dc.contributor.author |
Fouquet, Mireille |
dc.contributor.author |
Miret, Josep M. (Josep Maria) |
dc.contributor.author |
Valera Martín, Javier |
dc.date |
2018-02-16T12:22:05Z |
dc.date |
2019-09-28T22:21:33Z |
dc.date |
2018 |
dc.identifier |
1071-5797 |
dc.identifier |
http://hdl.handle.net/10459.1/62669 |
dc.identifier |
https://doi.org/10.1016/j.ffa.2017.09.006 |
dc.identifier.uri |
http://hdl.handle.net/10459.1/62669 |
dc.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. |
dc.description |
Research of the authors was partially supported by grants MTM2013-46949-P (Spanish MINECO) and 2014 SGR1666 (Generalitat de Catalunya). |
dc.language |
eng |
dc.publisher |
Elsevier |
dc.relation |
MINECO/PN2013-2016/MTM2013-46949-P |
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 |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.subject |
Finite field |
dc.subject |
Elliptic curve |
dc.subject |
Isogeny |
dc.subject |
Volcano |
dc.subject |
Distortion map |
dc.title |
Distorting the volcano |
dc.type |
article |
dc.type |
acceptedVersion |