Isogeny volcanoes of elliptic curves and sylow subgroups

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

doi:https://doi.org/10.1007/978-3-319-16295-9_9

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Issue date

2015

Author

Fouquet, Mireille

Miret, Josep M. (Josep Maria)

Valera Martín, Javier

Suggested citation

Fouquet, Mireille; Miret, Josep M. (Josep Maria); Valera Martín, Javier; . (2015) . Isogeny volcanoes of elliptic curves and sylow subgroups. Lecture Notes in Computer Science, 2015, vol. 8895. https://doi.org/10.1007/978-3-319-16295-9_9.

Abstract

Given an ordinary elliptic curve over a finite field located in the floor of its volcano of ℓ-isogenies, we present an efficient procedure to take an ascending path from the floor to the level of stability and back to the floor. As an application for regular volcanoes, we give an algorithm to compute all the vertices of their craters. In order to do this, we make use of the structure and generators of the ℓ-Sylow subgroups of the elliptic curves in the volcanoes.

Note

International Conference on Cryptology and Information Security in Latin America LATINCRYPT 2014: Progress in Cryptology - LATINCRYPT 2014 pp 162-175

URI

http://hdl.handle.net/10459.1/62667

DOI

https://doi.org/10.1007/978-3-319-16295-9_9

Is part of

Lecture Notes in Computer Science, 2015, vol. 8895