Distorting the volcano

Fouquet, Mireille; Miret, Josep M. (Josep Maria); Valera Martín, Javier

doi:https://doi.org/10.1016/j.ffa.2017.09.006

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Issue date

2018

Author

Fouquet, Mireille

Miret, Josep M. (Josep Maria)

Valera Martín, Javier

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.

URI

http://hdl.handle.net/10459.1/62669

DOI

https://doi.org/10.1016/j.ffa.2017.09.006

Is part of

Finite Fields and Their Applications, 2018, vol. 49, núm. C, p. 108-125

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Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2018