[-] Show simple item record

dc.contributor.advisorBanks, William David, 1964-en_US
dc.contributor.authorPemberton, Michael Paul, 1983-en_US
dc.date.issued2009eng
dc.date.submitted2009 Fallen_US
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.en_US
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on December 30, 2009).en_US
dc.descriptionThesis advisor: Dr. William Banks.en_US
dc.descriptionIncludes bibliographical references.en_US
dc.descriptionM.S. University of Missouri--Columbia 2009.en_US
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Applied mathematics.en_US
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.en_US
dc.format.extentvii, 76 pagesen_US
dc.identifier.oclc495469974en_US
dc.identifier.otherPembertonM-120809-T1047en_US
dc.identifier.urihttp://hdl.handle.net/10355/5364
dc.publisherUniversity of Missouri--Columbiaen_US
dc.relation.ispartof2009 Freely available theses (MU)en_US
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. Graduate School. Theses and Dissertations. Theses. 2009 Theses
dc.subject.lcshCurves, Ellipticen_US
dc.subject.lcshCryptographyen_US
dc.subject.lcshNumber theoryen_US
dc.subject.lcshFactorization (Mathematics)en_US
dc.titleElliptic curves and their applications in cryptographyen_US
dc.typeThesisen_US
thesis.degree.disciplineApplied mathematicseng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelMastersen_US
thesis.degree.nameM.S.en_US


Files in this item

[PDF]
[PDF]
[PDF]

This item appears in the following Collection(s)

[-] Show simple item record