Elliptic curves and their applications in cryptography

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Elliptic curves and their applications in cryptography

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/5364

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dc.contributor.advisor Banks, William David, 1964- en_US
dc.contributor.author Pemberton, Michael Paul, 1983- en_US
dc.date.accessioned 2010-02-09T17:56:55Z
dc.date.available 2010-02-09T17:56:55Z
dc.date.issued 2009 en_US
dc.date.submitted 2009 Fall en_US
dc.identifier.other PembertonM-120809-T1047 en_US
dc.identifier.uri http://hdl.handle.net/10355/5364
dc.description The 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.description Title from PDF of title page (University of Missouri--Columbia, viewed on December 30, 2009). en_US
dc.description Thesis advisor: Dr. William Banks. en_US
dc.description Includes bibliographical references. en_US
dc.description M.S. University of Missouri--Columbia 2009. en_US
dc.description Dissertations, Academic -- University of Missouri--Columbia -- Applied mathematics. en_US
dc.description.abstract In 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.extent vii, 76 pages en_US
dc.language.iso en_US en_US
dc.publisher University of Missouri--Columbia en_US
dc.relation.ispartof 2009 Freely available theses (MU) en_US
dc.subject.lcsh Curves, Elliptic en_US
dc.subject.lcsh Cryptography en_US
dc.subject.lcsh Number theory en_US
dc.subject.lcsh Factorization (Mathematics) en_US
dc.title Elliptic curves and their applications in cryptography en_US
dc.type Thesis en_US
thesis.degree.discipline Applied mathematics en_US
thesis.degree.grantor University of Missouri--Columbia en_US
thesis.degree.name M.S. en_US
thesis.degree.level Masters en_US
dc.identifier.oclc 495469974 en_US
dc.relation.ispartofcommunity University of Missouri-Columbia. Graduate School. Theses and Dissertations. Theses. 2009 Theses


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