Explicit 2-power torsion of genus 2 curves over finite fields
We give an efficient explicit algorithm to find the structure and generators of the maximal 2-subgroup of the Jacobian of a genus 2 curve over a finite field of odd characteristic. We use the 2-torsion points as seeds to successively perform a chain of halvings to ind divisors of increasing 2-power...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/469529 |
| Acceso en línea: | https://doi.org/10.3934/AMC.2010.4.155 https://hdl.handle.net/10459.1/469529 http://hdl.handle.net/10459.1/469529 |
| Access Level: | acceso abierto |
| Palabra clave: | Finite fields Genus 2 curves Jacobian |
| Sumario: | We give an efficient explicit algorithm to find the structure and generators of the maximal 2-subgroup of the Jacobian of a genus 2 curve over a finite field of odd characteristic. We use the 2-torsion points as seeds to successively perform a chain of halvings to ind divisors of increasing 2-power order. The halving loop requires a solution to certain degree 16 polynomials over the base ield, and the termination of the algorithm is based on the description of the graph structure of the maximal 2-subgroup. The structure of our algorithm is the natural extension of the even characteristic case. © 2010 AIMS-SDU. |
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