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Discreet Discrete Mathematics: Secret Communication Using Latin Squares and Quasigroups
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2017 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Diskret diskret matematik : Hemlig kommunikation med latinska kvadrater och kvasigrupper (Swedish)
Abstract [en]

This thesis describes methods of secret communication based on latin squares and their close relative, quasigroups. Different types of cryptosystems are described, including ciphers, public-key cryptosystems, and cryptographic hash functions. There is also a chapter devoted to different secret sharing schemes based on latin squares. The primary objective is to present previously described cryptosystems and secret sharing schemes in a more accessible manner, but this text also defines two new ciphers based on isotopic latin squares and reconstructs a lost proof related to row-latin squares.

Abstract [sv]

Denna uppsats beskriver kryptosystem och metoder för hemlighetsdelning baserade på latinska kvadrater och det närliggande konceptet kvasigrupper. Olika sorters chiffer, både symmetriska och asymmetriska, behandlas. Dessutom finns ett kapitel tillägnat kryptografiska hashfunktioner och ett tillägnat metoder för hemlighetsdelning. Huvudsyftet är att beskriva redan existerande metoder för hemlig kommunikation på ett mer lättillgängligt sätt och med nya exempel, men dessutom återskapas ett, till synes, förlorat bevis relaterat till rad-latinska kvadrater samt beskrivs två nya chiffer baserade på isotopa latinska kvadrater.

Place, publisher, year, edition, pages
2017. , 41 p.
Keyword [en]
Cryptology, Cryptography, Latin squares, Row-latin squares, Quasigroups, Secret sharing schemes
Keyword [sv]
Kryptologi, Kryptografi, Latinska kvadrater, Rad-latinska kvadrater, Kvasigrupper, Hemlighetsdelning
National Category
Mathematics Discrete Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-136860OAI: oai:DiVA.org:umu-136860DiVA: diva2:1114284
Available from: 2017-07-31 Created: 2017-06-22 Last updated: 2017-07-31Bibliographically approved

Open Access in DiVA

fulltext(390 kB)8 downloads
File information
File name FULLTEXT01.pdfFile size 390 kBChecksum SHA-512
578972921d7b430777e5679184031a1a6175e48f4366b8b5ba969e828385b1090974fda57f3501a20c12996e77f521116cb32cb07399608a9f8c934a367c16ca
Type fulltextMimetype application/pdf

By organisation
Department of Mathematics and Mathematical Statistics
MathematicsDiscrete Mathematics

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • asciidoc
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