Distorting the volcano

https://doi.org/10.1016/j.ffa.2017.09.006Get rights and content
Under an Elsevier user license
open archive

Abstract

Volcanoes of -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 -isogenies, we present a condition over an endomorphism φ of E in order to determine which -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. The condition is feasible when φ is a distortion map for a subgroup of order of E. We also provide some relationships among the crater sizes of volcanoes of m-isogenies whose elliptic curves belong to a volcano of -isogenies.

MSC

14H52
14K02

Keywords

Finite field
Elliptic curve
Isogeny
Volcano
Distortion map

Cited by (0)