Three gluings of elliptic curves Revised slides

Everett W. Howe

Description

Three-gluings of elliptic curves (Revised slides) Everett W. Howe Center for Communications Research, La Jolla GeoCrypt 2011 Bastia, Corsica, 20 June 2011 Everett W. Howe Three-gluings of elliptic curves 1 of 29

• jacobians isogenous


• e2 over


• communications research


• revised slides


• isomorphism ?

Sujets

• Weil im Schönbuch

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 21
• Langue: English

Extrait

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Everett W. Howe

GeoCrypt 2011 Bastia, Corsica, 20 June 2011

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Three-gluings of elliptic curves (Revised slides)

Center for Communications Research, La Jolla

9

Motivation

Two topics of interest Genus-2 curves with maps to elliptic curves Genus-2 curves with Jacobians isogenous to a product of elliptic curves

These are really the same topic. . .

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A construction

Given: Two elliptic curvesE 1 ,E 2 over a fieldk An isomorphismψ:E 1 [n]→E 2 [n]for somen>0, such thatψis an anti-isometry with respect to the Weil pairing

We will produce: A genus-2 curveC(possibly degenerate) Degree-nmapsC→E 1 andC→E 2

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E 1 [n]×E 1 [n] Weil

µ n

Given: Two elliptic curvesE 1 ,E 2 over a fieldk An isomorphismψ:E 1 [n]→E 2 [n]for somen>0, such thatψis an anti-isometry with respect to the Weil pairing

We will produce: A genus-2 curveC(possibly degenerate) Degree-nmapsC→E 1 andC→E 2

9 tructionAsnoc //