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International Conference on Cryptology and Information Security in Latin America

LATINCRYPT 2014: Progress in Cryptology - LATINCRYPT 2014 pp 162–175Cite as

Isogeny Volcanoes of Elliptic Curves and Sylow Subgroups

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8895))

Abstract

Given an ordinary elliptic curve over a finite field located in the floor of its volcano of \( \ell \)-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 \( \ell \)-Sylow subgroups of the elliptic curves in the volcanoes.

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Acknowledgments

The authors thank the reviewers for their valuable comments and specially Sorina Ionica for her suggestions which have improved this article. Research of the second and third authors was supported in part by grants MTM2013-46949-P (Spanish MINECO) and 2014 SGR1666 (Generalitat de Catalunya).

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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu, Université Paris Diderot - Paris 7, Paris, France

    Mireille Fouquet

  2. Dept. de Matemàtica, Universitat de Lleida, Lleida, Spain

    Josep M. Miret & Javier Valera

Authors
  1. Mireille Fouquet
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  2. Josep M. Miret
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  3. Javier Valera
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Corresponding author

Correspondence to Javier Valera .

Editor information

Editors and Affiliations

  1. University of Campinas, Campinas, Brazil

    Diego F. Aranha

  2. University of Waterloo, Waterloo, Ontario, Canada

    Alfred Menezes

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Fouquet, M., Miret, J.M., Valera, J. (2015). Isogeny Volcanoes of Elliptic Curves and Sylow Subgroups. In: Aranha, D., Menezes, A. (eds) Progress in Cryptology - LATINCRYPT 2014. LATINCRYPT 2014. Lecture Notes in Computer Science(), vol 8895. Springer, Cham. https://doi.org/10.1007/978-3-319-16295-9_9

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

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16294-2

  • Online ISBN: 978-3-319-16295-9

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