Volcanoes of ℓ-isogenies of elliptic curves over finite fields

This paper is devoted to the study of the volcanoes of ℓ-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship between the ℓ-Sylow subgroup of an elliptic curve and t...

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Detalhes bibliográficos
Autores: Miret, Josep M., Sadornil, Daniel, Tena, Juan, Tomàs, Rosana, Valls, Magda
Formato: artículo
Fecha de publicación:2007
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:138508
Acesso em linha:https://ddd.uab.cat/record/138508
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_PJTN05_08
Access Level:acceso abierto
Palavra-chave:Elliptic curves
Finite fields
Isogenies
Volcanoes
ℓ-Sylow subgroup
Algorithms
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spelling Volcanoes of ℓ-isogenies of elliptic curves over finite fieldsthe case ℓ = 3Miret, Josep M.Sadornil, DanielTena, JuanTomàs, RosanaValls, MagdaElliptic curvesFinite fieldsIsogeniesVolcanoesℓ-Sylow subgroupAlgorithmsThis paper is devoted to the study of the volcanoes of ℓ-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship between the ℓ-Sylow subgroup of an elliptic curve and the level of the volcano where it is placed. The particular case ℓ = 3 is studied in detail, giving an algorithm to determine the volcano of 3-isogenies of a given elliptic curve. Experimental results are also provided. 22007-01-0120072007-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/138508https://dx.doi.org/urn:doi:10.5565/PUBLMAT_PJTN05_08reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1385082026-06-06T12:50:31Z
dc.title.none.fl_str_mv Volcanoes of ℓ-isogenies of elliptic curves over finite fields
the case ℓ = 3
title Volcanoes of ℓ-isogenies of elliptic curves over finite fields
spellingShingle Volcanoes of ℓ-isogenies of elliptic curves over finite fields
Miret, Josep M.
Elliptic curves
Finite fields
Isogenies
Volcanoes
ℓ-Sylow subgroup
Algorithms
title_short Volcanoes of ℓ-isogenies of elliptic curves over finite fields
title_full Volcanoes of ℓ-isogenies of elliptic curves over finite fields
title_fullStr Volcanoes of ℓ-isogenies of elliptic curves over finite fields
title_full_unstemmed Volcanoes of ℓ-isogenies of elliptic curves over finite fields
title_sort Volcanoes of ℓ-isogenies of elliptic curves over finite fields
dc.creator.none.fl_str_mv Miret, Josep M.
Sadornil, Daniel
Tena, Juan
Tomàs, Rosana
Valls, Magda
author Miret, Josep M.
author_facet Miret, Josep M.
Sadornil, Daniel
Tena, Juan
Tomàs, Rosana
Valls, Magda
author_role author
author2 Sadornil, Daniel
Tena, Juan
Tomàs, Rosana
Valls, Magda
author2_role author
author
author
author
dc.subject.none.fl_str_mv Elliptic curves
Finite fields
Isogenies
Volcanoes
ℓ-Sylow subgroup
Algorithms
topic Elliptic curves
Finite fields
Isogenies
Volcanoes
ℓ-Sylow subgroup
Algorithms
description This paper is devoted to the study of the volcanoes of ℓ-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship between the ℓ-Sylow subgroup of an elliptic curve and the level of the volcano where it is placed. The particular case ℓ = 3 is studied in detail, giving an algorithm to determine the volcano of 3-isogenies of a given elliptic curve. Experimental results are also provided.
publishDate 2007
dc.date.none.fl_str_mv 2
2007-01-01
2007
2007-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/138508
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_PJTN05_08
url https://ddd.uab.cat/record/138508
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_PJTN05_08
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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