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Isogeny volcanoes of elliptic curves and sylow subgroups

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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.
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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
European research projects
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  • Articles publicats (Matemàtica) [329]
  • Grup de Recerca en Criptografia i Grafs (INSPIRES) [6]
  • Publicacions de projectes de recerca del Plan Nacional [2661]

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