Distorting the volcano

Volcanoes of ℓ–isogenies of elliptic curves are a special case of graphs with a cycle called crater. In this paper, given an elliptic curve E of a volcano of ℓ–isogenies, we present a condition over an endomorphism ϕ of E in order to determine which ℓ–isogenies of E are non-descending. The endomorph...

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Detalles Bibliográficos
Autores: Fouquet, Mireille, Miret, Josep M. (Josep Maria), Valera Martín, Javier
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
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:10459.1/62669
Acceso en línea:https://doi.org/10.1016/j.ffa.2017.09.006
http://hdl.handle.net/10459.1/62669
Access Level:acceso abierto
Palabra clave:Finite field
Elliptic curve
Isogeny
Volcano
Distortion map
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spelling Distorting the volcanoFouquet, MireilleMiret, Josep M. (Josep Maria)Valera Martín, JavierFinite fieldElliptic curveIsogenyVolcanoDistortion mapVolcanoes of ℓ–isogenies of elliptic curves are a special case of graphs with a cycle called crater. In this paper, given an elliptic curve E of a volcano of ℓ–isogenies, we present a condition over an endomorphism ϕ of E in order to determine which ℓ–isogenies of E are non-descending. The endomorphism ϕ is defined as the crater cycle of an m–volcano where E is located, with m 6= ℓ. The condition is feasible when ϕ is a distortion map for a subgroup of order ℓ of E. We also provide some relationships among the crater sizes of volcanoes of m–isogenies whose elliptic curves belong to a volcano of ℓ–isogenies.Research of the authors was partially supported by grants MTM2013-46949-P (Spanish MINECO) and 2014 SGR1666 (Generalitat de Catalunya).Elsevier2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionhttps://doi.org/10.1016/j.ffa.2017.09.006http://hdl.handle.net/10459.1/62669reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/grantAgreement/MINECO//MTM2013-46949-PVersió postprint del document publicat a https://doi.org/10.1016/j.ffa.2017.09.006Finite Fields and Their Applications, 2018, vol. 49, núm. C, p. 108-125cc-by-nc-nd (c) Elsevier, 2018info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/oai:recercat.cat:10459.1/626692026-05-29T05:05:01Z
dc.title.none.fl_str_mv Distorting the volcano
title Distorting the volcano
spellingShingle Distorting the volcano
Fouquet, Mireille
Finite field
Elliptic curve
Isogeny
Volcano
Distortion map
title_short Distorting the volcano
title_full Distorting the volcano
title_fullStr Distorting the volcano
title_full_unstemmed Distorting the volcano
title_sort Distorting the volcano
dc.creator.none.fl_str_mv Fouquet, Mireille
Miret, Josep M. (Josep Maria)
Valera Martín, Javier
author Fouquet, Mireille
author_facet Fouquet, Mireille
Miret, Josep M. (Josep Maria)
Valera Martín, Javier
author_role author
author2 Miret, Josep M. (Josep Maria)
Valera Martín, Javier
author2_role author
author
dc.subject.none.fl_str_mv Finite field
Elliptic curve
Isogeny
Volcano
Distortion map
topic Finite field
Elliptic curve
Isogeny
Volcano
Distortion map
description Volcanoes of ℓ–isogenies of elliptic curves are a special case of graphs with a cycle called crater. In this paper, given an elliptic curve E of a volcano of ℓ–isogenies, we present a condition over an endomorphism ϕ of E in order to determine which ℓ–isogenies of E are non-descending. The endomorphism ϕ is defined as the crater cycle of an m–volcano where E is located, with m 6= ℓ. The condition is feasible when ϕ is a distortion map for a subgroup of order ℓ of E. We also provide some relationships among the crater sizes of volcanoes of m–isogenies whose elliptic curves belong to a volcano of ℓ–isogenies.
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1016/j.ffa.2017.09.006
http://hdl.handle.net/10459.1/62669
url https://doi.org/10.1016/j.ffa.2017.09.006
http://hdl.handle.net/10459.1/62669
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MINECO//MTM2013-46949-P
Versió postprint del document publicat a https://doi.org/10.1016/j.ffa.2017.09.006
Finite Fields and Their Applications, 2018, vol. 49, núm. C, p. 108-125
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier, 2018
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier, 2018
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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