Algorithms for the construction of elliptic curves with given cardinality

Sebé, Francesc. (2013). Algorithms for the construction of elliptic curves with given cardinality Master Thesis, Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias

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Título Algorithms for the construction of elliptic curves with given cardinality
Autor(es) Sebé, Francesc
Resumen Trabajo fin de Máster. Máster en Matemáticas Avanzadas
Abstract
The objective of this thesis has been the implementation and comparison of two algorithms for generating an elliptic curve over a finite field with a given cardinality. The first one was proposed by Atkin and Morain in 1993 as part of their widely known primality test. The second one comes from a technical report by Agashe, Lauter and Venkatesan (2001). Both proposals are based on the construction of the Hilbert class polynomial modulo a prime number and the obtention of the j-invariant of the required elliptic curve as one of its roots. Prior to the implementation of those algorithms, a study on their mathematical background has been carried out. The two algorithms have been implemented in Sage, which is an open source software aimed to the implementation of mathematical algorithms. In the performed experiments, the first method has clearly outperformed the second one, in terms of running time.

Materia(s) http://udcdata.info/025453
Matemáticas
Editor(es) Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias
Director/Tutor Izquierdo, Milagros (Tutora)
Fecha 2013-10-24
Formato application/pdf
Identificador http://e-spacio.uned.es/fez/view/bibliuned:masterMatavanz-Fsebe
bibliuned:masterMatavanz-Fsebe
Idioma spa
Versión de la publicación publishedVersion
Nivel de acceso y licencia info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0
Tipo de recurso master Thesis
Tipo de acceso Acceso abierto

 
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Creado: Tue, 19 Nov 2013, 07:03:39 CET