Ciphers ndi akazitape

Masiku ano pa Math Corner, ndiyang’ana mutu womwe ndinakambirana pa Msonkhano wapachaka wa Sayansi wa Ana wa National Children’s Foundation. Maziko akuyang'ana ana ndi achinyamata omwe ali ndi zofuna za sayansi. Simukuyenera kukhala aluso kwambiri, koma muyenera kukhala ndi "mndandanda wasayansi." Magiredi abwino kwambiri safunikira. Yesani, mungakonde. Ngati ndinu wophunzira kusukulu ya pulayimale kapena kusekondale, lembani. Kaŵirikaŵiri makolo kapena sukulu ndiyo imapereka malipoti, koma sizimakhala choncho nthaŵi zonse. Pezani tsamba la Foundation ndikupeza.

M'sukulu muli nkhani zochulukirachulukira zokhuza "coding", kutanthauza ntchito yomwe kale imadziwika kuti "programming". Iyi ndi njira yodziwika kwa aphunzitsi ongolankhula. Amakumba njira zakale, kuwapatsa dzina latsopano, ndipo "kupita patsogolo" kumadzisamalira. Pali madera angapo kumene chodabwitsa choterechi chimachitika.

Titha kunena kuti ndimatsitsa ma didactics. Ayi. Pachitukuko cha chitukuko, nthawi zina timabwerera ku zomwe zinali, zosiyidwa ndipo tsopano zikutsitsimutsidwa. Koma ngodya yathu ndi masamu, osati filosofi.

Kukhala wa dera linalake kumatanthauzanso "zizindikiro zodziwika", kuwerenga kofala, zonena ndi mafanizo. Munthu amene waphunzira bwino chinenero cha Chipolishi "ku Szczebrzeszyn kuli chitsamba chachikulu, kachilomboka kakulira m'bango" nthawi yomweyo adzawululidwa ngati kazitape wa dziko lachilendo ngati sakuyankha funso la zomwe mbalameyo ikuchita. . Zoona akukanika!

Izi si nthabwala chabe. Mu December 1944, Ajeremani anayambitsa nkhondo yomaliza ku Ardennes ndi ndalama zambiri. Anasonkhanitsa asilikali olankhula Chingelezi bwino kuti asokoneze kuyenda kwa asilikali ogwirizana, mwachitsanzo powatsogolera njira yolakwika pamphambano za misewu. Patangopita nthawi pang'ono, anthu a ku America anayamba kufunsa asilikali mafunso okayikitsa, mayankho omwe angakhale omveka kwa munthu wochokera ku Texas, Nebraska kapena Georgia ndipo sangaganizidwe kwa munthu amene sanakulire kumeneko. Kusadziŵa zenizeni kunatsogolera mwachindunji ku kuphedwa.

Mpaka pano. Ndikupangira owerenga buku la Lukasz Badowski ndi Zaslaw Adamashek "Laboratory mu Drawer ya Desk - Masamu". Ili ndi buku labwino kwambiri lomwe likuwonetsa bwino kwambiri kuti masamu ndi othandiza pa chinthu china komanso kuti "kuyesa masamu" si mawu opanda pake. Zimaphatikizapo, mwa zina, zomwe zafotokozedwa za "katoni enigma" - chipangizo chomwe chingatitengere mphindi khumi ndi zisanu zokha kuti tipange ndikugwira ntchito ngati makina akuluakulu a cipher. Lingaliro lokhalo linali lodziwika bwino, olemba otchulidwawo adachita bwino, ndipo ndisintha pang'ono ndikukulunga muzovala zambiri za masamu.

Ma hacksaw a Cryptographic

M'misewu ina ya mudzi wanga wa dacha m'dera la Warsaw, msewuwo unachotsedwa posachedwapa kuchokera ku "trlinka" - ma slabs a hexagonal paving. Ulendowu unali wovuta, koma mzimu wa masamu unasangalala. Kuphimba ndege ndi ma polygon okhazikika (ie okhazikika) sikophweka. Zitha kukhala makona atatu, mabwalo ndi ma hexagon okhazikika.

Mwina ndidaseka pang'ono ndi chisangalalo chauzimu ichi, koma hexagon ndi chithunzi chokongola. Kwa izo mukhoza kupanga mwachilungamo bwino kubisa chipangizo. Geometry idzathandiza. Hexagon ili ndi masinthidwe ozungulira - imadzipiritsa yokha ikazunguliridwa ndi kuchuluka kwa madigiri 60. Munda wolembedwa, mwachitsanzo, ndi chilembo A kumtunda kumanzere chith. 1 mutatha kutembenuza ngodya iyi, idzagweranso mu bokosi A - chimodzimodzi ndi zilembo zina. Choncho tiyeni tidule masikweya asanu ndi limodzi kuchokera pagululi, lililonse likhale ndi zilembo zosiyana. Timayika gridi yopezeka motere papepala. M'magawo asanu ndi limodzi aulere, lowetsani zilembo zisanu ndi chimodzi zomwe tikufuna kubisa. Tiyeni titembenuzire pepalalo madigiri 60. Magawo asanu ndi limodzi atsopano adzawonekera - lowetsani zilembo zisanu ndi chimodzi za uthenga wathu.

Mpunga. 1. Macheza a chisangalalo cha masamu.

Kumanja chith. 1 tili ndi mawu olembedwa motere: "Pa siteshoniyi pali locomotive yolemera kwambiri."

Tsopano masamu ang'onoang'ono akusukulu abwera mothandiza. Kodi manambala awiri angasanjidwe bwanji mogwirizana?

Funso lopusa bwanji? Kwa awiri: chimodzi kutsogolo kapena chimzake.

Zabwino kwambiri. Ndipo manambala atatu?

Sizovutanso kulemba makonda onse:

123, 132, 213, 231, 312, 321.

Chabwino, ndi zinayi! Ikhoza kufotokozedwabe momveka bwino. Ganizirani lamulo la dongosolo lomwe ndayika:

1234, 1243, 1423, 4123, 1324, 1342,

1432, 4132, 2134, 2143, 2413, 4213,

2314, 2341, 2431, 4231, 3124, 3142,

3412, 4312, 3214, 3241, 3421, 4321

Pamene manambala ali asanu, timapeza 120 zoikamo zotheka. Tiyeni tiwaitane zilolezo. Chiwerengero cha zotheka permutations ya n manambala ndi mankhwala 1 2 3 ... n, otchedwa wamphamvu ndi kutchula mawu ofuula: 3!=6, 4!=24, 5!=120. Pa nambala yotsatira 6 tili ndi 6!=720. Tigwiritsa ntchito izi kupanga chishango chathu cha hexagonal cipher kukhala chovuta kwambiri.

Timasankha kusinthasintha kwa manambala kuchokera ku 0 mpaka 5, mwachitsanzo 351042. Disiki yathu ya hexagonal scrambling ili ndi dash pakati pamunda - kotero kuti ikhoza kuikidwa "pamalo a zero" - kukwera, monga mkuyu. 1. Timayika diski motere pa pepala lomwe tiyenera kulemba lipoti lathu, koma sitilemba nthawi yomweyo, koma titembenuzire katatu ndi madigiri a 60 (ie madigiri 180) ndikulowetsamo zilembo zisanu ndi chimodzi. minda yopanda kanthu. Timabwerera kumalo oyambira. Timatembenuza kuyimba kasanu ndi madigiri 60, ndiko kuti, ndi "mano" asanu a kuyimba kwathu. Timasindikiza. Malo otsatirawa ndi malo ozungulira madigiri 60 kuzungulira ziro. Malo achinayi ndi madigiri 0, awa ndi malo oyambira.

Kodi mukumvetsa zimene zinachitika? Tili ndi mwayi wowonjezera - kusokoneza "makina" athu nthawi zopitilira mazana asanu ndi awiri! Chifukwa chake, tili ndi maudindo awiri odziyimira pawokha a "automaton" - kusankha kwa gridi ndi kusankha kwa permutation. Gululi likhoza kusankhidwa mu 66 = 46656 njira, permutation 720. Izi zimapereka mwayi wa 33592320. Zopitilira 33 miliyoni! Pafupifupi pang'ono, chifukwa ma gridi ena sangathe kudulidwa papepala.

M'munsi gawo chith. 1 tili ndi uthenga wolembedwa motere: "Ndikukutumizirani magawo anayi a parachuti." Nkosavuta kumvetsetsa kuti mdani sayenera kudziwitsidwa za izi. Koma kodi adzamvetsa chilichonse mwa izi:

Zotsatira TPOROPVMANVEORDISZ

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

ngakhale ndi signature 351042?

Tikupanga Enigma, makina achijeremani omasulira mawu

Mpunga. 2. Chitsanzo cha kukhazikitsidwa koyambirira kwa makina athu obisa.

Zilolezo (AF) (BJ) (CL) (DW) (EI) (GT) (HO) (KS) (MX) (NU) (PZ) (RY).

Monga ndanenera kale, ndili ndi lingaliro lopanga makina otere a makatoni ku bukhu "Lab mu Drawer - Masamu". "Zomanga" zanga ndizosiyana pang'ono ndi zomwe olemba ake adapereka.

Makina a cipher omwe Ajeremani ankagwiritsa ntchito panthawi yankhondo anali ndi mfundo yosavuta, yofanana ndi yomwe tidawona ndi hex cipher. Nthawi zonse chinthu chomwecho: kuswa ntchito yovuta ya kalata yopita ku kalata ina. Iyenera kusinthidwa. Kodi mungachite bwanji kuti mukhale ndi ulamuliro pa izo?

Tiyeni tisankhe osati chilolezo chilichonse, koma chomwe chili ndi zozungulira kutalika kwa 2. Mwachidule, monga "Gaderipoluk" yomwe yafotokozedwa pano miyezi ingapo yapitayo, koma ikuphimba zilembo zonse za zilembo. Tiyeni tigwirizane pa zilembo 24 - popanda ą, ę, ć, ó, ń, ś, ó, ż, ź, v, q. Zilolezo zingati? Iyi ndi ntchito ya omaliza maphunziro a kusekondale (ayenera kuthetsa nthawi yomweyo). Angati? Zambiri za? Zikwi zingapo? Inde:

1912098225024001185793365052108800000000 (tisayese ngakhale kuwerenga nambala iyi). Pali mwayi wambiri wokhazikitsa malo a "zero". Ndipo zingakhale zovuta.

Makina athu amakhala ndi ma disc awiri ozungulira. Pa imodzi mwa izo, yomwe idakalipobe, palembedwa makalata. Zili ngati kuyimba kwa foni yakale, pomwe mudayimba nambala potembenuza kuyimba njira yonse. Rotary ndi yachiwiri yokhala ndi mtundu wa mtundu. Njira yosavuta ndiyo kuwayika pachokhacho chokhazikika pogwiritsa ntchito pini. M'malo mwa Nkhata Bay, mungagwiritse ntchito bolodi woonda kapena wandiweyani makatoni. Lukasz Badowski ndi Zasław Adamaszek amalimbikitsa kuyika ma disc onse mu bokosi la CD.

Tangoganizani tikufuna kulemba mawu akuti ARMATY (Mpunga. 2 ndi 3). Khazikitsani chipangizocho kuti chikhale ziro (muvi wokwera). Chilembo A chikufanana ndi F. Sinthani dera lamkati chilembo chimodzi kumanja. Tili ndi chilembo R cholembera, tsopano chikufanana ndi A. Pambuyo pa kusinthasintha kotsatira, tikuwona kuti chilembo M chikufanana ndi U. Kuzungulira kotsatira (chithunzi chachinayi) kumapereka makalata A - P. Pa kuyimba kwachisanu tili ndi T. - A. Pomaliza (bwalo lachisanu ndi chimodzi ) Y - Y Mdani mwina sangaganize kuti ma CFCFA athu adzakhala owopsa kwa iye. Ndipo "athu" adzawerenga bwanji kutumiza? Ayenera kukhala ndi makina omwewo, omwewo "okonzedwa", ndiko kuti, ndi chilolezo chomwecho. Cipher imayambira paziro. Chifukwa chake mtengo wa F ndi A. Tembenuzani kuyimba molunjika. Chilembo A tsopano chikugwirizana ndi R. Iye amatembenuzira kuyimba kumanja ndi pansi pa chilembo U kupeza M, ndi zina zotero. Kalaliki wa cipher akuthamangira kwa mkulu wa asilikali kuti: "General, ndikupereka lipoti, mfuti zikubwera!"

Mpunga. 3. Mfundo yogwiritsira ntchito pepala lathu Enigma.

Mpunga. 3. Mfundo yogwiritsira ntchito pepala lathu Enigma.

Kuthekera kwa Enigma yakale yotere ndi yodabwitsa. Tikhoza kusankha zina linanena bungwe permutations. Titha - ndipo pali mwayi wochulukirapo pano - osati ndi "serif" imodzi pafupipafupi, koma mwanjira ina, yosintha tsiku ndi tsiku, yofanana ndi hexagon (mwachitsanzo, zilembo zitatu zoyambirira, kenako zisanu ndi ziwiri, kenako zisanu ndi zitatu, zinayi ... .. etc.).

Mukuganiza bwanji?! Ndipo komabe kwa akatswiri a masamu aku Poland (Marian Reevski, Henryk wa Zigalski, Ndi Ruzicki) zachitika. Zimene anazipeza zinali zamtengo wapatali. M'mbuyomu, anali ndi gawo lofunikira kwambiri pa mbiri ya chitetezo chathu. Vaclav Sierra i Stanislav Mazurkevichamene anaphwanya malamulo a asilikali Russian mu 1920. Chingwe chotsekekacho chinapatsa Piłsudski mwayi wopanga njira yodziwika bwino kuchokera kumtsinje wa Vepsz.

Ndimakumbukira Vaslav Sierra (1882-1969). Iye ankawoneka ngati katswiri wa masamu amene kunja kunalibe. Sanathe kulankhula za kutenga nawo mbali mu chigonjetso mu 1920 zonse zankhondo ndi ... pazifukwa zandale (akuluakulu a Polish People's Republic sanakonde omwe amatiteteza ku Soviet Union).

Mpunga. 4. Permutation (AP) (BF) (CM) (DS) (EW) (GY) (HK) (IU) (JX) (LZ) (NR) (OT).

Mpunga. 5. Kukongola kokongola, koma osati koyenera kubisa. Nthawi zambiri.

Ntchito 1. Na chith. 4 muli ndi chilolezo china chopanga Enigma. Lembani zojambulazo ku xerograph. Pangani galimoto, lembani dzina lanu loyamba ndi lomaliza. CWONUE JTRYGT yanga. Ngati mukufuna kusunga zolemba zanu mwachinsinsi, gwiritsani ntchito Cardboard Enigma.

Ntchito 2. Lembani dzina lanu ndi dzina la imodzi mwa "magalimoto" omwe mudawawona, koma (tcheru!) ndi chowonjezera chowonjezera: sititembenuza notchi imodzi kumanja, koma molingana ndi dongosolo {1, 2, 3, 2, 1, 2, 3, 2, 1, ....} - ndiye kuti, woyamba ndi m'modzi, kenako awiri, atatu, kenako 2, kenako 1, kenako 2, ndi zina zotero, "wavelet" wotere. . Onetsetsani kuti dzina langa loyamba ndi lomaliza zasungidwa ngati CZTTAK SDBITH. Tsopano kodi mukumvetsa kuti makina a Enigma anali amphamvu bwanji?

Kuthetsa mavuto kwa omaliza maphunziro a kusekondale. Ndi zosankha zingati zosinthira za Enigma (mu mtundu uwu, monga tafotokozera m'nkhaniyi)? Tili ndi zilembo 24. Timasankha zilembo ziwiri zoyambirira - izi zitha kuchitika

njira. Awiri otsatirawa akhoza kusankhidwa

njira, zambiri

ndi zina. Pambuyo mawerengedwe ofanana (manambala onse ayenera kuchulukitsidwa), timapeza

151476660579404160000

Kenako gawani nambalayo ndi 12! (12 factorial), chifukwa awiriawiri omwewo amatha kupezeka mwanjira yosiyana. Chifukwa chake pamapeto timapeza "total"

316234143225,

Izi zangopitirira 300 biliyoni, zomwe sizikuwoneka ngati kuchuluka kwakukulu kwa makompyuta apamwamba masiku ano. Komabe, ngati dongosolo lachisawawa la zilolezo palokha likuganiziridwa, chiwerengerochi chikuwonjezeka kwambiri. Tikhozanso kuganizira za mitundu ina ya zilolezo.

Onaninso: