Distorting the volcano
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 endomorph...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2018 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/62669 |
| Acesso em linha: | https://doi.org/10.1016/j.ffa.2017.09.006 http://hdl.handle.net/10459.1/62669 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Finite field Elliptic curve Isogeny Volcano Distortion map |
| Resumo: | 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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