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Simuleringar av elliptiska kurvor för elliptisk kryptografi
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics.
2019 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Simulations of elliptic curves for elliptic cryptography (English)
Abstract [en]

This thesis describes the theory behind elliptic-curve Diffie-Hellman key exchanges. All the way from the definition of a group until how the operator over an elliptic curve forms an abelian group. This is illustrated with clear examples. After that a smaller study is made to determine if there is a connection betweenthe size of the underlying field, the amount of points on the curve and the order of the points to determine how hard it is to find out the secret key in elliptic-curve Diffie-Hellman key exchanges. No clear connection is found. Since elliptic curves over extension fields have more computational heavy operations, it is concluded that these curves serve no practical use in elliptic-curve Diffie-Hellman key exchange.

Abstract [sv]

Denna rapport går igenom teorin bakom Diffie-Hellmans nyckelutbyte över elliptiska kurvor. Från definitionen av en grupp hela vägen till hur operatorn över en elliptisk kurva utgör en abelsk grupp gås igenom och görs tydligt med konstruktiva exempel. Sedan görs en mindre undersökning av sambandet mellan storleken av den underliggande kroppen, antal punkter på kurvan och ordning av punkterna på kurvan, det vill säga svårigheten att hitta den hemliga nyckeln framtagen med Diffie-Hellmans nyckelutbyte för elliptiska kurvor. Ingen tydlig koppling hittas. Då elliptiska kurvor över utvidgade kroppar har mer beräkningstunga operationer dras slutsatsen att dessa kurvor inte är praktiska inom Diffie-Hellman nyckelutbyte över elliptiska kurvor.

Place, publisher, year, edition, pages
2019. , p. 58
Keywords [en]
Diffie-Hellman, elliptic curves, cryptography, ECDH, ECC
Keywords [sv]
Diffie-Hellman, elliptiska kurvor, kryptografi, ECDH, ECC
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-158133ISRN: LiTH-MAT-EX--2019/02--SEOAI: oai:DiVA.org:liu-158133DiVA, id: diva2:1330916
Subject / course
Mathematics
Supervisors
Examiners
Available from: 2019-06-27 Created: 2019-06-26 Last updated: 2019-06-27Bibliographically approved

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CiteExportLink to record
Permanent link

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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
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