Triviality and Nontriviality of Tate-Lichtenbaum Self Pairings
| dc.contributor.advisor | Washington, Lawrence C | en_US |
| dc.contributor.author | Schmoyer, Susan Lynn | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2007-06-22T05:35:32Z | |
| dc.date.available | 2007-06-22T05:35:32Z | |
| dc.date.issued | 2007-04-25 | |
| dc.description.abstract | Let 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.extent | 344429 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1903/6851 | |
| dc.language.iso | en_US | |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.title | Triviality and Nontriviality of Tate-Lichtenbaum Self Pairings | en_US |
| dc.type | Dissertation | en_US |
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