Distorting the volcano

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Issue date
2018Suggested citation
Fouquet, Mireille;
Miret, Josep M. (Josep Maria);
Valera Martín, Javier;
.
(2018)
.
Distorting the volcano.
Finite Fields and Their Applications, 2018, vol. 49, núm. C, p. 108-125.
https://doi.org/10.1016/j.ffa.2017.09.006.
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Show full item recordAbstract
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.
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Finite Fields and Their Applications, 2018, vol. 49, núm. C, p. 108-125European research projects
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