Ama-ciphers nezinhloli
EKhoneni Lezibalo lanamuhla, ngizobheka isihloko engixoxile ngaso Ekhempini yaminyaka yonke yeSayensi yeSisekelo Sezingane Yezingane. Isisekelo sifuna izingane kanye nentsha enentshisekelo yesayensi. Akudingeki ube nesiphiwo ngokwedlulele, kodwa udinga "ukulandelana kwesayensi." Amamaki esikole amahle kakhulu awadingeki. Izame, ungase uyithande. Uma ungumfundi wesikole samabanga aphansi noma esikoleni esiphakeme, faka isicelo. Ngokuvamile abazali noma isikole benza imibiko, kodwa lokhu akunjalo ngaso sonke isikhathi. Thola iwebhusayithi yeSisekelo futhi uthole.
Ziyanda izinkulumo esikoleni mayelana "nokubhala ngekhodi", kubhekiselwe kumsebenzi owawuwaziwa ngokuthi "uhlelo". Lena inqubo evamile yothisha bethiyori. Bamba izindlela ezindala, bazinike igama elisha, futhi "inqubekelaphambili" yenziwa iyodwa. Kunezindawo ezimbalwa lapho kwenzeka khona into enjalo ye-cyclical.
Kungaphethwa ngokuthi ngehlisa inani lama-didactics. Cha. Ekuthuthukisweni kwempucuko, ngezinye izikhathi sibuyela kulokho okwakukhona, kwashiywa futhi manje kuyavuselelwa. Kodwa ikhoneni lethu lingokwezibalo, hhayi ifilosofi.
Ukuba yingxenye yomphakathi kusho "izimpawu ezijwayelekile", ukufundwa okujwayelekile, izisho nemifanekiso. Lowo owafunda ngokuphelele ulimi lwesiPolish "kunehlathi elikhulu eSchebrzeszyn, ibhungane likhala emhlangeni" ngokushesha uzodalulwa njengenhloli yezwe langaphandle uma engaphenduli umbuzo walokho okwenziwa yi-woodpecker. Impela uyancishwa umoya!
Lokhu akulona nje ihlaya. Ngo-December 1944, amaJalimane aqala ukuhlasela kwawo kokugcina e-Ardennes ngezindleko ezinkulu. Bahlanganisa amasosha ayekhuluma isiNgisi kahle ukuze aphazamise ukuhamba kwamasosha ahlangene, isibonelo ngokuwaholela endleleni engafanele ezimpambanweni zemigwaqo. Ngemva komzuzwana wokumangala, abaseMelika baqala ukubuza amasosha imibuzo esolisayo, izimpendulo zazo ezaziyoba sobala kumuntu ovela eTexas, eNebraska noma eGeorgia futhi engenakucatshangwa kumuntu ongakhulelanga lapho. Ukungazi izinto ezingokoqobo kwaholela ngokuqondile ekubulaweni.
Ephuzwini. Ngincoma kubafundi incwadi kaLukasz Badowski kanye noZaslaw Adamashek "Laboratory in a Desk Drwer - Mathematics". Le yincwadi enhle kakhulu ekhombisa ngokumangalisayo ukuthi izibalo ziwusizo ngempela kokuthile nokuthi "ukuhlolwa kwezibalo" akuwona amagama angenalutho. Kuhlanganisa, phakathi kwezinye izinto, ukwakhiwa okuchazwe "kwe-cardboard enigma" - idivayisi ezosithatha imizuzu eyishumi nanhlanu kuphela ukuyidala futhi esebenza njengomshini onzima we-cipher. Umbono ngokwawo wawaziwa kakhulu, ababhali okukhulunywe ngabo bawusebenze kahle, futhi ngizowushintsha kancane bese ngiwugoqa ngezingubo zezibalo ezengeziwe.
amasaha
Komunye wemigwaqo yedolobhana lakithi lase-dacha endaweni engaphansi kweWarsaw, umgwaqo ogandaywe usanda kudilizwa ku-"trlinka" - ama-slabs angama-hexagonal paving. Ukugibela kwakungakhululekile, kodwa umphefumulo wesazi sezibalo wajabula. Ukumboza indiza ngamapholigoni avamile (okungukuthi avamile) akulula. Kungaba onxantathu kuphela, izikwele namahexagoni avamile.
Mhlawumbe ngidlale kancane ngale njabulo yomoya, kodwa i-hexagon iyisithombe esihle. Kusuka kuyo ungenza idivayisi yokubethela ephumelele kahle. Ijometri izosiza. Iheksagoni inokulinganisa okujikelezayo - iyazidlula yona lapho izungeziswa ngokuphindaphinda kwama-degree angama-60. Inkambu imakwe, isibonelo, ngohlamvu A phezulu kwesokunxele umkhiwane. 1 ngemva kokuphenduka ngale engeli, izophinde iwele ebhokisini A - futhi okufanayo nezinye izinhlamvu. Ngakho-ke ake sisike izikwele eziyisithupha kugridi, ngasinye sibe nohlamvu oluhlukile. Sibeka igridi etholwe ngale ndlela ephepheni. Ezinkambini eziyisithupha zamahhala, faka izinhlamvu eziyisithupha zombhalo esifuna ukuwubhala ngemfihlo. Masizungezise ishidi ngamadigri angama-60. Izinkambu eziyisithupha zizovela - faka izinhlamvu eziyisithupha ezilandelayo zomlayezo wethu.
Ilayisi. 1. Izingoma zenjabulo yezibalo.
Kwesokudla umkhiwane. 1 sinombhalo obhalwe ngale ndlela: "Kunesitimela esikhulu esisindayo esiteshini."
Manje izibalo zesikole ezincane zizoba usizo. Zingaki izindlela izinombolo ezimbili ezingahlelwa ngazo zihlobene?
Umbuzo oyisiphukuphuku? Okubili: okukodwa ngaphambili noma okunye.
Kuhle kakhulu. Futhi izinombolo ezintathu?
Akunzima futhi ukufaka kuhlu zonke izilungiselelo:
123, 132, 213, 231, 312, 321, XNUMX.
Hhayi-ke, ngeyesine! Kusengacaciswa ngokucacile. Qagela umthetho we-oda engiwubekayo:
1234, 1243, 1423, 4123, 1324, 1342,
1432, 4132, 2134, 2143, 2413, 4213,
2314, 2341, 2431, 4231, 3124, 3142,
3412, 4312, 3214, 3241, 3421, 4321
Uma izinombolo ziyisihlanu, sithola izilungiselelo ezingaba ngu-120. Asibabize izimvume. Inombolo yezimvume ezingenzeka zezinombolo ze-n umkhiqizo 1 2 3 ... n, obizwa eqinile futhi imakwe ngesibabazo: 3!=6, 4!=24, 5!=120. Enomboloni elandelayo u-6 sino-6!=720. Sizosebenzisa lokhu ukwenza isihlangu sethu se-hexagonal cipher sibe nzima kakhulu.
Sikhetha imvume yezinombolo ukusuka ku-0 kuye ku-5, isibonelo 351042. I-disk yethu ye-hexagonal scrambling ine-dash ensimini ephakathi - ukuze ibekwe "endaweni ye-zero" - ideshi phezulu, njengakufig. 1. Sibeka i-disk ngale ndlela ephepheni okufanele sibhale kulo umbiko wethu, kodwa asiwubhali ngaso leso sikhathi, kodwa siphendule izikhathi ezintathu ngama-degrees angu-60 (okungukuthi ama-180 degrees) bese ufaka izinhlamvu eziyisithupha amasimu angenalutho. Sibuyela endaweni yokuqala. Sivula ukudayela izikhathi ezinhlanu ngama-degree angama-60, okungukuthi, "ngamazinyo" amahlanu okudayela kwethu. Siyaphrinta. Isikhundla sesikali esilandelayo yindawo ezungeziswe ngamadigri angama-60 eduze kweziro. Isikhundla sesine singamadigri angu-0, lesi yindawo yokuqala.
Uyakuqonda ukuthi kwenzekeni? Sinethuba elengeziwe - ukuhlanganisa "umshini" wethu izikhathi ezingaphezu kwamakhulu ayisikhombisa! Ngakho-ke, sinezikhundla ezimbili ezizimele ze "automaton" - ukukhethwa kwegridi kanye nokukhetha kwemvume. Igridi ingakhethwa ku 66 = 46656 izindlela, permutation 720. Lokhu kunikeza 33592320 amathuba. Ama-ciphers angaphezu kwezigidi ezingu-33! Cishe kancane kancane, ngoba amanye amagridi awakwazi ukusikwa ephepheni.
Engxenyeni engezansi umkhiwane. 1 sinomlayezo ofakwe ikhodi kanje: "Ngikuthumelela izigaba ezine zamapharashuthi." Kulula ukuqonda ukuthi isitha akufanele sivunyelwe ukwazi ngalokhu. Kodwa ingabe uzokuqonda noma yikuphi kwalokhu:
ТПОРОПВМАНВЕОРДИЗЗ
YYLOAKVMDEYCHESH,
ngisho nesiginesha 351042?
Sakha i-Enigma, umshini we-cipher waseJalimane
Ilayisi. 2. Isibonelo sokusethwa kokuqala komshini wethu wokubethela.
Izimvume (AF) (BJ) (CL) (DW) (EI) (GT) (HO) (KS) (MX) (NU) (PZ) (RY).
Njengoba ngishilo kakade, nginombono wokudala umshini wamakhadibhodi onjalo encwadini ethi "Lab in a Drawer - Mathematics". “Ukwakha” kwami kuthe ukuhluka kulokho okunikezwe ababhali bawo.
Umshini wokubhala amazwi owasetshenziswa amaJalimane phakathi nempi wawunomgomo olula ngobuhlakani, othi ufane nalowo esawubona nge-hex cipher. Ngaso sonke isikhathi into efanayo: ukwephula isabelo esinzima sencwadi eya kwenye incwadi. Kufanele ithathelwe indawo. Kwenziwa kanjani ukuze ukwazi ukulawula?
Masikhethe hhayi noma yikuphi ukuvunyelwa, kodwa okunemijikelezo yobude obu-2. Kalula nje, into efana ne-"Gaderipoluk" echazwe lapha ezinyangeni ezimbalwa ezedlule, kodwa ehlanganisa zonke izinhlamvu zezinhlamvu. Masivumelane ngezinhlamvu ezingama-24 - ngaphandle kuka-ą, ę, ć, ó, ń, ś, ó, ż, ź, v, q. Zingaki izimvume ezinjalo? Lona umsebenzi wabafundi abaphothule esikoleni esiphakeme (kufanele bakwazi ukukuxazulula ngokushesha). Mangaki? Okuningi kwe? Izinkulungwane eziningana? Yebo:
1912098225024001185793365052108800000000 (singazami nokuyifunda le nombolo). Maningi kakhulu amathuba okuthi usethe indawo ethi "zero". Futhi kungaba nzima.
Umshini wethu unamadiski ayindilinga amabili. Komunye wabo, osamile, kubhalwe izincwadi. Kufana nokudayela kwefoni endala, lapho odayele khona inombolo ngokuphendula ukudayela yonke indawo. I-Rotary ingeyesibili enohlelo lombala. Indlela elula ukuyibeka kukhokho ovamile usebenzisa iphini. Esikhundleni sikakhokho, ungasebenzisa ibhodi elincanyana noma ikhadibhodi eliwugqinsi. U-Lukasz Badowski kanye no-Zasław Adamaszek batusa ukubeka womabili ama-disc ebhokisini le-CD.
Cabanga ukuthi sifuna ukubhala ngekhodi igama elithi ARMATY (Ilayisi. 2 kanye 3). Setha idivayisi endaweni eyiziro (umcibisholo uye phezulu). Uhlamvu A luhambisana no-F. Zungezisa isekethe yangaphakathi uhlamvu olulodwa uye kwesokudla. Sinohlamvu u-R okumele lufakwe ikhodi, manje luhambisana no-A. Ngemva kokuphenduka okulandelayo, sibona ukuthi uhlamvu M luhambisana no-U. Ukuzungezisa okulandelayo (umdwebo wesine) kunikeza ukuxhumana A - P. Edayilini lesihlanu sine-T - A. Ekugcineni (umbuthano wesithupha ) Y – Y Isitha cishe ngeke siqagele ukuthi ama-CFCFA ethu azoba yingozi kuso. Futhi "owethu" bazofunda kanjani ukuthunyelwa? Kumelwe babe nomshini ofanayo, ofanayo "ohleliwe", okungukuthi, onemvume efanayo. I-cipher iqala endaweni enguziro. Ngakho-ke inani lika-F lithi A. Guqula ukudayela ngokwewashi. Uhlamvu A manje luhlotshaniswa no-R. Uphendulela ukudayela kwesokudla futhi ngaphansi kohlamvu u-U uthola uM, njll. Umabhalane we-cipher ugijimela kujenene: “Jenene, ngiyabika, izibhamu ziyeza!”
Ilayisi. 3. Umgomo wokusebenza kwephepha lethu le-Enigma.
| Ilayisi. 3. Umgomo wokusebenza kwephepha lethu le-Enigma. | ||
Amathuba we-Enigma yakudala enjalo ayamangalisa. Singakhetha ezinye izimvume zokuphumayo. Singakwazi - futhi kunamathuba amaningi nakakhulu lapha - hhayi nge-"serif" eyodwa njalo, kodwa ngohlelo oluthile, olushintsha nsuku zonke, olufana ne-hexagon (isibonelo, izinhlamvu ezintathu zokuqala, bese ziyisikhombisa, bese ziyisishiyagalombili, ezine ... ... njll..).
Ungaqagela kanjani?! Futhi nokho kochwepheshe bezibalo basePoland (UMarian Reevski, Henryk Zigalski, UJerzy Ruzicki) kwenzeka. Ulwazi olutholwe ngaleyo ndlela lwalubaluleke kakhulu. Ngaphambili, babe negalelo elibalulekile ngokulinganayo emlandweni wokuzivikela kwethu. Vaclav Serpinski i UStanislav Mazurkevichowephula ikhodi yamasosha aseRussia ngo-1920. Ikhebula elivinjiwe lanikeza uPiłsudski ithuba lokwenza umzila odumile ukusuka eMfuleni iVepsz.
Ngikhumbula uVaslav Sierra (1882-1969). Wayebonakala eyisazi sezibalo okungekho ngaphandle kwakhe. Akakwazanga ukukhuluma ngokubamba iqhaza kwakhe ekunqobeni ngo-1920 kokubili ngenxa yezempi kanye ... ngezizathu zezombangazwe (iziphathimandla zasePoland People's Republic azizange zithande labo ababesivikela eSoviet Union).
Fig. 4. Imvume (AP) (BF) (CM) (DS) (EW) (GY) (HK) (IU) (JX) (LZ) (NR) (OT).
Ilayisi. 5. Umhlobiso omuhle, kodwa awufanele ukubethela. Njalo kakhulu.
Ukuzivocavoca 1. Na umkhiwane. 4 unenye imvume yokudala i-Enigma. Kopisha umdwebo ku-xerograph. Yakha imoto, bhala igama nesibongo sakho. I-CWONUE JTRYGT yami. Uma udinga ukugcina amanothi akho eyimfihlo, sebenzisa i-Cardboard Enigma.
Ukuzivocavoca 2. Bethela igama lakho nesibongo senye "yezimoto" ozibonile, kodwa (qaphela!) ngenkinga eyengeziwe: asijikeli inothi eyodwa kwesokudla, kodwa ngokohlelo {1, 2, 3, 2, 1, 2, 3, 2, 1, ....} - okungukuthi, okokuqala ngomunye, bese kuba ababili, bese kuba ngabathathu, bese kuba 2, bese futhi ngo-1, bese kuba 2, njll., "wavelet" enjalo. . Qiniseka ukuthi igama lami nesibongo zibethelwe njenge-CZTTAK SDBITH. Manje uyaqonda ukuthi wawunamandla kangakanani umshini we-Enigma?
Ukuxazulula izinkinga kwabaphothule esikoleni esiphakeme. Zingaki izinketho zokucushwa ze-Enigma (kule nguqulo, njengoba kuchazwe esihlokweni)? Sinezinhlamvu ezingama-24. Sikhetha ipheya yokuqala yezinhlamvu - lokhu kungenziwa
izindlela. Ipheya elandelayo ingakhethwa kuyo
izindlela, okuningi
njll. Ngemuva kwezibalo ezihambisanayo (zonke izinombolo kufanele ziphindaphindwe), sithola
151476660579404160000
Bese uhlukanisa leyo nombolo ngo-12! (12 factorial), ngoba amapheya afanayo angatholakala ngendlela ehlukile. Ngakho-ke ekugcineni sithola "ingqikithi"
316234143225,
lokho kungaphezu nje kwezigidi eziyizinkulungwane ezingu-300, okungabonakali njengenani elikhulu ngokumangalisayo lamakhompiyutha amakhulu anamuhla. Kodwa-ke, uma ukuhleleka okungahleliwe kwezimvume ngokwazo kucatshangelwa, le nombolo ikhula kakhulu. Singacabanga nangezinye izinhlobo zezimvume.
Bheka futhi:
