kus vaba koefitsient <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/d7db113a15325721c9fea613a379026f.jpg\" style=\"display:block;margin: 0 auto;\" \/>\u00a0\u2014 see on meie saladus <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/093bd4575a590bed819e6ec9f9b41aa0.jpg\" style=\"display:block;margin: 0 auto;\" \/>, ja iga j\u00e4rgmise <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/6c33d819871b32ff7d347d00408d02d1.jpg\" style=\"display:block;margin: 0 auto;\" \/> liikme jaoks on juhuslikult valitud positiivne koefitsient. Kui naasta algse n\u00e4ite juurde ja eeldada, et <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/c6ff5a7ad5a6a82ae31c583148ea5274.jpg\" style=\"display:block;margin: 0 auto;\" \/>, siis saame funktsiooni <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/b3386ca5ec27e0dacd17874d6f5720c8.jpg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<p>Sellel etapil saame genereerida fragmente, \u00fchendades <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/50a46de4540f90ddba6b1bbfa3702892.jpg\" style=\"display:block;margin: 0 auto;\" \/> ainulaadsed t\u00e4isarvud <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/fcbc7f0b6d9353e6eae0fafe4a06a4f2.jpg\" style=\"display:block;margin: 0 auto;\" \/>, kus <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/c58e20b2b97950112194f6a51707289c.jpg\" style=\"display:block;margin: 0 auto;\" \/> (sest see on meie saladus). Antud n\u00e4ites soovime jagada nelja fragmenti, mille l\u00e4vi on kolm, seega genereerime juhuslikult punktid <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/720b820e264f0314cb2e14ab6502ee96.jpg\" style=\"display:block;margin: 0 auto;\" \/> ja saadame \u00fche punkti iga\u00fchele neljast usaldusv\u00e4\u00e4rsest inimesest, kes on v\u00f5tmehoidjad. \u00dctleme ka inimestele, et <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/c441ff2a652b58011e13d60855c7e404.jpg\" style=\"display:block;margin: 0 auto;\" \/>, kuna see loetakse avalikuks informatsiooniks ja on vajalik taastamiseks. <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/2011019c98b6d1a77a0cd25a3667c9e4.jpg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<h1>Saladuse taastamine<\/h1>\n<p>\nOleme juba arutanud pol\u00fcnoomilise interpolatsiooni m\u00f5istet ja seda, et see on Shamir'i l\u00e4ve skeemi alus. <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/6f93e17d2d2ce5659972b98a9c8eee83.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Kui kolm neljast usaldusv\u00e4\u00e4rsest isikust soovivad taastada <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/9b5ba8c78e395d3dee229e222c31d85a.jpg\" style=\"display:block;margin: 0 auto;\" \/>, peavad nad lihtsalt interpoleerima <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/cfec467c0571c4d54d74938c5667146f.jpg\" style=\"display:block;margin: 0 auto;\" \/> oma unikaalsete punktidega. Selleks saavad nad m\u00e4\u00e4rata oma punktid <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/035e1f8407434fdbe1b8814d7fd3ee1f.jpg\" style=\"display:block;margin: 0 auto;\" \/> ja arvutada Lagrange'i interpoleerimispol\u00fcnomi, kasutades j\u00e4rgmist valemit. Kui programmeerimine on teile arusaadavam kui matemaatika, siis pi \u2014 see on p\u00f5him\u00f5tteliselt operaator <code>for<\/code>, mis korrutab k\u00f5ik tulemused, ja sigma \u2014 see on <code>for<\/code>, mis liidab k\u00f5ik kokku.<\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/01a47d3bc38f07f7b65da2ca1f772e28.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/cc0039bc38e27a62161bc0fde3b1472d.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nKoormuse anal\u00fc\u00fcsi korral <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/b41d5abefcac0bb813291063f0a56404.jpg\" style=\"display:block;margin: 0 auto;\" \/> Me saame seda j\u00e4rgmiselt lahendada ja tagastada meie algse pol\u00fcnomi:<\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/b7af6d68d1fa639442f96ed11cc96bd7.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nKuna me teame, et <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/df250c5c331d0a2903867efcad71d325.jpg\" style=\"display:block;margin: 0 auto;\" \/>, taastamine <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/a6968a889776d0caa3db0dd6e10842d4.jpg\" style=\"display:block;margin: 0 auto;\" \/> toimub lihtsalt:<\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/b89862098c973d18a75a104092364a04.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><\/p>\n<h1>Kasutades ebaturvalist t\u00e4isarvude aritmeetikat<\/h1>\n<p>\nKuigi me rakendasime Shamir'i p\u00f5hiideed edukalt <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/626be5c238019fc0a2ff08798b8e620c.jpg\" style=\"display:block;margin: 0 auto;\" \/>, meil on probleem, millele oleme seni t\u00e4helepanu p\u00f6\u00f6ranud. Meie pol\u00fcnoomfunktsioon kasutab ebaturvalist t\u00e4isarvude aritmeetikat. Pidage meeles, et iga t\u00e4iendava punkti kohta, mille r\u00fcndaja meie funktsiooni graafikul saab, j\u00e4\u00e4b v\u00e4hem v\u00f5imalusi teiste punktide jaoks. Saate seda ise n\u00e4ha, kui ehitate graafiku pol\u00fcnoomfunktsiooni puhul, kasutades t\u00e4isarvude aritmeetikat. See on meie v\u00e4ljendatud turvalisuse eesm\u00e4rgi jaoks vastutustundetu, sest kurjategija ei tohiks mitte midagist teada saada, enne kui tal ei ole v\u00e4hemalt <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/d5278c748b7713fc387c37425d43656d.jpg\" style=\"display:block;margin: 0 auto;\" \/> fragmente.<\/p>\n<p>Kuidas demonstreerida, kui n\u00f5rk on t\u00e4isarvude aritmeetika skeem, kaalume stsenaariumi, kus kurjategija sai kaks punkti <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/ebe75137fa19aaccdc733618707de3c0.jpg\" style=\"display:block;margin: 0 auto;\" \/> ja teab avalikku teavet, et <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/45dc1dbd7564637c96d1c8383af19e15.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Sellest teabest saab ta tuletada <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/16e75561bf051ecd3232f0560f75e494.jpg\" style=\"display:block;margin: 0 auto;\" \/>, mille v\u00e4\u00e4rtus on kaks, ja sisestada tuntud v\u00e4\u00e4rtused valemisse <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/e6c550b9a0d630e62d5be66e61ff3a89.jpg\" style=\"display:block;margin: 0 auto;\" \/> ja <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/e2a3c2a324c159cf73852513dda5ff3b.jpg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/003b535b08b5de17b573c7af61110dbb.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\n Seej\u00e4rel saab kurjategija leida <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/76d496e3442e88c7d5a238612f2ee8da.jpg\" style=\"display:block;margin: 0 auto;\" \/>, arvutades <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/96ef9b4a0657cd258978e2eda974bd09.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/8e677012c61e1cc45f1f3be6e44aa1c1.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nKuna oleme m\u00e4\u00e4ratlenud <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/62af08665bef7cd3fc447411455352c6.jpg\" style=\"display:block;margin: 0 auto;\" \/> nagu juhuslikult valitud positiivsed t\u00e4isarvud, on olemas piiratud hulk v\u00f5imalikke <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/66c39a1014c0acab55fea137f28a6d0f.jpg\" style=\"display:block;margin: 0 auto;\" \/>Selle teabe abil v\u00f5ib kurjategija v\u00e4lja selgitada <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/0c3caaa1e189ffea0001ca9ad08a65d1.jpg\" style=\"display:block;margin: 0 auto;\" \/>, kuna k\u00f5ik, mis on \u00fcle 5, muudab <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/104807891ce9ab1d3adc649f8d1dcd29.jpg\" style=\"display:block;margin: 0 auto;\" \/> negatiivseks. See osutub t\u00f5eks, kuna oleme kindlaks teinud <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/cf2bebff28344be58b02c492fd0e49ba.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Seej\u00e4rel v\u00f5ib kurjategija arvutada v\u00f5imalikke v\u00e4\u00e4rtusi <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/7c9c09333ee4ab432122e959892daeda.jpg\" style=\"display:block;margin: 0 auto;\" \/>, asendades <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/c5d88d7a2488ae0c40e5ec3edb66dd2d.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u00fches <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/8fd97c507a4d2bc8d4e4619e10e97063.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/1f2fb897dc37702dd543a6d7783339cb.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nPiiratud valikute hulgaga <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/9960ad727ecf47084cacfb9f487f329a.jpg\" style=\"display:block;margin: 0 auto;\" \/> saab arusaadavaks, kui lihtne on v\u00e4\u00e4rtusi hankida ja kontrollida <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/47f9786e9728ed72e10dd505d7445b41.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Siin on vaid viis varianti.<\/p>\n<h1>Probleemi lahendamine ebaturvalise t\u00e4isarvuaritmetiaga<\/h1>\n<p>\nSelle haavatavuse k\u00f5rvaldamiseks soovitab Shamir kasutada moodulaarset aritmeetikat, asendades <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/503fd220af76c5e96cce3a84a4673f91.jpg\" style=\"display:block;margin: 0 auto;\" \/> j\u00e4rgnevaga <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/49ab2b2ee61d6551a1b41f6a1795a295.jpg\" style=\"display:block;margin: 0 auto;\" \/>, kus <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/bb5a5adda52f7d4dd401efd8a040be69.jpg\" style=\"display:block;margin: 0 auto;\" \/> ja <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/1e062a8784dfb6da2bc708d3de027042.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u2014 k\u00f5igi prime arvude hulk.<\/p>\n<p>Korraks meenutame, kuidas moodulaarne aritmeetika t\u00f6\u00f6tab. Kellade m\u00f5isted on juba tuttavad. Need kasutavad kellasid, mis on <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/93520a0c8bdbbe57ab424e58c3bbfe30.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Kui tunni k\u00e4si m\u00f6\u00f6dub kaheteistk\u00fcmnest, naaseb see \u00fchenumbrisse. Selle s\u00fcsteemi huvitav omadus on see, et lihtsalt kelladele vaatamisega ei saa me selgeks, kui mitu ringi tund k\u00e4si on teinud. Kuid kui me teame, et tunni k\u00e4si on m\u00f6\u00f6dunud 12 neli korda, saab kergesti kindlaks m\u00e4\u00e4rata m\u00f6\u00f6dunud tundide arvu lihtsa valemi abil <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/5b8b7655f38ee900b989fdc070616a6b.jpg\" style=\"display:block;margin: 0 auto;\" \/>, kus <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/0ec5da4245e1eac619b42bb62f682773.jpg\" style=\"display:block;margin: 0 auto;\" \/>\u00a0\u2014 see on meie jagaja (siin <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/a8656dac61ddb1097f06781c5b5aad69.jpg\" style=\"display:block;margin: 0 auto;\" \/>), <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/3ba5b3dc4f29fac3c9d4f5f2072d688b.jpg\" style=\"display:block;margin: 0 auto;\" \/>\u00a0\u2014 see on koefitsient (kui palju kordi jagaja tervikuna l\u00e4heb algsesse numbrisse, siin <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/ac9bb70e1511109b0181e14b6227f57e.jpg\" style=\"display:block;margin: 0 auto;\" \/>), and <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/57b6842c2bfd39b19ce428e5b9345946.jpg\" style=\"display:block;margin: 0 auto;\" \/>\u00a0\u2014 see on j\u00e4\u00e4k, mille tavaliselt annab tagasi mooduli operaator (siin <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/28f71e672ecc717d2bd1845e27273398.jpg\" style=\"display:block;margin: 0 auto;\" \/>). Nende v\u00e4\u00e4rtuste tundmine v\u00f5imaldab meil lahendada v\u00f5rrandi <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/9548f9d6b522258582be1f8968752866.jpg\" style=\"display:block;margin: 0 auto;\" \/>, kuid kui j\u00e4tame koefitsiendi vahele, siis me kunagi ei suuda algset v\u00e4\u00e4rtust taastada.<\/p>\n<p>Saame demonstreerida, kuidas see suurendab meie skeemi turvalisust, rakendades skeemi meie varasemale n\u00e4itele ja kasutades <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/c0f760bdd2b67444bd233d4ea7fe5e72.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Meie uus pol\u00fcnoomi funktsioon <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/afddb9747f68076bc6dbe9b5cf60d107.jpg\" style=\"display:block;margin: 0 auto;\" \/>, ning uued punktid <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/da9d9ecfcf949b6be4bc8e3a29d670ab.jpg\" style=\"display:block;margin: 0 auto;\" \/>. N\u00fc\u00fcd saavad v\u00f5tmehoidjad taas kasutada pol\u00fcnoom interpolatsiooni, et taastada meie funktsioon, kuid seekord peavad liitmise ja korrutamise toimingud olema koos mooduliga v\u00e4hendatud <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/f94ae5343347b38dc64228472b564f0e.jpg\" style=\"display:block;margin: 0 auto;\" \/> (nt <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/d19138189cd40c6c01ab68d3d6b7027b.jpg\" style=\"display:block;margin: 0 auto;\" \/>).<\/p>\n<p>Kasutades seda uut n\u00e4idet, oletame, et r\u00fcndaja teab kahte uut punkti, <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/4f13c2640360f124305f3f023d6cfa83.jpg\" style=\"display:block;margin: 0 auto;\" \/>, ning avalik teave <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/376e0e059b761e3f3e7473d8d2d3428f.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Seekord j\u00e4releandja, tuginedes kogu teabele, mis tal on, j\u00e4reldab j\u00e4rgmised funktsioonid, kus <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/f0aedf279cc2418e2d62d51e63e324b2.jpg\" style=\"display:block;margin: 0 auto;\" \/>\u00a0\u2014 k\u00f5ik positiivsed t\u00e4isarvud, ja <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/c92efad35129d61013f6e37ec1907fd3.jpg\" style=\"display:block;margin: 0 auto;\" \/> esindab mooduli koefitsiendi <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/c2679ec08a40d7aa13a9d375b610642c.jpg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/0f6d09b6c15f013e9a445fef060f8091.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nN\u00fc\u00fcd leiab meie r\u00fcndaja taas <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/8e01640ea802740996150d09277cbf1f.jpg\" style=\"display:block;margin: 0 auto;\" \/>, arvutades <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/78fa395ca715c36835c38f4fe16d63e0.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/d739d7e52d675aeba9abcc6ada4097e1.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nSiis ta \u00fcritab j\u00e4lle j\u00e4reldada <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/e47c9bd27ac92787c287b7db249a345f.jpg\" style=\"display:block;margin: 0 auto;\" \/>, asendades <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/15c82f6824ad986351d3358c32b28f26.jpg\" style=\"display:block;margin: 0 auto;\" \/> \u00fches <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/56cddebdf83ddc105aa8aba91bd0bb38.jpg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/6e9643108864d1d2cf9e04bed493fff7.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nSeekord on tal t\u00f5sine probleem. Valemilt puuduvad v\u00e4\u00e4rtused <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/217282ca338c79dd058db66f405b07a0.jpg\" style=\"display:block;margin: 0 auto;\" \/>, <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/fb908d84b7eac873bba662cf69d95b95.jpg\" style=\"display:block;margin: 0 auto;\" \/> ja <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/83389928ca52ffce5266fe6a414e1f18.jpg\" style=\"display:block;margin: 0 auto;\" \/>. Kuna nende muutuja kombinatsioone on l\u00f5putult, ei saa ta mingit t\u00e4iendavat teavet.<\/p>\n<h1>Turvakaalutlused<\/h1>\n<p>\nShamira sekreetide jagamise skeem pakub <i>teabeooria perspektiivist turvalisust<\/i>. See t\u00e4hendab, et matemaatika on vastupidav isegi pahatahtlikule isikule, kellel on piiramatu arvutusressurss. Siiski sisaldab skeem endiselt mitmeid tuntud probleeme.<\/p>\n<p>N\u00e4iteks ei loo Shamira skeem <i>kontrollitavaid fragmente<\/i>, ehkki inimesed v\u00f5ivad vabalt esituda vale fragmente ja h\u00e4irida \u00f5ige salajase taastamist. Vaenulik fragmentide hoidja, kellel on piisavalt teavet, v\u00f5ib isegi toota teise fragmendi, muutes <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/8f646ae3193da8c9be778eceb315e902.jpg\" style=\"display:block;margin: 0 auto;\" \/> oma \u00e4ran\u00e4gemise j\u00e4rgi. See probleem lahendatakse <i>kontrollitavate sekreetide jagamise skeemide abil<\/i>, nagu Feldmani skeem.<\/p>\n<p>Teine probleem on see, et iga fragmendi pikkus on sama mis vastava salajase pikkus, nii et salajase pikkust on lihtne kindlaks teha. Seda probleemi lahendatakse triviaalsete <i>t\u00e4itmistega<\/i> salajaste juhuslike numbrite fikseeritud pikkusega.<\/p>\n<p>L\u00f5puks on oluline m\u00e4rkida, et meie mured seoses turvalisusega v\u00f5ivad ulatuda kaugemale skeemist endast. Reaalsetes kr\u00fcptograafilistes rakendustes eksisteerib sageli oht k\u00f5rvalkanalite r\u00fcnnakuteks, kus r\u00fcndaja \u00fcritab v\u00e4lja t\u00f5mmata kasulikku teavet, p\u00f5hinedes rakenduse t\u00e4itmise ajale, vahem\u00e4llu salvestamisele, t\u00f5rkeidele jne. Kui see tekitab muret, tuleks arenduse k\u00e4igus hoolikalt kaaluda kaitsemeetmete, nagu funktsioonide ja pideva t\u00e4itmisaja otsing, kasutamist, v\u00e4ltida m\u00e4lu talletamist ketta ning planeerida mitmeid muid aspekte, mis \u00fcletavad selle artikli ulatust.<\/p>\n<h1>Demos<\/h1>\n<p>\nVDS-l on v\u00f5imalik installida: <noindex><a rel=\"nofollow\" href=\"https:\/\/ericrafaloff.com\/shamirs-secret-sharing-scheme\/\">sellel lehel<\/a><\/noindex> on interaktiivne demo Shamir'i salajaste jagamise skeemist. Demonstreerimine on tehtud raamatukogu baasil <noindex><a rel=\"nofollow\" href=\"https:\/\/github.com\/gburca\/ssss-js\/\">ssss-js<\/a><\/noindex>, mis on iseenesest populaarse programmi JavaScripti port <noindex><a rel=\"nofollow\" href=\"http:\/\/point-at-infinity.org\/ssss\/\">ssss<\/a><\/noindex>. Pange t\u00e4hele, et suurte v\u00e4\u00e4rtuste arvutamine <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/4d8ec4bf92d337e22ed38aef8c2afa60.jpg\" style=\"display:block;margin: 0 auto;\" \/>, <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/cadfa859ca9627c9c3d63d52e1270de2.jpg\" style=\"display:block;margin: 0 auto;\" \/> ja <img decoding=\"async\" alt=\"Shamira saladuse jagamise skeem\" src=\"\/wp-content\/uploads\/2019\/12\/c66b23e0128c4b7a50e9d8b0ed99e406.jpg\" style=\"display:block;margin: 0 auto;\" \/> v\u00f5ib v\u00f5tta aega.<br \/>\n<br \/>Allikas: <a content=\"nofollow\" rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/431392\/\">habr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u0446\u0435\u043d\u0430\u0440\u0438\u0439, \u043a\u043e\u0433\u0434\u0430 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u0431\u0435\u0441\u043f\u0435\u0447\u0438\u0442\u044c \u0431\u0435\u0437\u043e\u043f\u0430\u0441\u043d\u043e\u0441\u0442\u044c \u0431\u0430\u043d\u043a\u043e\u0432\u0441\u043a\u043e\u0433\u043e \u0445\u0440\u0430\u043d\u0438\u043b\u0438\u0449\u0430. \u041e\u043d\u043e \u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e \u043d\u0435\u043f\u0440\u0438\u0441\u0442\u0443\u043f\u043d\u044b\u043c \u0431\u0435\u0437 \u043a\u043b\u044e\u0447\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0432\u0430\u043c \u0432\u044b\u0434\u0430\u044e\u0442 \u0432 \u043f\u0435\u0440\u0432\u044b\u0439 \u0436\u0435 \u0434\u0435\u043d\u044c \u0440\u0430\u0431\u043e\u0442\u044b. \u0412\u0430\u0448\u0430 \u0446\u0435\u043b\u044c\u00a0\u2014 \u043d\u0430\u0434\u0451\u0436\u043d\u043e \u0441\u043e\u0445\u0440\u0430\u043d\u0438\u0442\u044c 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