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Elliptic Curves Cryptography
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
2012 (English)Independent thesis Advanced level (degree of Master (Two Years)), 15 credits / 22,5 HE creditsStudent thesis
Abstract [en]

In the thesis we study the elliptic curves and its use in cryptography. Elliptic curvesencompasses a vast area of mathematics. Elliptic curves have basics in group theory andnumber theory. The points on elliptic curve forms a group under the operation of addition.We study the structure of this group. We describe Hasse’s theorem to estimate the numberof points on the curve. We also discuss that the elliptic curve group may or may not becyclic over finite fields. Elliptic curves have applications in cryptography, we describe theapplication of elliptic curves for discrete logarithm problem and ElGamal cryptosystem.

Place, publisher, year, edition, pages
2012. , 42 p.
Keyword [en]
Group Theory and Number Theory; Elliptic Curves; Elliptic Curves over Finite Fields; Applications of Elliptic Curves.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-17544OAI: oai:DiVA.org:lnu-17544DiVA: diva2:501947
Subject / course
Mathematics
Educational program
Mathematics and Modelling, Master Programme, 120 credits
Presentation
2012-02-07, B2034, Linnéuniversitetet, Linnaeus University, Växjö, 14:00 (English)
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2012-02-14 Created: 2012-02-14 Last updated: 2012-02-14Bibliographically approved

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Elliptic Curves Cryptography(507 kB)456 downloads
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • 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
  • html
  • text
  • asciidoc
  • rtf