Elliptic curves with j = 0, 1728 and low embedding degree

Elliptic curves over a finite field Fq with j-invariant 0 or 1728, both supersingular and ordinary, whose embedding degree k is low are studied. In the ordinary case we give conditions characterizing such elliptic curves with fixed embedding degree with respect to a subgroup of prime order . For k =...

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Detalhes bibliográficos
Autores: Miret, Josep M., Sadornil Renedo, Daniel|||0000-0003-4066-4138, Tena, Juan G.
Tipo de documento: artigo
Data de publicação:2016
País:España
Recursos:Universidad de Cantabria (UC)
Repositório:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglês
OAI Identifier:oai:repositorio.unican.es:10902/11302
Acesso em linha:http://hdl.handle.net/10902/11302
Access Level:Acceso aberto
Palavra-chave:Elliptic curves
Embedding degree
Distorsion maps
Pairing-based Cryptography
Bateman-Horn's Conjecture
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spelling Elliptic curves with j = 0, 1728 and low embedding degreeMiret, Josep M.Sadornil Renedo, Daniel|||0000-0003-4066-4138Tena, Juan G.Elliptic curvesEmbedding degreeDistorsion mapsPairing-based CryptographyBateman-Horn's ConjectureElliptic curves over a finite field Fq with j-invariant 0 or 1728, both supersingular and ordinary, whose embedding degree k is low are studied. In the ordinary case we give conditions characterizing such elliptic curves with fixed embedding degree with respect to a subgroup of prime order . For k = 1, 2, these conditions give parameterizations of q in terms of and two integers m, n. We show several examples of families with infinitely many curves. Similar parameterizations for k ? 3 need a fixed kth root of the unity in the underlying field. Moreover, when the elliptic curve admits distortion maps, an example is provided.Taylor & FrancisUniversidad de Cantabria20162016-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/11302International Journal of Computer Mathematics, 2016, Vol. 93, No. 12, 2042?2053reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/113022026-06-02T12:39:31Z
dc.title.none.fl_str_mv Elliptic curves with j = 0, 1728 and low embedding degree
title Elliptic curves with j = 0, 1728 and low embedding degree
spellingShingle Elliptic curves with j = 0, 1728 and low embedding degree
Miret, Josep M.
Elliptic curves
Embedding degree
Distorsion maps
Pairing-based Cryptography
Bateman-Horn's Conjecture
title_short Elliptic curves with j = 0, 1728 and low embedding degree
title_full Elliptic curves with j = 0, 1728 and low embedding degree
title_fullStr Elliptic curves with j = 0, 1728 and low embedding degree
title_full_unstemmed Elliptic curves with j = 0, 1728 and low embedding degree
title_sort Elliptic curves with j = 0, 1728 and low embedding degree
dc.creator.none.fl_str_mv Miret, Josep M.
Sadornil Renedo, Daniel|||0000-0003-4066-4138
Tena, Juan G.
author Miret, Josep M.
author_facet Miret, Josep M.
Sadornil Renedo, Daniel|||0000-0003-4066-4138
Tena, Juan G.
author_role author
author2 Sadornil Renedo, Daniel|||0000-0003-4066-4138
Tena, Juan G.
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Elliptic curves
Embedding degree
Distorsion maps
Pairing-based Cryptography
Bateman-Horn's Conjecture
topic Elliptic curves
Embedding degree
Distorsion maps
Pairing-based Cryptography
Bateman-Horn's Conjecture
description Elliptic curves over a finite field Fq with j-invariant 0 or 1728, both supersingular and ordinary, whose embedding degree k is low are studied. In the ordinary case we give conditions characterizing such elliptic curves with fixed embedding degree with respect to a subgroup of prime order . For k = 1, 2, these conditions give parameterizations of q in terms of and two integers m, n. We show several examples of families with infinitely many curves. Similar parameterizations for k ? 3 need a fixed kth root of the unity in the underlying field. Moreover, when the elliptic curve admits distortion maps, an example is provided.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10902/11302
url http://hdl.handle.net/10902/11302
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
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
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv International Journal of Computer Mathematics, 2016, Vol. 93, No. 12, 2042?2053
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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