Year: 2007
Type: dissertation
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.
Author: Susan Lynn Schmoyer
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W206543630