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Elliptic Curves CryptographyPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2012 (English)Independent thesis Advanced level (degree of Master (Two Years)), 15 credits / 22,5 HE creditsStudent thesis
##### Abstract [en]

##### 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

#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt375",{id:"formSmash:j_idt375",widgetVar:"widget_formSmash_j_idt375",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt381",{id:"formSmash:j_idt381",widgetVar:"widget_formSmash_j_idt381",multiple:true});
##### Examiners

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2012-02-14 Created: 2012-02-14 Last updated: 2012-02-14Bibliographically approved

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.

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