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Título:
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Distorting the volcano
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Autor/a:
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Fouquet, Mireille; Miret, Josep M. (Josep Maria); Valera Martín, Javier
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Notas:
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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.
Research of the authors was partially supported by grants MTM2013-46949-P (Spanish MINECO) and 2014 SGR1666 (Generalitat de Catalunya). |
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Materia(s):
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-Finite field
-Elliptic curve
-Isogeny
-Volcano
-Distortion map |
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Derechos:
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cc-by-nc-nd (c) Elsevier, 2018
http://creativecommons.org/licenses/by-nc-nd/4.0/
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Tipo de documento:
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article
acceptedVersion |
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Editor:
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Elsevier
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