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[{"key": "dc.contributor.advisor", "value": "Rajala, Tapio", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Heikkil\u00e4, Annika", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2025-03-18T06:10:43Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2025-03-18T06:10:43Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2025", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/100758", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa perehdyt\u00e4\u00e4n siihen, kuinka puolalaiset matemaatikot Marian Rejewski, Jerzy R\u00f3\u017cycki ja Henryk Zygalski mursivat saksalaisten Enigma-koneen salakirjoituksen hy\u00f6dynt\u00e4m\u00e4ll\u00e4 permutaatioteoriaa. Enigman salaus perustuu permutaatioiden tuloihin, ja tutkielmassa k\u00e4sitell\u00e4\u00e4n koodin murtamiseen k\u00e4ytettyj\u00e4 metodeja. \n\nLyhyen johdanto-osuuden j\u00e4lkeen k\u00e4yd\u00e4\u00e4n ensimm\u00e4isess\u00e4 kappaleessa l\u00e4pi matemaattisia tuloksia aiheeseen liittyen. Aluksi esitell\u00e4\u00e4n permutaation k\u00e4site ja sen eri notaatioesitykset. T\u00e4m\u00e4n j\u00e4lkeen esitell\u00e4\u00e4n ryhm\u00e4n m\u00e4\u00e4ritelm\u00e4 ja permutaatioiden ominaisuuksia. Kappaleessa k\u00e4yd\u00e4\u00e4n l\u00e4pi my\u00f6s my\u00f6hemmin k\u00e4ytett\u00e4v\u00e4n syklihajotelman ja transposition m\u00e4\u00e4ritelm\u00e4t, sek\u00e4 Rejewskin hy\u00f6dynt\u00e4mi\u00e4 lauseita ja niiden todistukset. \n\nToisessa kappaleessa k\u00e4sitell\u00e4\u00e4n lyhyelti salakirjoituksen historiaa ja eri salakirjoitusmenetelmi\u00e4 ja -laitteita. Kappaleessa esitell\u00e4\u00e4n sekoitus- ja korvausmenetelm\u00e4t ja annetaan n\u00e4ist\u00e4 esimerkit. Lis\u00e4ksi esitell\u00e4\u00e4n Albertin salakirjoituskiekko, johon Enigman salaus osin perustuu. \n\nKolmannessa kappaleessa tarkastellaan Enigma-laitteen rakennetta sek\u00e4 toimintaperiaate ja nimet\u00e4\u00e4n laitteen k\u00e4ytt\u00e4m\u00e4t permutaatiot. \n\nNelj\u00e4nness\u00e4 kappaleessa k\u00e4yd\u00e4\u00e4n aluksi l\u00e4pi Enigman teoreettisten asetusten lukum\u00e4\u00e4r\u00e4. Koska t\u00e4m\u00e4 lukum\u00e4\u00e4r\u00e4 ei vastaa todellisuutta siit\u00e4 vaihtoehtojen lukum\u00e4\u00e4r\u00e4st\u00e4, mist\u00e4 matemaatikot ty\u00f6ns\u00e4 aloittivat, esitell\u00e4\u00e4n my\u00f6s todellisen l\u00e4ht\u00f6tilanteen vaihtoehtojen m\u00e4\u00e4r\u00e4. Seuraavaksi kappaleessa l\u00e4hdet\u00e4\u00e4n esittelem\u00e4\u00e4n Rejewskin ty\u00f6t\u00e4 salauksen ratkaisemisessa. My\u00f6hemmin ty\u00f6t\u00e4 jatkoivat h\u00e4nen kanssaan R\u00f3\u017cycki ja Zygalski. Lis\u00e4ksi kerrotaan saksalaisten tekemist\u00e4 jatkuvista muutoksista Enigma-salaukseen ja puolalaisten kehitt\u00e4mist\u00e4 metodeista n\u00e4ihin muutoksiin reagoiden. \n\nViidenness\u00e4 kappaleessa kerrotaan ratkaisuty\u00f6n siirtymisest\u00e4 Iso-Britanniaan toisen maailmansodan alussa sek\u00e4 lyhyelti Bletchley Parkissa tehdyst\u00e4 ratkaisuty\u00f6st\u00e4 sodan aikana. Lopuksi tehd\u00e4\u00e4n lyhyt yhteenveto matemaatikoiden panoksesta Enigma-koodin ratkaisemisessa ennen toista maailmansotaa ja sen aikana.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2025-03-18T06:10:42Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2025-03-18T06:10:43Z (GMT). No. of bitstreams: 0\n Previous issue date: 2025", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "47", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": null, "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "Enigma", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "permutaatiot", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Rejewski", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Permutaatiot Enigma-salauksen ratkaisemisessa", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202503182573", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikan opettajankoulutus", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teacher education programme in Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.copyright", "value": "\u00a9 The Author(s)", "language": "fi", "element": "rights", "qualifier": "copyright", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.yso", "value": "salakirjoitus", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "toinen maailmansota", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "historia", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "kryptografia", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "salaus", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "kryptologia", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.description.accessibilityfeature", "value": "unknown accessibility", "language": "en", "element": "description", "qualifier": "accessibilityfeature", "schema": "dc"}, {"key": "dc.description.accessibilityfeature", "value": "ei tietoa saavutettavuudesta", "language": "fi", "element": "description", "qualifier": "accessibilityfeature", "schema": "dc"}]
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