dc.contributor.author
Fouquet, Mireille
dc.contributor.author
Miret, Josep M. (Josep Maria)
dc.contributor.author
Valera Martín, Javier
dc.date.accessioned
2024-12-05T21:32:42Z
dc.date.available
2024-12-05T21:32:42Z
dc.date.issued
2018-02-16T12:22:05Z
dc.date.issued
2019-09-28T22:21:33Z
dc.identifier
https://doi.org/10.1016/j.ffa.2017.09.006
dc.identifier
http://hdl.handle.net/10459.1/62669
dc.identifier.uri
http://hdl.handle.net/10459.1/62669
dc.description.abstract
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.
dc.description.abstract
Research of the authors was partially supported by grants MTM2013-46949-P (Spanish MINECO) and 2014 SGR1666 (Generalitat de Catalunya).
dc.relation
info:eu-repo/grantAgreement/MINECO//MTM2013-46949-P/ES/CRIPTOGRAFIA CON CURVAS ALGEBRAICAS PARA LA E-SOCIEDAD/
dc.relation
Versió postprint del document publicat a https://doi.org/10.1016/j.ffa.2017.09.006
dc.relation
Finite Fields and Their Applications, 2018, vol. 49, núm. C, p. 108-125
dc.rights
cc-by-nc-nd (c) Elsevier, 2018
dc.rights
info:eu-repo/semantics/openAccess
dc.rights
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject
Elliptic curve
dc.subject
Distortion map
dc.title
Distorting the volcano
