Ciphers nevasori
MuMath Corner yanhasi, ndichatarisa nyaya yandakurukura paNational Children's Foundation's pagore reSainzi Camp yevana. Nheyo iri kutsvaga vana nevechidiki vane zvido zvesainzi. Iwe haufanirwe kunge uine chipo chakanyanya, asi iwe unofanirwa kuve ne "sainzi streak." mamakisi echikoro akanaka kwazvo haadiwi. Edza, ungazvifarira. Kana iwe uri mukuru wechikoro chepuraimari kana mudzidzi wechikoro chesekondari, shandisa. Kazhinji vabereki kana kuti chikoro ndicho chinoita mishumo, asi izvi hazvisizvo nguva dzose. Tsvaga webhusaiti yeNheyo uye uzive.
Muchikoro mune kutaura kwakawanda nezve "coding", zvichireva chiitiko chaimbozivikanwa se "programming". Iyi inzira yakajairika yevadzidzisi vedzidziso. Vanochera nzira dzekare, vanovapa zita idzva, uye "kufambira mberi" kunogadzirwa pachako. Kune nzvimbo dzakati wandei uko kwakadai cyclical phenomenon inoitika.
Zvinogona kugumiswa kuti ndinodzikisira didactics. Aihwa. Mukukura kwebudiriro, dzimwe nguva tinodzokera kune zvaive, zvakasiiwa uye zvino zviri kumutsiridzwa. Asi kona yedu ndeyemasvomhu, kwete yehuzivi.
Kuva weimwe nharaunda zvinoreva zvakare "zviratidzo zvakajairika", kuverenga kwakajairika, zvirevo nemifananidzo. Uyo akanyatsodzidza mutauro wechiPolish "kune gwenzi guru muSzczebrzeszyn, bete riri kurira mutsanga" richabva rabudiswa pachena semusori weimwe nyika kana akasapindura mubvunzo wezvinenge zvichiitwa nehuni. Chokwadi ari kudzipwa!
Uku hakusi kuseka chete. Muna Zvita 1944, maGerman akatanga kurwisa kwavo kwekupedzisira muArdennes nemubhadharo mukuru. Vakaunganidza varwi vaitaura Chirungu zvakanaka kuti vavhiringidze kufamba kwemauto aibatana, semuenzaniso nokuvatungamirira munzira isiri iyo pamharadzano dzenzira. Mushure mechinguva chekushamisika, vaAmerica vakatanga kubvunza varwi mibvunzo inonyumwira, mhinduro dzayo dzaizova pachena kune munhu anobva kuTexas, Nebraska kana Georgia uye zvisingagoneki kune mumwe munhu asina kukurira ikoko. Kusaziva chokwadi kwakaita kuti aurayiwe.
Kusvika padanho. Ini ndinokurudzira kuvaverengi bhuku raLukasz Badowski naZaslaw Adamashek "Laboratory muDhidhirowa reDesk - Mathematics". Iri ibhuku rinoshamisa rinoratidza zvakajeka kuti masvomhu anobatsira pane chimwe chinhu uye kuti "kuedza kwemasvomhu" haasi mazwi asina chinhu. Inosanganisira, pakati pezvimwe zvinhu, kuvakwa kwakatsanangurwa kwe "cardboard enigma" - chigadziro chichatitorera maminetsi gumi nemashanu chete kugadzira uye chinoshanda seyakakomba cipher muchina. Pfungwa yacho pachayo yainyatsozivikanwa, vanyori vakataurwa vakaigadzira zvakanaka, uye ini ndichaishandura zvishoma ndoiputira mune dzimwe mbatya dzemasvomhu.
hacksaws
Pane imwe yemigwagwa yemusha wangu wedacha muruwa rweWarsaw, mugwagwa uchangobva kubviswa kubva ku "trlinka" - hexagonal paving slabs. Kukwira kwacho kwakanga kusina kugadzikana, asi mweya wenyanzvi wemasvomhu wakafara. Kuvhara ndege neyakajairwa (kureva yenguva dzose) polygons hazvisi nyore. Inogona kungova makona matatu, masikweya uye mahexagoni akajairwa.
Pamwe ndakaseka zvishoma nemufaro uyu wepamweya, asi hexagon ine chimiro chakanaka. Kubva pairi unogona kugadzira yakabudirira encryption mudziyo. Geometry ichabatsira. Iyo hexagon ine kutenderera kuenzanirana - inozviputira pachayo kana ichitenderedzwa nemultiple ye60 madhigirii. Munda wamaka, semuenzaniso, netsamba A kumusoro kuruboshwe fig. 1 mushure mekutenderera nekona iyi, inowirawo mubhokisi A - uye zvakafanana nemamwe mavara. Saka ngaticheke mativi matanhatu kubva pagridi, rimwe nerimwe riine mavara akasiyana. Isu tinoisa grid yakawanikwa nenzira iyi pane pepa pepa. Muzvikamu zvitanhatu zvemahara, isa mavara matanhatu ezvinyorwa zvatiri kuda kunyora. Ngatitenderei pepa 60 madhigirii. Minda mitsva mitanhatu ichaonekwa - isa mavara matanhatu anotevera emharidzo yedu.
Mupunga. 1. Madimikira emufaro wemasvomhu.
Kurudyi fig. 1 tine chinyorwa chakanyorwa nenzira iyi: "Pachiteshi pane chitsiga chihombe chinorema."
Iye zvino svomhu shoma dzekuchikoro dzichauya zvakanaka. Inzira ngani nhamba mbiri dzinogona kurongwa dzichienderana kune imwe neimwe?
Mubvunzo webenzi? Kune maviri: ingave imwe pamberi kana imwe.
Fine. Uye nhamba nhatu?
Hazvina zvakare kuoma kunyora ese masetin'i:
123, 132, 213, 231, 312, 321.
Zvakanaka, ndezvechina! Inogona kuramba ichinyatsotsanangurwa. Fungidzira mutemo wekuraira wandinoisa:
1234, 1243, 1423, 4123, 1324, 1342,
1432, 4132, 2134, 2143, 2413, 4213,
2314, 2341, 2431, 4231, 3124, 3142,
3412, 4312, 3214, 3241, 3421, 4321
Kana manhamba ari mashanu, tinowana 120 inogoneka marongero. Ngativadaidze permutations. Nhamba yezvinogoneka mvumo yen nhamba ndeye chigadzirwa 1 2 3 ... n, yakadanwa yakasimba uye inoratidzwa nemashoko okudanidzira: 3!=6, 4!=24, 5!=120. Pa nhamba inotevera 6 tine 6!=720. Tichashandisa izvi kuita kuti hexagonal cipher shield yedu iwedzere kuoma.
Tinosarudza kubvumirwa kwenhamba kubva ku0 kusvika ku5, semuenzaniso 351042. Yedu hexagonal scrambling disk ine dash mumunda wepakati - kuitira kuti inogona kuiswa "munzvimbo ye zero" - dash kumusoro, semuonde. 1. Tinoisa diski nenzira iyi pane pepa ratinofanira kunyora mushumo wedu, asi hatinyore pakarepo, asi shandura katatu ne 60 degrees (kureva 180 degrees) uye isa mavara matanhatu mukati. minda isina chinhu. Tinodzokera kunzvimbo yekutanga. Isu tinoshandura dial kashanu ne60 degrees, ndiko kuti, ne "mazino" mashanu edhivha yedu. Tinodhinda. Chiyero chinotevera chinzvimbo inzvimbo inotenderedzwa 60 madhigirii kutenderedza zero. Nzvimbo yechina ndeye 0 madhigirii, iyi ndiyo nzvimbo yekutanga.
Unonzwisisa here zvakaitika? Tine mumwe mukana - kuomesa "muchina" wedu nekanopfuura mazana manomwe! Saka, tine nzvimbo mbiri dzakasununguka dze "automaton" - kusarudzwa kwegridhi uye kusarudzwa kwemvumo. Iyo grid inogona kusarudzwa mu 66 = 46656 nzira, permutation 720. Izvi zvinopa 33592320 mikana. Kupfuura 33 miriyoni ciphers! Zvinenge zvishoma zvishoma, nokuti mamwe magridi haagone kuchekwa kubva pabepa.
Muchikamu chepasi fig. 1 tine meseji yakanyorwa seizvi: "Ndiri kukutumirai mapoka mana eparachuti." Zviri nyore kunzwisisa kuti muvengi haafaniri kubvumirwa kuziva pamusoro peizvi. Asi achanzwisisa here chimwe cheizvi:
ТПОРОПВМАНВЕОРДИЗЗ
YYLOAKVMDEYCHESH,
kunyangwe nesaini 351042?
Tiri kuvaka Enigma, muchina weGerman cipher
Mupunga. 2. Muenzaniso wekutanga kuseta yemuchina wedu wekunyorera.
Permutations (AF) (BJ) (CL) (DW) (EI) (GT) (HO) (KS) (MX) (NU) (PZ) (RY).
Sezvandambotaura, ndine chikwereti chepfungwa yekugadzira kadhibhodhi muchina wakadaro kubhuku rinonzi "Lab in a Drawer - Mathematics". "Kuvaka" kwangu kwakasiyana nekwakapihwa nevanyori vayo.
Cipher muchina waishandiswa nemaGermany munguva yehondo waiva nenhevedzano yakapfava, yakati fananei neiyo yatakaona ine hex cipher. Nguva dzose zvakafanana: kuputsa basa rakaoma retsamba kune imwe tsamba. Inofanira kutsiviwa. Nzira yekuzviita sei kuti uve nesimba pamusoro payo?
Ngatisarudzei kwete chero mvumo, asi iyo ine mitsara yehurefu 2. Zvichitaurwa zviri nyore, chimwe chinhu chakadai se "Gaderipoluk" inotsanangurwa pano mwedzi mishomanana yapfuura, asi kuvhara mavara ose e-alfabheti. Ngatibvumirane pamabhii makumi maviri nemana - pasina ą, ę, ć, ó, ń, ś, ó, ż, ź, v, q. Mangani emvumo dzakadaro? Iri ibasa revanopedza chikoro chesekondari (vanofanira kukwanisa kurigadzirisa ipapo ipapo). Zvingani? Zvizhinji? Zviuru zvakawanda? Ehe:
1912098225024001185793365052108800000000 (ngatisatomboedza kuverenga iyi nhamba). Kune akawanda mikana yekuseta iyo "zero" chinzvimbo. Uye zvinogona kuva zvakaoma.
Muchina wedu une maviri akatenderera discs. Pane rimwe rawo, richiripo, pakanyorwa tsamba. Zvakaita sedhiya rerunhare rwekare, kwawakachaira nhamba nekutenderedza dial nzira yese. Rotary ndiyo yechipiri ine ruvara rwemavara. Nzira iri nyore ndeyekuiisa pane yenguva dzose cork uchishandisa pini. Panzvimbo yekork, unogona kushandisa bhodhi rakatetepa kana gobvu kadhibhodhi. Lukasz Badowski naZasław Adamaszek vanokurudzira kuisa ese madhisiki mubhokisi reCD.
Fungidzira isu tinoda kukodha izwi rekuti ARMATY (Mupunga. 2uye 3) Gadzirisa mudziyo kusvika zero chinzvimbo (museve kumusoro). Vara A rinoenderana naF. Tenderedza dunhu remukati vara rimwe kurudyi. Tine vara R kuti encode, zvino rinoenderana A. Mushure kutenderera kunotevera, tinoona kuti vara M rinoenderana U. Kutenderera kunotevera (mufananidzo wechina) kunopa tsamba A - P. Pachishanu dial tine T. - A. Pakupedzisira (denderedzwa rechitanhatu) Y – Y Muvengi angasafungidzira kuti maCFCFA edu angava nengozi kwaari. Uye "vedu" vachaverenga sei kutumira? Vanofanira kuva nemuchina wakafanana, wakafanana "wakarongwa", kureva kuti, nemvumo yakafanana. Cipher inotangira panzvimbo zero. Saka kukosha kweF ndiko A. Shandura dhiyairi newachi. Vara A zvino rava kubatanidzwa naR. Anotendeudzira dayira kurudyi uye pasi pebhii U anowana M, zvichingodaro. Munyori we<em>cipher anomhanyira kumukuru wemauto: “General, ndiri kushuma, pfuti dziri kuuya!”
Mupunga. 3. Nheyo yekushanda kwepepa redu Enigma.
| Mupunga. 3. Nheyo yekushanda kwepepa redu Enigma. | ||
Mikana yeakadaro Enigma yekare inoshamisa. Tinogona kusarudza dzimwe goho permutations. Tinogona - uye kune mimwe mikana pano - kwete ne "serif" imwe nguva dzose, asi mune imwe nguva, zuva nezuva kuchinja kurongeka, yakafanana nehexagon (semuenzaniso, mabhii matatu ekutanga, zvino manomwe, zvino masere, mana ... .. nezvimwewo ..).
Ungafungidzira sei?! Uye zvakadaro kune vePolish masvomhu (Marian Reevski, Henryk Zigalski, Jerzy Ruzicki) zvakaitika. Mashoko akawanikwa aikosha zvikuru. Kare, vaive nemupiro wakakosha zvakaenzana kunhoroondo yekudzivirira kwedu. Vaclav Serpinski i Stanislav Mazurkevichuyo akatyora mutemo wemauto eRussia muna 1920. Tambo yakavharwa yakapa Piłsudski mukana wekuita mafambiro akakurumbira kubva kuRwizi rweVepsz.
Ndinoyeuka Vaslav Sierpinski (1882-1969). Aiita senyanzvi yemasvomhu yakanga isipo. Haana kukwanisa kutaura nezvekutora chikamu kwake mukukunda muna 1920 zvese zvechiuto uye ... nekuda kwezvikonzero zvezvematongerwo enyika (zviremera zvePolish People's Republic zvaisada avo vakatidzivirira kubva kuSoviet Union).
Mupunga. 4. Permutation (AP) (BF) (CM) (DS) (EW) (GY) (HK) (IU) (JX) (LZ) (NR) (OT).
Mupunga. 5. Kushongedza kwakanaka, asi kusina kukodzera encryption. Nguva zhinji.
1 basa. Na fig. 4 une imwe mvumo yekugadzira Enigma. Kopa mufananidzo kune xerograph. Vaka mota, kodhi zita rako rekutanga nerekupedzisira. Yangu CWONUE JTRYGT. Kana iwe uchida kuchengetedza zvinyorwa zvako zvakavanzika, shandisa Cardboard Enigma.
2 basa. Nyora zita rako uye surname yeimwe ye "mota" yawaona, asi (kutarisisa!) nekuwedzera kuoma: isu hatitendeuke notch imwe kurudyi, asi zvinoenderana nechirongwa {1, 2, 3, 2, 1, 2, 3, 2, 1, ....} - ndiko kuti, kutanga nemumwe, kotevera nevaviri, kozotevera nevatatu, kozoti 2, kozotevera 1 zvakare, ipapo na2, zvichingodaro, "wavelet" yakadaro. . Ita shuwa kuti zita rangu rekutanga nerekupedzisira rakanyorwa se CZTTAK SDBITH. Zvino unonzwisisa here simba remuchina weEnigma?
Kugadzirisa dambudziko kune vakapedza chikoro chesekondari. Ingani sarudzo dzekugadzirisa Enigma (mune iyi vhezheni, sezvakatsanangurwa muchinyorwa)? Tine mavara makumi maviri nemana. Isu tinosarudza mabhii ekutanga - izvi zvinogona kuitwa pa
nzira. Vanotevera vaviri vanogona kusarudzwa pa
nzira, zvakawanda
etc. Mushure mekuverenga kunoenderana (nhamba dzese dzinofanira kuwanzwa), tinowana
151476660579404160000
Zvadaro patsanura nhamba iyoyo ne12! (12 factorial), nekuti mapaya mamwe chete anogona kuwanikwa mune imwe hurongwa. Saka pakupedzisira tinowana "total"
316234143225,
izvo zvinongopfuura 300 bhiriyoni, izvo zvisingaratidzike senhamba inokatyamadza yemakomputa makuru anhasi. Nekudaro, kana iyo yakasarudzika kurongeka kwemvumo pachayo yakaverengerwa, iyi nhamba inowedzera zvakanyanya. Tinogonawo kufunga nezvemamwe marudzi emvumo.
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