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dc.contributor.advisorBanks, William David, 1964-eng
dc.contributor.authorPemberton, Michael Paul, 1983-eng
dc.date.issued2009eng
dc.date.submitted2009 Falleng
dc.descriptionThe entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.eng
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on December 30, 2009).eng
dc.descriptionThesis advisor: Dr. William Banks.eng
dc.descriptionIncludes bibliographical references.eng
dc.descriptionM.S. University of Missouri--Columbia 2009.eng
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Applied mathematics.eng
dc.description.abstractIn 1985, Koblitz and Miller proposed elliptic curves to be used for public key cryptosystems. This present thesis examines the role of elliptic curves on cryptography and basic problems involving implementation and security of some elliptic curve cryptosystems. Some of the aspects we are concerned with include: Methods to determine the number of points on an elliptic curve over a finite field; Implementation of cryptosystems based on the discrete logarithm problem for elliptic curves defined over a finite field; Examine an elliptic curve analogue of the RSA cryptosystem. We provide answers to these and discuss a number of applications for number theory, such as factorization and primality testing.eng
dc.format.extentvii, 76 pageseng
dc.identifier.oclc495469974eng
dc.identifier.otherPembertonM-120809-T1047eng
dc.identifier.urihttp://hdl.handle.net/10355/5364eng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartof2009 Freely available theses (MU)eng
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. Graduate School. Theses and Dissertations. Theses. 2009 Theseseng
dc.subject.lcshCurves, Ellipticeng
dc.subject.lcshCryptographyeng
dc.subject.lcshNumber theoryeng
dc.subject.lcshFactorization (Mathematics)eng
dc.titleElliptic curves and their applications in cryptographyeng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelMasterseng
thesis.degree.nameM.S.eng


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