Equation, macode, ciphers, masvomhu uye nhetembo

Michal Shurek anoti nezvake: “Ndakaberekwa muna 1946. Ndakapedza kudzidza kuWarsaw University muna 1968 uye kubvira ipapo ndanga ndichishanda kuFaculty of Mathematics, Informatics and Mechanics. Sainzi nyanzvi: algebraic geometry. Ini nguva pfupi yadarika ndakabata nevector bundles. Chii chinonzi vector beam? Saka, mavheti anoda kusungirirwa zvakasimba neshinda, uye isu tatova neboka. Shamwari yangu yefizikisi Anthony Sim akandiita kuti ndibatane neMudiki Technician (anobvuma kuti anofanirwa kunge achiwana mari kubva mubhadharo yangu). Ndakanyora zvinyorwa zvishoma ndokubva ndagara, uye kubvira muna 1978 unogona kuverenga mwedzi woga woga zvandinofunga nezvemasvomhu. Ndinoda makomo uye, pasinei nekurema, ndinoedza kufamba. Ndinofunga vadzidzisi ndivo vakanyanya kukosha. Ini ndaizochengeta vezvematongerwo enyika, chero vangasarudza, munzvimbo inochengetedzwa zvakanyanya kuti vasazopukunyuka. Dyisa kamwe pazuva. Bea rinobva kuTulek rinondida.

Equation yakafanana necipher yenyanzvi yemasvomhu. Kugadzirisa equations, iyo quintessence yemasvomhu, kuverenga kweciphertext. Izvi zvakaonekwa nevafundisi kubva muzana ramakore rechiXNUMX. John Paul II, uyo aiziva masvomhu, akanyora uye akataura izvi kakawanda mumharidzo dzake - zvinosuruvarisa kuti chokwadi chakadzimwa mundangariro dzangu.

Muchikoro sayenzi, inomiririrwa Pythagoras semunyori weiyo theorem pane kumwe kutsamira mugonyo rekurudyi. Saka yakava chikamu cheuzivi hwedu hweEurocentric. Uye zvakadaro Pythagoras ane humwe hunhu hwakanaka. Ndiye iye akaisa kuvadzidzi vake basa re "kuziva nyika", kubva "chii chiri kuseri kwechikomo ichi?" asati adzidza nyeredzi. Ndokusaka veEurope "vakawana" budiriro yekare, uye kwete zvinopesana.

Vamwe vaverengi vanorangariraViète mapataniuye"; vaverengi vakura vazhinji vanorangarira temu pachayo kubva kuchikoro uye nezve chokwadi chekuti mubvunzo wakabuda muquadratic equations. Aya maitiro ari "ideologically" encryption ruzivo.

Hameno mumwe Francois Viet (1540-1603) aiita zvekunyora padare raHenry IV (mambo wekutanga weFrance kubva kudzinza reBourbon, 1553-1610) uye akakwanisa kutyora cipher yakashandiswa nemaBritish muhondo neFrance. Saka akaita basa rakafanana nerenyanzvi dzemasvomhu dzekuPoland (vakatungamirwa naMarian Rejewski) vakawana zvakavanzika zveGerman Enigma cipher muchina Hondo Yenyika II isati yasvika.

fashion theme

Ndizvozvo. Musoro wekuti "codes uye ciphers" wagara wave mufashoni mukudzidzisa. Ndakatonyora pamusoro peizvi kakawanda, uye mumwedzi miviri pachava nedzimwe dzakatevedzana. Panguva ino ndiri kunyora pasi pechiratidzo chefirimu pamusoro pehondo ya1920, uko kukunda kwakakonzerwa zvikuru nekuputswa kwebumbiro remauto eBolshevik nechikwata chaitungamirwa nevadiki panguva iyoyo. Vaclav Serpinsky (1882-1969). Kwete, haisati yave Enigma, ingori sumo. Ndinorangarira chiitiko chemufirimu apo Józef Piłsudski (akaridzwa naDaniil Olbrychski) anoti kumukuru wedhipatimendi recipher:

Iwo mameseji akadhindwa akatakura meseji yakakosha: Mauto aTukhachevsky aisazogamuchira rutsigiro. Unogona kurwisa!

Ndaiziva Vaclav Sierpinski (kana ndingataura kudaro: Ndakanga ndiri mudzidzi wechidiki, akanga ari purofesa ane mukurumbira), akapinda hurukuro dzake uye seminamato. Akapa fungidziro yenyanzvi yakasvava, yakatsauswa, yakabatikana nechirango chake uye kusaona imwe nyika. Ainyatsodzidzisa, akatarisana nebhodhi, asingatarise vateereri ... asi ainzwa senyanzvi. Imwe nzira kana imwe, aiva nemamwe masvomhu mano - somuenzaniso, kugadzirisa matambudziko. Kune vamwe, masayendisiti akashata pakugadzirisa mapuzzle, asi vane kunzwisisa kwakadzama kwedzidziso yese uye vanokwanisa kutanga nzvimbo dzese dzekusika. Tinoda ese ari maviri - kunyangwe yekutanga ichafamba nekukurumidza.

Vaclav Sierpinski haana kumbotaura nezve zvaakaita muna 1920. Kutozosvikira muna 1939, ikoku zvamazvirokwazvo kwaifanira kuvanzwa pachivande, uye pashure pa1945, avo vakarwa neSoviet Russia havana kufarikanya tsitsi dzezviremera panguva iyoyo. Kutenda kwangu kuti masayendisiti anodiwa, seuto, anopupurirwa: "muchiitiko chete." Heino Mutungamiri Roosevelt anodana Einstein:

Nyanzvi yemasvomhu yekuRussia inonzi Igor Arnold yakataura pachena uye zvinosuruvarisa kuti hondo ine simba guru pakuvandudzwa kwemasvomhu nefizikisi (radar neGPS zvakare zvine mavambo echiuto). Ini handipindi muhunhu hwekushandiswa kwebhomba reatomu: heino kuwedzera kwehondo kwegore uye kufa kwemamiriyoni akati wandei emasoja avo - pane kutambura kwevanhu vasina mhosva.

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Ndinotizira kunzvimbo dzinozivikanwa - k.Vazhinji vedu takatamba nemakodhi, pamwe ndichitsvaga, pamwe zvakangodaro. Manyorero akareruka, akavakirwa pamusimboti wekutsiva mabhii nemamwe mavara kana dzimwe nhamba, anogaroputswa kana tikangobata mashoma mashoma (somuenzaniso, tinofungidzira zita ramambo). Statistical analysis inobatsirawo nhasi. Zvakaipisisa, kana zvinhu zvose zvichichinja. Asi chakanyanya kushata ndechekuti kana pasina nguva dzose. Funga nezvekodhi inotsanangurwa muThe Adventures of the Good Soldier Schweik. Tora bhuku, somuenzaniso, Mafashamo. Heano mazano ari papeji yekutanga nerechipiri.

Tinoda kukodha izwi rekuti "CAT". Tinovhura papeji 1 uye yechipiri inotevera. Tinoona kuti papeji 1, vara K rinotanga kuoneka munzvimbo yechi59. Tinowana izwi rechimakumi mashanu nepfumbamwe kune rumwe rutivi, kune rumwe rutivi. Izwi rokuti "a". Zvino vara O. Kuruboshwe ishoko rechi16, uye regumi nenhanhatu kurudyi ndi“Mr.” Tsamba T iri pachinzvimbo chechi95, kana ndakaverenga zvakanaka, uye izwi rechimakumi mapfumbamwe neshanu kubva kurudyi ndi "o". Saka, CAT = 1 ISHE O.

Cipher "risingagoneki", asi rinononoka zvinorwadza pakunyora uye ... nekufungidzira. Ngatitii tinoda kupfuudza vara M. Tinogona kutarisa kana tikaisa encode neshoko rokuti "Wołodyjowski". Uye mushure medu vari kutogadzira chitokisi chejeri. Tinogona chete kuvimba nekutsiva! Uye zvakare, counterintelligence inocherekedza mishumo yevashandi vepachivande avo kwenguva yakati vatengi vanga vachitenga nemoyo unoda vhoriyamu yekutanga yeMafashamo.

Chinyorwa changu mupiro kune iyi thesis: kunyangwe pfungwa dzinoshamisa dzemasvomhu dzinogona kuwana mashandisiro mumuitiro unonzwisiswa zvakanyanya. Semuyenzaniso, zvinogoneka here kufungidzira kuwanikwa kwemasvomhu kushoma pane bvunzo yekupatsanurwa ne... ne47?

Tinohuda rini muupenyu? Uye kana zvakadaro, zvichava nyore kuedza kuiparadzanisa. Kana ikapatsanura, zvino zvakanaka, kana zvisiri, zvino ... chechipiri zvakanaka (tinoziva kuti hazviparadzanise).

Nzira yekugovera sei uye nei

Mushure mesumo iyi, ngatienderei mberi.Imi vaverengi munoziva here zviratidzo zvekuparadzana? Zvirokwazvo. Kunyange manhamba anoguma muna 2, 4, 6, 8, kana zero. Nhamba inogovaniswa nenhatu kana huwandu hwenhamba dzayo huchipatsanurwa netatu. Saizvozvovo, nechiratidzo chekupatsanurwa nepfumbamwe - huwandu hwenhamba hunofanirwa kupatsanurwa nepfumbamwe.

Ndiani anoida? Ndinenge ndichinyepa kana ndikatendeudzira Muverengi kuti akanakira chimwe chinhu kunze ... mabasa echikoro. Zvakanaka, uye chimwe chimiro chekuparadzanisa ne 4 (uye chii, Muverengi? Zvimwe iwe uchaishandisa kana iwe uchida kuziva kuti Olympiad inotevera inowira gore ripi ...). Asi chimiro chekuparadzaniswa ne47? Uyu watova musoro. Tichazomboziva here kana chimwe chinhu chinoparadzaniswa ne47? Kana hongu, tora karukureta uone.

Izvi. Wataura chokwadi, Muverengi. Uye zvakadaro, ramba uchiverenga. Ndapota.

Kupatsanurwa na47: Nhamba 100+ inopatsanurika ne 47 kana uye chete kana 47 ichigovaniswa ne +8.

Nyanzvi yemasvomhu ichanyemwerera nekugutsikana: "Gee, tsvarakadenga." Asi masvomhu isvomhu. Uchapupu hune basa, uye tinoteerera kunaka kwahwo. Nzira yekuratidza sei hunhu hwedu? Zviri nyore kwazvo. Bvisa kubva pa100 + nhamba 94 - 47 = 47 (2 -). Tinowana 100+-94+47=6+48=6(+8).

Tabvisa nhamba inogovanwa ne47, saka kana 6 (+ 8) ichigovaniswa na47, saka zana +. Asi nhamba 100 inonyanyoda 6, zvinoreva kuti 47 (+ 6) inopatsanurwa ne 8 kana uye chete kana ari + 47. Kupera kwehumbowo.

Ngatione Mimwe mienzaniso.

8805685 inogovaniswa ne47? Kana tichinyatsozvifarira, tinozozviziva nekukasika nekungopatsanura sezvataidzidziswa kuchikoro chepuraimari. Imwe nzira kana imwe, ikozvino nhare yeserura ine calculator. Kuparadzaniswa? Hongu, zvakavanzika 187355.

Eya, ngationei kuti chiratidzo chokuparadzana chinotiudzei. Isu tinobvisa manhamba maviri ekupedzisira, towedzera ne8, wedzera mhedzisiro ku "truncated nhamba" uye ita zvimwechete nenhamba inobuda.

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

Tinoona kuti 94 inopatsanurwa ne 47 (iyo quotient ndi 2), zvinoreva kuti nhamba yekutanga inopatsanurika zvakare. Fine. Asi zvakadini kana tikaramba tichinakidzwa?

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

Zvino tinofanira kumira. Makumi mana nenomwe anopatsanurwa ne 47, handiti?

Tinofanira kurega chaizvoizvo here? Ko kana tikaenda mberi? Ah Mwari wangu, chero chinhu chinogona kuitika ... ini ndichasiya zvinyorwa. Pamwe chete kutanga:

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

Asi, zvinosuwisa, zvinopinda muropa sekutsenga mhodzi ...

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

Ah, makumi mana nemanomwe. Zvakaitika kare. Chii chinotevera? . Same. Nhamba dzinoenda muchiuno seizvi:

Zvinonakidza chaizvo. Zvishwe zvakawanda.

Two inotevera mienzaniso.

Tinoda kuziva kana 10017627 inopatsanurwa ne 47. Sei tichida ruzivo urwu? Tinoyeuka musimboti: nhamo kune ruzivo rusingabatsiri muzivi. Zivo inogara iripo kune chimwe chinhu. Zvichava zvechimwe chinhu, asi ikozvino handisi kuzotsanangura. Mamwe maakaundi mashoma:

10017627 → 100176 + 8 27 = 100392.

"Akachinja babamukuru kubva demo kuita tsvimbo." Chii chatinowana kubva pane zvese izvi?

Zvakanaka, ngatidzokorore mafambiro enyaya. Kureva kuti ticharamba tichiita izvi (ndiko kuti, izwi rekuti “iterate”).

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

Ngatimisei mutambo, tigovane semuchikoro (kana kuti karukureta): 235 = 5 47. Bhingo. Nhamba yekutanga 10017627 inoparadzaniswa ne47.

Kuita zvakanaka!

Ko kana tikaenda mberi? Vimba neni, unogona kuzviongorora.

Uye chimwe chokwadi chinonakidza. Tinoda kutarisa kana 799 inopatsanurwa ne 47. Isu tinoshandisa disibility function. Isu tinobvisa manhamba maviri ekupedzisira, towedzera nhamba inobuda ne8 uye towedzera kune chasara:

799 → 7 + 8 99 = 7 + 792 = 799.

Chii chatinacho? Ko 799 inogovaniswa ne47 kana uye chete kana 799 ichigovaniswa ne47? Hongu, ndizvozvo, asi hapana masvomhu anodiwa pane izvi !!! Oiri ine mafuta (zvishoma mafuta aya ane mafuta).

Nezveshizha, mahara uye kupera kwemajee!

Dzimwe nyaya mbiri. Ndeipi nzvimbo yakanaka yekuvanza shizha? Mhinduro iri pachena: musango! Asi ungahuwana sei ipapo?

Chechipiri chatinoziva kubva mumabhuku anotaura nezvemakororo ataverenga kare kare. Vapambi vakagadzira mepu yenzvimbo yavakaviga pfuma. Vamwe vakaiba kana kukunda pakurwa. Asi mepu yacho yaisaratidza kuti yaiitirwa chitsuwa chipi. Uye zvitsvakire iwe! Zvechokwadi, makororo akakunda izvi (kutambudzwa) - zvinyorwa zvandiri kutaura nezvazvo zvinogonawo kutorwa uchishandisa nzira dzakadaro.

Kupera kwemajee. Muverengi! Isu tinogadzira cipher. Ndiri musori wepachivande uye ndinoshandisa "Junior Technician" sebhokisi rangu rekuonana. Nditumire mameseji akavharidzirwa sezvizvi.

Chekutanga, shandura zvinyorwa kuita tambo yenhamba uchishandisa kodhi: AB CDEFGH IJ KLMN ON 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

Sezvauri kuona, isu hatishandise madhiakiriti echiPolish (kureva pasina ą, ę, ć, ń, ó, ś) uye asiri wechiPolish q, v - asi asiri wechiPolish x aripo kana zvikaitika. Ngatisanganise mamwe makumi maviri neshanu senzvimbo (nzvimbo pakati pemazwi). O, chinhu chakakosha. Ndokumbira uise kodhi nhamba 25.

Unoziva zvazvinoreva. Unoenda kushamwari yemasvomhu.

Maziso eshamwari akabva awedzera kushamisika.

Unopindura uchidada:

Nyanzvi yemasvomhu inokupa hunhu uhu ... uye iwe unotoziva kuti basa rinotaridzika risingataridzike rinoshandiswa encryption.

nokuti muenzaniso wakadaro chiito chakatsanangurwa

100+→+8.

Saka, kana iwe uchida kuziva kuti nhamba inorevei, se77777777 mune yakavharidzirwa meseji, unoshandisa basa

100+→+8

kusvika wawana nhamba iri pakati pe1 kusvika 25. Zvino tarisa kodhi yealphanumeric yakajeka. Ngationei: 77777777 →… Ndinokusiyirai izvi sebasa. Asi ngationei kuti vara 48 rinovanza chii? Ngativerenge:

48 → 0 + 8 48 = 384.

Ipapo isu tinosangana:

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

Kuguma hakusi kuoneka. Mushure menguva yechimakumi matanhatu (!) chete ndipo pachazoonekwa nhamba isingasviki 25. Uyu ndi3, zvinoreva kuti 48 ndiro vara C.

Uye shoko iri rinotipa chii? (Ndinoda kukuyeuchidza kuti tinoshandisa kodhi nhamba 47):

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

Zvakanaka, funga nezvazvo, chii chakanyanya kuomarara, mamwe maakaundi. Tatanga. Early 80. Mutemo unozivikanwa:

80 → 0 + 8 80 = 640 → 6 + 8 40 = 326.

Inoenderera seizvi:

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

Idya! Tsamba yekutanga yeshoko ndiK. Phew, iri nyore, asi inotora nguva yakareba sei?

Ngationeiwo kuti idambudziko rakawanda sei ratinofanira kuita nenhamba inoti 1234567. Panguva yechigumi nenhanhatu chete ndipo patichawana nhamba isingasviki makumi maviri neshanu, zvinoti 25. Saka 12 ndiL.

Zvakanaka, mumwe angati, asi basa remasvomhu iri riri nyore zvekuti kuigadzira pakombuta kunobva kwatyora kodhi. Hongu ichokwadi. Aya maverengero akareruka emakombuta. idea with public cipher uye zvakare nezvekuita kuti masvomhu anetsa komputa. Ngaishande kweanenge makore zana. Achadzima meseji yacho here? Hazvina basa. Hazvina basa kwenguva yakareba. Izvi ndizvo (zvizhinji kana zvishoma) izvo zvinorehwa neruzhinji ciphers. Vanogona kuputswa kana ukashanda kwenguva yakareba ... kusvikira nhau dzisisina basa.

 yagara ichibereka "counterweapons". Zvose zvakatanga nebakatwa nenhoo. Iyo Chakavanzika Services inobhadhara mazakwatira emari kune vane zvipo vane masvomhu kuti vagadzire nzira dzekunyorera idzo makomputa (kusanganisira ayo akagadzirwa nesu) haazokwanise kupaza muzana ramakore rechiXNUMX.

Makore makumi maviri nemaviri? Hazvina kunyanya kuoma kuziva kuti kwatova nevanhu vakawanda munyika vachararama muzana rino remakore rakanaka!

Ah huh? Ko kana ndikabvunza (ini, Iye Chakavanzika Officer akabatwa ne "Mudiki Technician") kunyora nekodhi nhamba 23? Kana 17? Nyore:

Ngatisambofanira kushandisa masvomhu nokuda kwezvinangwa zvakadaro.

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Musoro wechinyorwa ndewe nhetembo. Anei nazvo izvi?

Kufanana nei? Nhetembo zvakare inovharira nyika.

Sei?

Nemaitiro avo - akafanana nealgebraic.