Triviality and Nontriviality of Tate-Lichtenbaum Self Pairings

dc.contributor.advisorWashington, Lawrence Cen_US
dc.contributor.authorSchmoyer, Susan Lynnen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2007-06-22T05:35:32Z
dc.date.available2007-06-22T05:35:32Z
dc.date.issued2007-04-25
dc.description.abstractLet E be an elliptic curve defined over F_q and suppose that E[n] subset E(F_q). For attacking the elliptic curve discrete logarithm problem it is useful to know when points pair with themselves nontrivially under the Tate-Lichtenbaum pairing. In this thesis we characterize when all points in E[n] have trivial self pairings. This result is expressed in terms of the action of the Frobenius endomorphism on E[n^2]. We then generalize this result to Jacobians of algebraic curves of arbitrary genus.en_US
dc.format.extent344429 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/6851
dc.language.isoen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledMathematicsen_US
dc.titleTriviality and Nontriviality of Tate-Lichtenbaum Self Pairingsen_US
dc.typeDissertationen_US

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