Ganizirani zochitika zomwe muyenera kuteteza banki. Imatengedwa kuti ndi yosagonjetseka popanda kiyi, yomwe mumapatsidwa tsiku loyamba la ntchito. Cholinga chanu ndikusunga makiyi mosamala.

Tiyerekeze kuti mwasankha kusunga kiyi nthawi zonse, ndikupereka mwayi wosungirako ngati pakufunika. Koma mudzazindikira mwachangu kuti yankho lotere silikhala bwino muzochita, chifukwa kupezeka kwanu kwakuthupi kumafunika nthawi iliyonse mukatsegula zosungirako. Nanga bwanji za tchuthi chomwe munalonjezedwa? Kuphatikiza apo, funsoli ndi lowopsa kwambiri: bwanji ngati mwataya kiyi yanu yokhayo?

Poganizira zatchuthi chanu, mwaganiza zopanga kiyiyo ndikuyipereka kwa wogwira ntchito wina. Komabe, mukumvetsetsa kuti izi sizoyeneranso. Mwa kuwirikiza kuchuluka kwa makiyi, mumawonjezeranso mwayi wakuba makiyi.

Pothedwa nzeru, mumawononga chobwereza ndikusankha kugawa kiyi yoyambirira pakati. Tsopano, mungaganize kuti anthu awiri odalirika okhala ndi zidutswa zazikulu ayenera kukhalapo kuti atole makiyi ndikutsegula chipindacho. Izi zikutanthauza kuti wakuba amafunika kuba zidutswa ziwiri, zomwe zimakhala zovuta kuwirikiza kawiri kuposa kuba kiyi imodzi. Komabe, posakhalitsa mukuzindikira kuti chiwembuchi sichili bwino kuposa kiyi imodzi yokha, chifukwa ngati wina ataya theka la kiyi, fungulo lonse silingathe kubwezeretsedwa.

Vutoli litha kuthetsedwa ndi makiyi owonjezera ndi zokhoma, koma njirayi idzafunika mwachangu много makiyi ndi maloko. Mukuganiza kuti mapangidwe abwino akakhala kugawana makiyi kuti chitetezo chisadalire munthu m'modzi. Mumaganizanso kuti payenera kukhala malire a chiwerengero cha zidutswa kuti ngati chidutswa chimodzi chitayika (kapena ngati munthu apita kutchuthi), fungulo lonse limakhalabe logwira ntchito.

Momwe mungagawire chinsinsi

Mtundu uwu wa kasamalidwe kofunikira udaganiziridwa ndi Adi Shamir mu 1979 pomwe adasindikiza ntchito yake "Mmene Mungagawane Chinsinsi". Nkhaniyi ikufotokoza mwachidule zomwe zimatchedwa threshold scheme pogawa bwino mtengo wachinsinsi (monga cryptographic key) mu magawo. Ndiye, liti komanso liti pokhapokha kuchokera zigawo zasonkhanitsidwa, mutha kubwezeretsa chinsinsi mosavuta .

Kuchokera pamalingaliro achitetezo, chinthu chofunikira kwambiri pachiwembuchi ndikuti wowukirayo sayenera kudziwa chilichonse pokhapokha ngati ali ndi vuto. magawo. Ngakhale kukhalapo mbali siziyenera kupereka zambiri. Timatcha malowa chitetezo cha semantic.

Kutanthauzira kwa polynomial

Pulogalamu ya Shamir yomangidwa mozungulira lingaliro kutanthauzira kwa polynomial. Ngati simulidziwa bwino lingaliro ili, ndilosavuta. M'malo mwake, ngati munajambulapo mfundo pa graph ndikuzilumikiza ndi mizere kapena ma curve, mwazigwiritsa kale!

Kupyolera mu mfundo ziwiri mukhoza kujambula chiwerengero chopanda malire cha ma polynomials a digiri 2. Kuti musankhe imodzi yokha kuchokera kwa iwo, mukufunikira mfundo yachitatu. Chithunzi: Wikipedia

Ganizirani polynomial ndi digiri yoyamba, . Ngati mukufuna kukonza ntchitoyi pa graph, ndi mfundo zingati zomwe mukufuna? Chabwino, tikudziwa kuti iyi ndi ntchito ya mzere yomwe imapanga mzere ndipo imafunikira mfundo ziwiri. Kenako, ganizirani ntchito ya polynomial yokhala ndi digiri yachiwiri, . Iyi ndi ntchito ya quadratic, kotero osachepera mfundo zitatu zimafunika kukonza graph. Nanga bwanji polynomial yokhala ndi digiri yachitatu? Pafupifupi mfundo zinayi. Ndi zina zotero.

Chinthu chozizira kwambiri pa katunduyu ndi chakuti, kupatsidwa digiri ya ntchito ya polynomial komanso osachepera mfundo, tikhoza kupeza mfundo zina za ntchito ya polynomial iyi. Timatcha extrapolation ya mfundo zowonjezera izi kutanthauzira kwa polynomial.

Kupanga chinsinsi

Mwina mwazindikira kale kuti apa ndi pomwe chiwembu chanzeru cha Shamir chimayamba. Tinene chinsinsi chathu Ndi . Tikhoza kutembenuka mpaka pa graph ndikubwera ndi ntchito ya polynomial yokhala ndi digiri , zomwe zikukwaniritsa mfundo imeneyi. Tiye tikukumbutseni zimenezo adzakhala pakhomo lathu la zidutswa zofunika, kotero ngati ife tiika malire kwa zidutswa zitatu, tiyenera kusankha polynomial ntchito ndi digiri awiri.

Polynomial yathu idzakhala ndi mawonekedwe kumene и - manambala osankhidwa mwachisawawa. Tikungopanga polynomial yokhala ndi digiri , pomwe coefficient yaulere  - Ichi ndi chinsinsi chathu , ndi chilichonse chotsatira mawu akuti pali coefficient yosankhidwa mwachisawawa. Ngati tibwerera ku chitsanzo choyambirira ndikulingalira zimenezo , ndiye timapeza ntchito .

Panthawiyi tikhoza kupanga zidutswa pogwirizanitsa manambala apadera mu kumene (chifukwa ndi chinsinsi chathu). Muchitsanzo ichi, tikufuna kugawa zidutswa zinayi zokhala ndi magawo atatu, kotero timapanga mfundo mwachisawawa. ndi kutumiza mfundo imodzi kwa aliyense wa anthu anayi odalirika, osunga makiyi. Timadziwitsanso anthu zimenezo , popeza izi zimaonedwa kuti ndizodziwika kwa anthu onse ndipo ndizofunikira kuti zibwezeretsedwe .

Kubwezeretsa chinsinsi

Takambirana kale za lingaliro la polynomial interpolation ndi momwe limakhazikitsira dongosolo la Shamir. . Pamene atatu aliwonse a matrasti anayi akufuna kubwezeretsa , amangofunika kumasulira ndi mfundo zakezake zapadera. Kuti achite izi, amatha kudziwa mfundo zawo ndikuwerengera Lagrange interpolation polynomial pogwiritsa ntchito njira iyi. Ngati mapulogalamu amamveka bwino kwa inu kuposa masamu, ndiye kuti pi ndiye woyendetsa for, zomwe zimachulukitsa zotsatira zonse, ndipo sigma ndi for, zomwe zimawonjezera chilichonse.

pa tikhoza kuthetsa motere ndikubwezeretsa ntchito yathu yoyambirira ya polynomial:

Chifukwa tikudziwa zimenezo , kuchira zachitika mophweka:

Kugwiritsa ntchito masamu opanda chitetezo

Ngakhale tagwiritsa ntchito bwino lingaliro loyambirira la Shamir , tatsala ndi vuto lomwe talinyalanyaza mpaka pano. Ntchito yathu ya polynomial imagwiritsa ntchito masamu osatetezedwa. Zindikirani kuti pazowonjezera zilizonse zomwe wowukira amapeza pazithunzi za ntchito yathu, pali mwayi wocheperako pamfundo zina. Mutha kuwona izi ndi maso anu mukamakonzekera kuchuluka kwa mfundo za ntchito ya polynomial pogwiritsa ntchito masamu owerengeka. Izi ndizosemphana ndi cholinga chathu chachitetezo chomwe tanena, chifukwa wowukirayo sayenera kudziwa chilichonse mpaka atapeza zidutswa.

Kuti musonyeze kuti chiwerengero cha masamu chili chofooka bwanji, taganizirani zimene zinachitika pamene woukira wina anapeza mfundo ziwiri. ndipo amadziwa zambiri za anthu . Kuchokera pazidziwitso izi akhoza kuganiza , yofanana ndi ziwiri, ndikulumikiza zomwe zimadziwika mu fomula и .

Wowukirayo atha kupeza , kuwerengera :

Popeza tafotokoza monga manambala abwino osankhidwa mwachisawawa, pali chiwerengero chochepa chotheka . Pogwiritsa ntchito chidziwitsochi, wowukirayo amatha kuzindikira , popeza chilichonse choposa 5 chidzachita zoipa. Izi zimakhala zowona popeza tatsimikiza

Wowukirayo atha kuwerengera zomwe zingatheke m'malo в :

Ndi zosankha zochepa za zimadziwikiratu kuti ndizosavuta kusankha ndikuwunika zomwe zili zofunika . Pali zosankha zisanu zokha pano.

Kuthetsa vuto ndi masamu osatetezedwa

Kuti athetse chiwopsezo ichi, Shamir akuwonetsa kugwiritsa ntchito masamu modular, m'malo pa kumene и - mndandanda wa nambala zonse zofunika.

Tiyeni tikumbukire mwachangu momwe masamu a modular amagwirira ntchito. Wotchi yokhala ndi manja ndi lingaliro lodziwika bwino. Amagwiritsa ntchito wotchi . Mwamsanga pamene dzanja la ola likudutsa khumi ndi ziwiri, limabwerera ku imodzi. Chinthu chochititsa chidwi cha dongosololi ndikuti pongoyang'ana pa wotchi, sitingathe kudziwa kuchuluka kwa kusintha kwa ola. Komabe, ngati tidziwa kuti ola ladutsa 12 kanayi, tingathe kudziwa kuchuluka kwa maola omwe adutsa pogwiritsa ntchito njira yosavuta. kumene  ndiye gawo lathu (pano ),  ndi coefficient (kangati kagawo kakang'ono kamalowa mu nambala yoyambirira popanda chotsalira, apa ), ndipo  ndi yotsalira, yomwe nthawi zambiri imabweza foni ya opareshoni ya modulo (apa ). Kudziwa mfundo zonsezi kumatithandiza kuthetsa equation , koma ngati taphonya coefficient, sitidzatha kubwezeretsa mtengo woyambirira.

Titha kuwonetsa momwe izi zimasinthira chitetezo cha chiwembu chathu pogwiritsa ntchito chiwembuchi ku chitsanzo chathu cham'mbuyomu ndikugwiritsa ntchito . Ntchito yathu yatsopano ya polynomial , ndi mfundo zatsopano . Tsopano osunga makiyi atha kugwiritsanso ntchito kutanthauzira kwa polynomial kuti amangenso ntchito yathu, nthawi ino yokha kuwonjezera ndi kuchulukitsa ntchito ziyenera kutsagana ndi kuchepetsa modulo. (mwachitsanzo ).

Pogwiritsa ntchito chitsanzo chatsopanochi, tiyeni tiyerekeze kuti wowukirayo adaphunzira ziwiri mwazinthu zatsopanozi, , ndi zambiri zapagulu . Panthawiyi, wowukirayo, kutengera zambiri zomwe ali nazo, amatulutsa ntchito zotsatirazi, komwe  ndi seti ya nambala zonse zabwino, ndi imayimira modulus coefficient .

Tsopano wowukira wathu wapezanso , kuwerengera :

Kenako amayesanso m'malo в :

Nthawi ino ali ndi vuto lalikulu. Makhalidwe akusowa , и . Popeza pali mitundu yambiri yosakanizidwa ya mitundu iyi, sangapeze zambiri zowonjezera.

Malingaliro a Chitetezo

Chiwembu chogawana chinsinsi cha Shamir chikuwonetsa chitetezo pamalingaliro a chidziwitso cha chidziwitso. Izi zikutanthauza kuti masamu amalephera ngakhale kwa wowukira yemwe ali ndi mphamvu zopanda malire za kompyuta. Komabe, derali lili ndi nkhani zingapo zodziwika.

Mwachitsanzo, chiwembu cha Shamir sichipanga zidutswa kuti zifufuzidwe, ndiye kuti, anthu amatha kupereka mwaufulu zidutswa zabodza ndikusokoneza kubwezeretsa chinsinsi cholondola. Wosunga zidutswa za chidani yemwe ali ndi chidziwitso chokwanira atha kupanga kachidutswa kena mwakusintha mwa kufuna kwanu. Vutoli limathetsedwa pogwiritsa ntchito zotsimikizirika zogawirana mwachinsinsi, monga dongosolo la Feldman.

Vuto lina ndiloti kutalika kwa chidutswa chilichonse ndi chofanana ndi kutalika kwa chinsinsi chofanana, choncho kutalika kwa chinsinsi kumakhala kosavuta kudziwa. Vutoli litha kuthetsedwa mwapang'ono padding chinsinsi chokhala ndi manambala osasinthasintha mpaka utali wokhazikika.

Pomaliza, ndikofunikira kuzindikira kuti nkhawa zathu zachitetezo zitha kupitilira kapangidwe kake. Pazinthu zenizeni zapadziko lapansi, nthawi zambiri pamakhala chiwopsezo cha kuwukira kumbali komwe wowukira amayesa kutulutsa zidziwitso zothandiza panthawi yogwiritsira ntchito, kusungitsa, kuwonongeka, ndi zina zambiri. Ngati izi ndizodetsa nkhawa, kuganizira mozama kuyenera kuperekedwa panthawi yachitukuko kugwiritsa ntchito njira zodzitetezera monga ntchito ndi kuyang'ana nthawi zonse, kulepheretsa kukumbukira kusungidwa ku diski, ndi zina zambiri zomwe zili pamwamba pa nkhaniyi.

Chotsatsa

pa tsamba ili Pali chionetsero chophatikizana cha chiwembu chogawana mwachinsinsi cha Shamir. Chiwonetsero chozikidwa pa laibulale sss-js, lomwe palokha ndi doko la JavaScript la pulogalamu yotchuka ma sss. Dziwani kuti kuwerengera zikhalidwe zazikulu , и zingatenge kanthawi.

Source: www.habr.com