Izibalo, amakhodi, ama-cipher, izibalo kanye nezinkondlo

UMichal Shurek uthi ngaye: “Ngazalwa ngo-1946. Ngaphothula eNyuvesi yaseWarsaw ngo-1968 futhi kusukela lapho bengisebenza eFaculty of Mathematics, Informatics and Mechanics. Ubuchwepheshe besayensi: i-algebraic geometry. Ngisanda kusebenzelana nezinqwaba ze-vector. Iyini i-vector beam? Ngakho-ke, ama-vectors adinga ukuboshwa ngokuqinile ngentambo, futhi sesivele sinenqwaba. Umngani wami oyisazi sefiziksi u-Anthony Sim ungenze ngajoyina i-Young Technician (uyavuma ukuthi kufanele athole izinzuzo ezinkokhelweni zami). Ngabhala izihloko ezimbalwa ngase ngihlala, futhi kusukela ngo-1978 ungakwazi ukufunda nyanga zonke lokho engikucabangayo ngezibalo. Ngiyazithanda izintaba futhi, naphezu kokukhuluphala, ngiyazama ukuhamba. Ngicabanga ukuthi othisha yibona ababaluleke kakhulu. Bengingagcina osopolitiki, kungakhathaliseki ukuthi bakhethani, endaweni egadwe kakhulu ukuze bangakwazi ukuphunyuka. Yondla kanye ngosuku. I-beagle yaseTulek iyangithanda.

I-equation ifana ne-cipher yesazi sezibalo. Ukuxazulula izibalo, i-quintessence yezibalo, ukufundwa kwe-ciphertext. Lokhu kuye kwaqashelwa izazi zemfundiso yenkolo kusukela ngekhulu lesi-XNUMX. UJohn Paul II, owayazi izibalo, wabhala futhi wakusho lokhu izikhathi eziningana ezintshumayelweni zakhe - ngeshwa, amaqiniso asuliwe enkumbulweni yami.

Esikoleni isayensi, imelwe I-Pythagoras njengombhali wethiyori kokuncika okuthile kunxantathu ongakwesokudla. Ngakho-ke yaba yingxenye yefilosofi yethu ye-Eurocentric. Futhi nokho uPythagoras unobuhle obuningi. Nguye owabeka kubafundi bakhe umsebenzi "wokufunda umhlaba", kusukela "kuyini ngemuva kwaleli gquma?" ngaphambi kokutadisha izinkanyezi. Yingakho abaseYurophu "bathola" impucuko yasendulo, hhayi ngokuphambene nalokho.

Abanye abafundi bayakhumbulaAmaphethini we-Viètefuthi"; abafundi abaningi asebekhulile bayalikhumbula ithemu ngokwalo besesikoleni kanye neqiniso lokuthi umbuzo uvele kuma-quadratic equations. Lezi zimo "zingokwengqondo" ukubethela ulwazi.

Akumangazi noyedwa UFrancois Viet (1540-1603) wayebambe iqhaza ekubhalweni kwemfihlo enkantolo kaHenry IV (inkosi yokuqala yaseFrance evela ebukhosini baseBourbon, 1553-1610) futhi wakwazi ukuphula i-cipher eyasetshenziswa amaBrithani empini neFrance. Ngakho wadlala indima efanayo nezazi zezibalo zasePoland (eziholwa nguMarian Rejewski), ezathola izimfihlo zomshini wokuhlanganisa i-German Enigma cipher ngaphambi kweMpi Yezwe II.

indaba ephathwayo yemfashini

Impela. Isihloko esithi "amakhodi nama-ciphers" sekuyisikhathi eside saba yimfashini ekufundiseni. Sengike ngabhala ngalokhu izikhathi eziningana, futhi ezinyangeni ezimbili kuzoba nolunye uchungechunge. Kulokhu ngibhala ngaphansi kwefilimu ekhuluma ngempi ka-1920, lapho ukunqoba kwakubangelwa kakhulu ukwephulwa kwemithetho yamasosha amaBolshevik yiqembu elaliholwa abasha ngaleso sikhathi. UVaclav Sierpinski (1882-1969). Cha, akukabi i-Enigma, isingeniso nje. Ngikhumbula isigcawu sefilimu lapho u-Józef Piłsudski (odlalwa u-Daniil Olbrychski) ethi kunhloko yomnyango we-cipher:

Imilayezo ekhonjiwe yayiphethe umyalezo obalulekile: Amasosha kaTukhachevsky ayengeke athole ukwesekwa. Ungakwazi ukuhlasela!

Ngangazi uVaclav Sierpinski (uma ngingasho kanjalo: Ngangingumfundi osemusha, wayenguprofesa odumile), waya ezifundweni zakhe nasezifundweni zakhe. Wanikeza umbono wesazi esibunile, esingenangqondo, esimatasa nesiyalo sakhe futhi singawuboni omunye umhlaba. Wayefundisa ngokuqondile, ebheke ebhodini, engabheki izethameli ... kodwa wazizwa enguchwepheshe ovelele. Ngandlela-thile, wayenamakhono athile ezibalo - isibonelo, ukuxazulula izinkinga. Kukhona abanye—ososayensi ababi kakhulu ekuxazululeni izindida, kodwa abanokuqonda okujulile kwayo yonke ithiyori futhi abakwaziyo ukuqalisa yonke imikhakha yokusungula. Sidinga kokubili - nakuba eyokuqala izohamba ngokushesha.

UVaclav Sierpinski akakaze akhulume ngezimpumelelo zakhe ngo-1920. Kuze kube ngu-1939, lokhu kwakudingeka kugcinwe kuyimfihlo, futhi ngemva kuka-1945, labo ababelwa neSoviet Russia babengakujabuleli ukuzwelana neziphathimandla zangaleso sikhathi. Ukuqiniseka kwami ​​​​kokuthi ososayensi bayadingeka, njengebutho, kufakazelwa: "uma kwenzeka." Nangu uMongameli Roosevelt ebiza u-Einstein:

Isazi sezibalo saseRussia esivelele u-Igor Arnold sasho ngokusobala nangokudabukisayo ukuthi impi yaba nethonya elikhulu ekuthuthukisweni kwezibalo ne-physics (i-radar ne-GPS nazo zinemvelaphi yezempi). Angingeni esicini sokuziphatha sokusetshenziswa kwebhomu le-athomu: nansi ukunwetshwa kwempi unyaka kanye nokufa kwezigidi ezimbalwa zamasosha abo - kukhona ukuhlupheka kwabantu abangenacala.

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Ngibalekela ezindaweni engizaziyo - k. Abaningi bethu badlale ngamakhodi, mhlawumbe behlola, mhlawumbe kanjalo nje. Ama-ciphers alula, asekelwe esimisweni sokushintsha izinhlamvu ngezinye izinhlamvu noma ezinye izinombolo, aphulwa njalo uma sibamba izinkomba ezimbalwa kuphela (isibonelo, siqagela igama lenkosi). Ukuhlaziywa kwezibalo nakho kuyasiza namuhla. Okubi nakakhulu, lapho yonke into iyashintsha. Kodwa okubi kakhulu lapho kungekho njalo. Cabangela ikhodi echazwe ku-Adventures of the Good Soldier Schweik. Ngokwesibonelo, thatha incwadi ethi, UZamcolo. Nakhu ukusikisela ekhasini lokuqala nelesibili.

Sifuna ukubhala ngekhodi igama elithi "CAT". Sivula ekhasini 1 nangomzuzwana olandelayo. Sithola ukuthi ekhasini 1, uhlamvu K luvela okokuqala endaweni yama-59. Sithola igama lamashumi amahlanu nesishiyagalolunye ngakolunye uhlangothi. Igama elithi "i". Manje uhlamvu O. Kwesokunxele igama le-16, kanti eleshumi nesithupha kwesokudla lithi "Mnu." Uhlamvu T lusendaweni yama-95, uma ngibale kahle, futhi igama lamashumi ayisishiyagalolunye nesihlanu elisuka kwesokudla lithi "o". Ngakho, IKATI = 1 INKOSI O.

I-cipher "engenakulinganiswa", nakuba ihamba kancane kabuhlungu kokubili ekubetheleni kanye ... ngokuqagela. Ake sithi sifuna ukudlulisa uhlamvu M. Singabheka ukuthi siyalubhala yini igama elithi "Wołodyjowski". Futhi emva kwethu sebevele balungisa isitokisi sejele. Singathembela kuphela esikhundleni! Ngaphezu kwalokho, i-counterintelligence iphawula imibiko yabasebenzi abayimfihlo ukuthi isikhathi esithile amakhasimende abelokhu ethenga ngokuzithandela umthamo wokuqala weSikhukhula.

Isihloko sami siwumnikelo kule thesis: ngisho nemibono eyinqaba kakhulu yezibalo ingathola ukusetshenziswa kumkhuba oqondwa kabanzi. Isibonelo, kungenzeka yini ukucabanga ukutholwa kwezibalo okungasebenziseki kangako kunokuhlolwa kokuhlukaniswa ngo ... ngo-47?

Sikudinga nini empilweni? Futhi uma kunjalo, kuyoba lula ukuzama ukuyihlukanisa. Uma ihlukanisa, khona-ke kuhle, uma kungenjalo, ke ... okwesibili kuhle (siyazi ukuthi akuhlukanisi).

Indlela yokwaba futhi kungani

Ngemva kwalesi singeniso, ake siqhubekele phambili.Ingabe nina bafundi enizaziyo izimpawu zokuhlukana? Nakanjani. Ngisho nezinombolo zigcina ngo-2, 4, 6, 8, noma ziro. Inombolo ihlukaniswa ngokuthathu uma isamba samadijithi ayo sihlukaniswa ngokuthathu. Ngokufanayo, ngesibonakaliso sokuhlukaniswa ngesishiyagalolunye - isamba samadijithi kufanele sihlukaniseke ngesishiyagalolunye.

Ubani oyidingayo? Ngizobe ngiqamba amanga uma ngiqinisekisa uMfundi ukuthi ulungele noma yini enye ngaphandle... izabelo zesikole. Yebo, nesinye isici sokuhlukaniswa ngo-4 (futhi kuyini, Mfundi? Mhlawumbe uzoyisebenzisa uma ufuna ukwazi ukuthi i-Olympiad elandelayo iwela muphi unyaka ...). Kodwa isici sokuhlukaniswa ngama-47? Sekuyikhanda elibuhlungu. Siyoke sazi ukuthi into ihlukaniswa ngama-47? Uma kunjalo, thatha umshini wokubala ubone.

It. Uqinisile Mfundi. Nokho, qhubeka funda. Ngiyacela.

Uphawu lokuhlukaniswa ngo-47: Inombolo 100+ ihlukaniseka ngo-47 uma futhi kuphela uma u-47 ehlukaniswa ngo-+8.

Isazi sezibalo sizomamatheka ngokwaneliseka: "Gee, pretty." Kodwa izibalo ziyizibalo. Ubufakazi bubalulekile, futhi siyanaka nobuhle bayo. Ukufakazela kanjani isimilo sethu? Kulula kakhulu. Susa ku-100 + inombolo 94 - 47 = 47 (2 -). Sithola 100+-94+47=6+48=6(+8).

Sisuse inombolo ehlukanisekayo ngo-47, ngakho-ke uma u-6 (+ 8) ehlukaniswa ngo-47, kanjalo no-100 +. Kodwa inombolo u-6 ilingana no-47, okusho ukuthi u-6 (+ 8) uhlukaniswa ngo-47 uma futhi kuphela uma engu-+8. Ukuphela kobufakazi.

Asibone Ezinye izibonelo.

8805685 ihlukaniswa ngama-47? Uma sikuthakasela ngempela, sizothola ngokushesha nje ngokusehlukanisa njengoba safundiswa esikoleni samabanga aphansi. Ngandlela thize, manje sekukhona umshini wokubala kuwo wonke amaselula. Ihlukene? Yebo, yangasese 187355.

Hhayi-ke, ake sibone ukuthi isibonakaliso sokuhlukana sisitshelani. Sinqamula amadijithi amabili okugcina, siwaphindaphinde ngo-8, engeza umphumela "kunombolo encishisiwe" futhi wenze okufanayo ngenombolo ewumphumela.

8805685 → 88056 + 8 85 = 88736 → 887 + 8 36 = 1175 → 11 + 8 75 = 611 → 6 + 8 11 = 94.

Siyabona ukuthi u-94 uhlukaniswa ngo-47 (i-quotient ngu-2), okusho ukuthi inombolo yokuqala nayo iyahlukaniswa. Kuhle kakhulu. Kodwa kuthiwani uma siqhubeka sizijabulisa?

94 → 0 + 8 94 = 752 → 7 + 8 52 = 423 → 4 + 8 23 = 188 → 1 + 8 88 = 705 → 7 + 8 5 = 47.

Manje kufanele siyeke. Amashumi amane nesikhombisa ahlukaniswa ngama-47, akunjalo?

Ingabe ngempela kudingeka siyeke? Kuthiwani uma sidlulela phambili? O Nkulunkulu wami, kungenzeka noma yini ... ngizoyiyeka imininingwane. Mhlawumbe isiqalo nje:

47 → 0 + 8 47 = 376 → 3 + 8 76 = 611 → 6 + 8 11 = 94 → 0 + 8 94 = 752.

Kodwa, ngeshwa, kuyalutha njengokuhlafuna imbewu ...

752 → 7 + 8 * 52 = 423 → 4 + 8 * 23 = 188 → 1 + 8 * 88 = 705 → 7 + 8 * 5 = 47.

Ah, amashumi amane nesikhombisa. Kwenzeka ngaphambilini. Yini elandelayo? . Ngokufanayo. Izinombolo zihamba ngendlela kanje:

Kuyathakazelisa ngempela. Amaluphu amaningi.

Amabili izibonelo ezilandelayo.

Sifuna ukwazi ukuthi u-10017627 uhlukaniswa ngu-47. Kungani sidinga lolu lwazi? Sikhumbula isimiso: maye ngolwazi olungasizi owaziyo. Ulwazi luhlale lukhona kokuthile. Kuyoba yinto ethile, kodwa manje ngeke ngichaze. Amanye ama-akhawunti ambalwa:

10017627 → 100176 + 8 27 = 100392.

"Washintsha umalume wakhe waba yinduku." Sitholani kukho konke lokhu?

Ake siphinde inkambo yecala. Okungukuthi, sizoqhubeka sikwenza lokhu (okungukuthi, igama elithi “phinda”).

100392 → 1003 + 8 92 = 1739 → 17 + 8 39 = 329 → 3 + 8 29 = 235.

Asiwumise umdlalo, sihlukanise njengasesikoleni (noma emshinini wokubala): 235 = 5 47. Ibhingo. Inombolo yoqobo ethi 10017627 ihlukaniswa ngama-47.

Wenze kahle!

Kuthiwani uma sidlulela phambili? Ngithembe, ungakubheka.

Futhi elinye iqiniso elithakazelisayo. Sifuna ukuhlola ukuthi ingabe i-799 ihlukaniseka ngo-47. Sisebenzisa umsebenzi wokuhlukanisa. Sinqamula amadijithi amabili okugcina, siphindaphinda inombolo ewumphumela ngo-8 bese wengeza kokusele:

799 → 7 + 8 99 = 7 + 792 = 799.

Yini esinayo? Ingabe u-799 uhlukaniswa ngo-47 uma futhi kuphela uma u-799 ehlukaniswa ngo-47? Yebo, kunjalo, kodwa azikho izibalo ezidingekayo kulokhu !!! Amafutha anamafutha (okungenani lawa mafutha anamafutha).

Mayelana neqabunga, izigebengu kanye nokuphela kwamahlaya!

Ezinye izindaba ezimbili. Ikuphi indawo engcono kakhulu yokufihla iqabunga? Impendulo isobala: ehlathini! Kodwa ungayithola kanjani-ke?

Owesibili siwazi ezincwadini ezikhuluma ngezigebengu esizifunde kudala. Izigebengu zenza imephu yendawo lapho zigqibe khona umcebo. Abanye bake bayintshontsha noma bayinqoba impi. Kodwa ibalazwe alizange libonise ukuthi lalihloselwe isiphi isiqhingi. Futhi zibheke! Yebo, ama-pirates abhekana nalokhu (ukuhlukunyezwa) - ama-ciphers engikhuluma ngawo nawo angakhishwa ngokusebenzisa lezi zindlela.

Ukuphela kwamahlaya. Mfundi! Sakha i-cipher. Ngiyinhloli yomshoshaphansi futhi ngisebenzisa i-"Junior Technician" njengebhokisi lami lokuxhumana. Ngidlulisele imilayezo ebethelwe kanje.

Okokuqala, guqula umbhalo ube uchungechunge lwezinombolo usebenzisa ikhodi: AB CDEFGH IJ KLMN OP RST UWX Y Z1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Njengoba ungabona, asisebenzisi izinhlamvu zesi-Polish (okungukuthi ngaphandle kuka-ą, ę, ć, ń, ó, ś) kanye no-q okungesona isiPolishi q, v - kodwa u-x ongeyena owe-Polish ukhona uma kwenzeka. Masifake amanye angama-25 njengesikhala (isikhala phakathi kwamagama). O, into ebaluleke kakhulu. Sicela ufake inombolo yekhodi 47.

Uyazi ukuthi kusho ukuthini lokho. Uya kumngane wezibalo.

Ehlahle amehlo umngani ngokumangala.

Uphendula ngokuziqhenya:

Isazi sezibalo sikunikeza lesi sici... futhi usuvele uyazi ukuthi umsebenzi obukeka ungabonakali usetshenziselwa ukubethela.

ngoba iphethini elinjalo liyisenzo esichaziwe

100+→+8.

Ngakho-ke, uma ufuna ukwazi ukuthi inombolo isho ukuthini, njengokuthi 77777777 kumlayezo obethelwe, usebenzisa umsebenzi

100 + → + 8

uze uthole inombolo ephakathi kuka-1 no-25. Manje bheka ikhodi yezinhlamvu nezinombolo ecacile. Ake sibone: 77777777 →… Lokhu ngikushiyela njengomsebenzi. Kodwa ake sibone ukuthi yiluphi uhlamvu 48 olufihlayo? Masifunde:

48 → 0 + 8 48 = 384.

Bese sitholana ngokulandelana:

384 → 3 + 8 84 = 675 → 6 + 8 75 = 606 → 6 + 8 6 = 54 → 0 + 8 54 = 432…

Isiphetho asibonakali. Kuphela ngemva kwesikhathi samashumi ayisithupha (!) lapho kuzovela inombolo engaphansi kwama-25. Lona ngu-3, ​​okusho ukuthi u-48 uwuhlamvu C.

Futhi lomlayezo usinikani? (Ngifuna ukukukhumbuza ukuthi sisebenzisa ikhodi inombolo 47):

80 - 152 - 136 - 546 - 695719 - 100 - 224 - 555 - 412 - 111 - 640 - 102 - 152 - 12881 - 444 - 77777777 - 59 - 408 373 1234567 341 - XNUMX XNUMX

Awu, cabanga ngakho, yini eyinkimbinkimbi, amanye ama-akhawunti. Sesiqalile. Early 80. Umthetho owaziwayo:

80 → 0 + 8 80 = 640 → 6 + 8 40 = 326.

Iqhubeka kanje:

326 → 211 → 90 → 720 → 167 → 537 → 301 → 11.

Yidla! Incwadi yokuqala yomlayezo ithi K. Phew, kulula, kodwa kuzothatha isikhathi esingakanani?

Ake sibone futhi ukuthi ingakanani inkinga okufanele sibe nayo ngenombolo ethi 1234567. Ngesikhathi seshumi nesithupha kuphela sizothola inombolo engaphansi kuka-25, okungukuthi u-12. Ngakho-ke u-1234567 ngu-L.

Kulungile, omunye angase athi, kodwa lokhu kusebenza kwe-arithmetic kulula kangangokuthi ukuyihlela kukhompuyutha kuzophula ikhodi ngokushesha. Yebo kuyiqiniso. Lezi izibalo zekhompyutha ezilula. umqondo nge i-cipher yomphakathi futhi kumayelana nokwenza izibalo zibe nzima kukhompyutha. Ivumele isebenze okungenani iminyaka eyikhulu. Ingabe uzosusa ukubethela umlayezo? Akunandaba. Ngeke kube nandaba isikhathi eside. Yilokhu (okuncane noma okuncane) okumayelana nama-ciphers omphakathi. Zingaphulwa uma usebenza isikhathi eside ... kuze kube yilapho izindaba zingasabalulekile.

 ihlale izale "counterwears". Konke kwaqala ngenkemba nesihlangu. I-Secret Services ikhokha izizumbulu zemali kochwepheshe bezibalo abanesiphiwo ukuze basungule izindlela zokubethela amakhompyutha (kuhlanganise nalawo adalwe yithi) angeke akwazi ukuwaqhekeza ngekhulu lesi-XNUMX.

ekhulwini lamashumi amabili nambili? Akunzima kangako ukwazi ukuthi kakade sekunabantu abaningi emhlabeni abayophila kuleli khulu leminyaka elihle!

Oh huh? Kuthiwani uma ngicela (mina, Isikhulu Esiyimfihlo ethintwe “Uchwepheshe Omusha”) ukuthi ngibhale ngekhodi inombolo 23? Noma 17? Kulula:

Kwangathi singelokothe ​​sisebenzise izibalo kulezo zinhloso.

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Isihloko sendatshana sikhuluma ngezinkondlo. Uhlangene ngani nalokhu?

Njengani? Izinkondlo zibuye zibethele umhlaba.

Kanjani?

Ngezindlela zabo - ezifana ne-algebraic.