Equations, ma code, ciphers, masamu ndi ndakatulo

Michal Shurek anati ponena za iye: “Ndinabadwa mu 1946. Ndinamaliza maphunziro anga ku yunivesite ya Warsaw mu 1968 ndipo kuyambira pamenepo ndakhala ndikugwira ntchito ku Faculty of Mathematics, Informatics and Mechanics. Katswiri wa sayansi: algebraic geometry. Posachedwa ndidakumana ndi ma vector bundles. Kodi mtengo wa vector ndi chiyani? Choncho, ma vectors ayenera kumangirizidwa mwamphamvu ndi ulusi, ndipo tili ndi gulu kale. Mnzanga wasayansi Anthony Sim adandipangitsa kuti ndilowe nawo a Young Technician (akuvomereza kuti akuyenera kulandira malipiro anga). Ndinalemba zolemba zingapo kenako ndinakhala, ndipo kuyambira 1978 mutha kuwerenga mwezi uliwonse zomwe ndikuganiza za masamu. Ndimakonda mapiri ndipo, ngakhale kuti ndine wonenepa kwambiri, ndimayesetsa kuyenda. Ndikuganiza kuti aphunzitsi ndi ofunika kwambiri. Ndikadasunga andale, zilizonse zomwe angasankhe, m'malo otetezedwa kwambiri kuti asathawe. Dyetsani kamodzi patsiku. Chinsomba cha ku Tulek chimandikonda.

Equation ili ngati cipher kwa katswiri wa masamu. Kuthetsa ma equation, quintessence ya masamu, ndikuwerenga kwa ciphertext. Izi zadziwika ndi akatswiri azaumulungu kuyambira zaka za zana la XNUMX. John Paul II, yemwe ankadziwa masamu, analemba ndi kutchula izi kangapo mu ulaliki wake - mwatsoka, mfundo zachotsedwa m'chikumbukiro changa.

Mu sayansi ya sukulu, imayimiridwa Pythagoras monga mlembi wa theorem pa kudalira kwina mu makona atatu oyenera. Chifukwa chake idakhala gawo la filosofi yathu ya Eurocentric. Ndipo komabe Pythagoras ali ndi zabwino zambiri. Ndi iye amene anapatsa ophunzira ake udindo "wophunzira dziko lapansi", kuchokera "kuseri kwa phirili ndi chiyani?" asanaphunzire za nyenyezi. Ndicho chifukwa chake anthu a ku Ulaya "anapeza" zitukuko zakale, osati mosemphanitsa.

Owerenga ena amakumbukiraZithunzi za Viètendi"; owerenga ambiri achikulire amakumbukira mawu omwewo kuchokera kusukulu komanso pafupifupi kuti funso lidawonekera mu quadratic equations. Nthawi zonse izi ndi "malingaliro" kubisa zambiri.

Palibe zodabwitsa mmodzi Francois Viet (1540-1603) anali kuchita cryptography pa khoti Henry IV (woyamba French mfumu ku Bourbon mafumu, 1553-1610) ndipo anatha kuswa cipher ntchito British pa nkhondo ndi France. Chifukwa chake adachitanso chimodzimodzi ndi akatswiri a masamu aku Poland (otsogozedwa ndi Marian Rejewski), omwe adapeza zinsinsi zamakina a German Enigma cipher Nkhondo Yachiwiri Yadziko Lonse isanachitike.

mafashoni theme

Ndendende. Mutu wakuti "ma codes ndi ciphers" wakhala wamakono pophunzitsa. Ndalemba kale za izi kangapo, ndipo m'miyezi iwiri padzakhala mndandanda wina. Nthawi ino ndikulemba ndikuwonetsa filimu yonena za nkhondo ya 1920, pomwe kupambanaku kudachitika makamaka chifukwa chakuphwanya malamulo a gulu lankhondo la Bolshevik ndi gulu lotsogozedwa ndi achinyamata panthawiyo. Vaclav Sierra (1882-1969). Ayi, si Enigma pano, ndi mawu oyamba. Ndikukumbukira chochitika cha mufilimuyi pomwe Józef Piłsudski (woseweredwa ndi Daniil Olbrychski) akunena kwa mkulu wa dipatimenti ya cipher:

Mauthenga osinthidwawo anali ndi uthenga wofunikira: Asilikali a Tukhachevsky sakanalandira chithandizo. Mutha kuwukira!

Ndinamudziwa Vaclav Sierpinski (ngati ndinganene choncho: Ndinali wophunzira wamng'ono, anali pulofesa wotchuka), ndinapita ku maphunziro ake ndi masemina. Anapereka chithunzi cha wophunzira wofota, wopanda nzeru, wotanganidwa ndi maphunziro ake komanso osawona dziko lina. Anaphunzitsa mwachindunji, moyang'anizana ndi bolodi, osayang'ana omvera ... koma adamva ngati katswiri wodziwika bwino. Mwanjira ina, iye anali ndi luso la masamu - mwachitsanzo, kuthetsa mavuto. Palinso ena—asayansi amene amalephera kuthetsa ma puzzles, koma amene amamvetsa bwino chiphunzitso chonsecho ndipo amatha kuyambitsa mbali zonse za kulenga. Timafunikira zonse ziwiri - ngakhale yoyamba iyenda mwachangu.

Vaclav Sierpinski sanalankhulepo za zomwe adachita mu 1920. Kufikira 1939, izi zinayenera kubisidwadi, ndipo pambuyo pa 1945, amene anamenyana ndi Soviet Russia sanasangalale ndi chifundo cha akuluakulu a panthaŵiyo. Chikhulupiriro changa chakuti asayansi akufunika, monga gulu lankhondo, amatsimikiziridwa: "pokhapokha." Nayi Purezidenti Roosevelt akuyitana Einstein:

Katswiri wodziwika bwino wa masamu wa ku Russia Igor Arnold ananena momveka bwino komanso momvetsa chisoni kuti nkhondoyi inakhudza kwambiri masamu ndi physics (rada ndi GPS zinali ndi chiyambi chankhondo). Sindikupita kuzinthu zamakhalidwe abwino zogwiritsira ntchito bomba la atomiki: apa pali kuwonjezereka kwa nkhondo kwa chaka chimodzi ndi imfa ya mamiliyoni angapo a asilikali awo - pali kuzunzika kwa anthu osalakwa.

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Ndimathawira kumadera omwe ndimawadziwa - k. Ambiri aife tinkasewera ndi ma code, mwina kukafufuza, mwina monga choncho. Ma ciphers osavuta, ozikidwa pa mfundo yosinthira zilembo ndi zilembo zina kapena manambala ena, amasweka pafupipafupi ngati tingopeza zidziwitso zochepa (mwachitsanzo, tikuganiza kuti dzina la mfumu). Kusanthula ziwerengero kumathandizanso masiku ano. Choipa kwambiri, pamene chirichonse chikusintha. Koma choyipa kwambiri ndi pamene palibe chizolowezi. Talingalirani malamulo ofotokozedwa mu The Adventures of the Good Soldier Schweik. Mwachitsanzo, talingalirani buku lakuti, The Flood. Nazi malingaliro omwe ali patsamba loyamba ndi lachiwiri.

Tikufuna kuyika mawu oti "CAT". Timatsegula patsamba 1 ndi sekondi yotsatira. Tikupeza kuti patsamba 1, chilembo K chikuwonekera koyamba pa malo a 59. Ife tikupeza mawu makumi asanu ndi anayi kumbali inayo, mbali inayo. Ndi mawu "a". Tsopano chilembo O. Kumanzere ndi mawu a 16, ndipo chakhumi ndi chisanu ndi chimodzi kumanja ndi "Bambo." Chilembo T chili pa malo a 95, ngati ndinawerenga molondola, ndipo mawu makumi asanu ndi anayi mphambu asanu kuchokera kumanja ndi "o". Chifukwa chake, Mphaka = 1 AMBUYE O.

Cipher "yosatheka", ngakhale imachedwa pang'onopang'ono pobisa komanso ... Tiyerekeze kuti tikufuna kupatsira chilembo M. Tikhoza kuyang'ana ngati tiyilemba ndi mawu oti "Wołodyjowski". Ndipo pambuyo pathu akukonza kale chipinda cha ndende. Titha kungodalira m'malo! Kuphatikiza apo, counterintelligence imalemba malipoti a antchito achinsinsi omwe kwa nthawi yayitali makasitomala akhala akugula mofunitsitsa buku loyamba la Chigumula.

Nkhani yanga ndikuthandizira ku lingaliro ili: ngakhale malingaliro odabwitsa kwambiri a masamu amatha kugwiritsidwa ntchito m'njira yomveka bwino. Mwachitsanzo, kodi ndizotheka kuganiza zakupeza masamu osathandiza kuposa momwe mungagawidwe ... ndi 47?

Kodi ndi liti pamene timafunikira moyo? Ndipo ngati ndi choncho, kudzakhala kosavuta kuyesa kulilekanitsa. Ngati igawanika, ndiye kuti ndi yabwino, ngati sichoncho, ndiye ... chachiwiri ndi chabwino (tikudziwa kuti sichigawanitsa).

Momwe mungagawire komanso chifukwa

Pambuyo pa mawu oyambawa, tiyeni tipitirire.Kodi inu owerenga mukudziwa zizindikiro zogawanika? Ndithudi. Ngakhale manambala amatha ndi 2, 4, 6, 8, kapena ziro. Nambala imagawika ndi atatu ngati kuchuluka kwa manambala ake kugawika ndi atatu. Mofananamo, ndi chizindikiro cha kugawanika ndi zisanu ndi zinayi - chiwerengero cha manambala chiyenera kugawidwa ndi zisanu ndi zinayi.

Ndani akuchifuna? Ndikanama ngati nditatsimikizira Wowerengayo kuti anali wabwino kwa china chilichonse kupatula ... ntchito zakusukulu. Chabwino, ndi gawo lina la kugawanika ndi 4 (ndipo ndi chiyani, Reader? Mwinamwake mudzagwiritsa ntchito pamene mukufuna kudziwa chaka chomwe Olympiad yotsatira ikugwera ...). Koma gawo la kugawanika ndi 47? Uwu uli kale mutu. Kodi tidzadziwa ngati china chake chigawika ndi 47? Ngati inde, tengani chowerengera ndikuwona.

Izi ndi. Mukulondola, Reader. Ndipo komabe, werenganibe. Mwalandilidwa.

Chiwonetsero cha kugawanika ndi 47: Nambala 100+ imagawidwa ndi 47 pokhapokha ngati 47 igawidwa ndi +8.

Katswiri wa masamu adzamwetulira mokhutira: "Gee, wokongola." Koma masamu ndi masamu. Umboni ndi wofunika, ndipo timalabadira kukongola kwake. Kodi tingasonyeze bwanji khalidwe lathu? Ndi zophweka kwambiri. Chotsani ku 100 + nambala 94 - 47 = 47 (2 -). Timapeza 100+-94+47=6+48=6(+8).

Tachotsa nambala yomwe imagawika ndi 47, ndiye ngati 6 (+ 8) igawika ndi 47, ndiye kuti 100 +. Koma nambala 6 ndi coprime ku 47, kutanthauza kuti 6 (+ 8) amagawidwa ndi 47 ngati ndi + 8. Mapeto a umboni.

Tiyeni tiwone Zitsanzo zina.

8805685 imagawidwa ndi 47? Ngati tili ndi chidwi ndi izi, tidzadziwa posachedwa potigawanitsa monga momwe tidaphunzitsira kusukulu ya pulaimale. Mwanjira ina, tsopano pali chowerengera mu foni iliyonse yam'manja. Wogawanika? Inde, payekha 187355.

Chabwino, tiyeni tiwone chimene chizindikiro cha kugawanika chikutiuza. Timadula manambala awiri omaliza, kuwachulukitsa ndi 8, onjezerani zotsatira ku "nambala yochepetsedwa" ndikuchita chimodzimodzi ndi chiwerengerocho.

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

Tikuwona kuti 94 imagawidwa ndi 47 (quotient ndi 2), zomwe zikutanthauza kuti nambala yoyambirira imagawikanso. Chabwino. Koma bwanji ngati tipitirizabe kusangalala?

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

Tsopano tiyenera kusiya. Makumi anayi ndi asanu ndi awiri amagawidwa ndi 47, sichoncho?

Kodi tiyeneradi kusiya? Bwanji ngati titapitirira? O Mulungu wanga, chilichonse chitha kuchitika ... sindidzasiya tsatanetsatane. Mwina chiyambi chabe:

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

Koma, mwatsoka, ndizovuta monga kutafuna njere ...

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

Ah, makumi anayi ndi seveni. Zinachitika kale. Chotsatira ndi chiyani? . Momwemonso. Nambala zimayenda mozungulira motere:

Ndizosangalatsa kwenikweni. Malupu ambiri.

Awiri zitsanzo zotsatirazi.

Tikufuna kudziwa ngati 10017627 imagawika ndi 47. N’chifukwa chiyani timafunika kudziwa zimenezi? Timakumbukira mfundo yakuti: Tsoka ku chidziwitso chomwe sichithandiza wodziwa. Chidziwitso chilipo nthawi zonse pa chinachake. Zidzakhala za chinachake, koma tsopano sindifotokoza. Maakaunti enanso angapo:

10017627 → 100176 + 8 27 = 100392.

"Anawasintha amalume ake kukhala nkhwangwa kukhala ndodo." Kodi timapeza chiyani kuchokera ku zonsezi?

Chabwino, tiyeni tibwereze zochitikazo. Ndiko kuti, tidzapitiriza kuchita izi (ndiko kuti, mawu oti "kubwereza").

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

Tiyeni tiyime masewera, gawani ngati kusukulu (kapena pa chowerengera): 235 = 5 47. Bingo. Nambala yoyambirira 10017627 imagawidwa ndi 47.

Mwachita bwino!

Bwanji ngati titapitirira? Ndikhulupirireni mutha kuziwona.

Ndipo mfundo ina yosangalatsa. Tikufuna kuwona ngati 799 ikugawanika ndi 47. Timagwiritsa ntchito ntchito yogawa. Timadula manambala awiri omaliza, kuchulukitsa chiwerengerocho ndi 8 ndikuwonjezera zomwe zatsala:

799 → 7 + 8 99 = 7 + 792 = 799.

Kodi tili ndi chiyani? Kodi 799 imagawidwa ndi 47 ngati 799 igawidwa ndi 47? Inde, koma palibe masamu omwe amafunikira pa izi !!! Mafutawa ali ndi mafuta (osachepera mafuta awa ndi mafuta).

Za tsamba, achifwamba ndi kutha kwa nthabwala!

Nkhani zina ziwiri. Malo abwino kwambiri obisala tsamba ndi ati? Yankho ndi lodziwikiratu: m'nkhalango! Koma mungachipeze bwanji pamenepo?

Chachiwiri chimene timachidziwa m’mabuku onena za achifwamba omwe tinawerenga kalekale. Achifwambawo anapanga mapu a malo amene anakwirira chumacho. Ena anaba kapena kupambana pankhondoyo. Koma mapu sanasonyeze chilumba chimene anakonzera. Ndipo dziyang'aneni nokha! Inde, achifwamba adalimbana ndi izi (kuzunzika) - zilembo zomwe ndikunena zitha kutulutsidwanso pogwiritsa ntchito njira zotere.

Mapeto a nthabwala. Wowerenga! Timapanga cipher. Ndine kazitape wobisika ndipo ndimagwiritsa ntchito "Junior Technician" ngati bokosi langa lolumikizana. Nditumizireni mauthenga obisika motere.

Choyamba, sinthani mawuwo kukhala mndandanda wa manambala pogwiritsa ntchito code: AB CDEFGH IJ KLMN PA 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

Monga mukuonera, sitigwiritsa ntchito zilembo za Chipolishi (ie popanda ą, ę, ć, ń, ó, ś) ndi q, v - koma osati Chipolishi x alipo basi. Tiyeni tiphatikizepo ena 25 ngati danga (danga pakati pa mawu). O, chinthu chofunikira kwambiri. Chonde lembani nambala 47.

Inu mukudziwa chimene izo zikutanthauza. Inu mumapita kwa bwenzi masamu.

Mnzakeyo anangotuluka maso modabwa.

Mukuyankha monyadira:

Katswiri wa masamu amakupatsirani izi ... ndipo mukudziwa kale kuti chinthu chowoneka bwino chimagwiritsidwa ntchito pobisalira.

chifukwa chitsanzo choterocho ndi ntchito yofotokozedwa

100+→+8.

Chifukwa chake, mukafuna kudziwa zomwe nambala imatanthauza, monga 77777777 mu uthenga wobisika, mumagwiritsa ntchito ntchitoyi.

100+→+8

mpaka mutapeza nambala pakati pa 1 ndi 25. Tsopano yang'anani pa nambala ya zilembo zachidule. Tiyeni tiwone: 77777777 →… Ndikusiyirani izi ngati ntchito. Koma tiyeni tiwone kuti kalata 48 imabisa chiyani? Tiyeni tiwerenge:

48 → 0 + 8 48 = 384.

Kenako timapita motsatira:

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

Mapeto sali kuonekera. Pokhapokha ikatha nthawi ya makumi asanu ndi limodzi (!) nambala yosakwana 25 idzawonekera. Ichi ndi 3, kutanthauza 48 ndi chilembo C.

Nanga uthenga umenewu umatipatsa ciani? (Ndikufuna kukukumbutsani kuti timagwiritsa ntchito nambala 47):

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

Chabwino, taganizirani za izo, zomwe ziri zovuta kwambiri, nkhani zina. Tayamba. Kumayambiriro kwa zaka 80. Lamulo lodziwika:

80 → 0 + 8 80 = 640 → 6 + 8 40 = 326.

Ikupitilira motere:

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

Idyani! Kalata yoyamba ya uthengawo ndi K. Phew, yosavuta, koma itenga nthawi yayitali bwanji?

Tiyeni tiwonenso zovuta zomwe tiyenera kukhala nazo ndi nambala 1234567. Pa nthawi yakhumi ndi chisanu ndi chimodzi tidzapeza nambala yosakwana 25, yomwe ndi 12. Kotero 1234567 ndi L.

Chabwino, wina anganene, koma ntchito ya masamuyi ndiyosavuta kotero kuti kuyipanga pakompyuta kumaswa nthawi yomweyo. Inde ndi zoona. Awa ndi mawerengedwe osavuta apakompyuta. malingaliro ndi cipher pagulu komanso ndikupangitsa mawerengedwe kukhala ovuta pakompyuta. Chiloleni icho chigwire ntchito kwa zaka zana limodzi. Kodi adzasintha uthengawo? Zilibe kanthu. Zilibe kanthu kwa nthawi yayitali. Izi ndi (zochuluka kapena zochepa) zomwe ma ciphers a anthu onse ali nazo. Iwo akhoza kusweka ngati inu ntchito kwa nthawi yaitali kwambiri ... mpaka nkhani zilibenso zofunika.

 zakhala zikubala "zida zolimbana nazo". Zonsezi zinayamba ndi lupanga ndi chishango. A Secret Services amapereka ndalama zambiri kwa akatswiri a masamu aluso kuti apange njira zolembera zomwe makompyuta (kuphatikiza omwe adapangidwa ndi ife) sadzatha kusweka mzaka za zana la XNUMX.

zaka makumi awiri mphambu ziwiri? Sikovuta kwambiri kudziŵa kuti pali kale anthu ambiri padziko lapansi amene adzakhala m’zaka za zana lokongolali!

O ndi? Bwanji ngati nditafunsa (ine, Ofesi Yachinsinsi yemwe adalumikizidwa ndi "Technician Wachichepere") kuti alembe ndi nambala 23? kapena 17? Zosavuta:

Tisagwiritse ntchito masamu pazifukwa zotere.

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Mutu wa nkhaniyi ndi wa ndakatulo. Kodi iye akuyenera kuchita chiyani nazo?

Monga chiyani? Ndakatulo imabisanso dziko lapansi.

Motani?

Mwa njira zawo - zofanana ndi algebraic.