Isogeny Volcanoes and the SEA Algorithm

  • Mireille Fouquet
  • François Morain
Conference paper

DOI: 10.1007/3-540-45455-1_23

Volume 2369 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Fouquet M., Morain F. (2002) Isogeny Volcanoes and the SEA Algorithm. In: Fieker C., Kohel D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg

Abstract

Recently, Kohel gave algorithms to compute the conductor of the endomorphism ring of an ordinary elliptic curve, given the cardinality of the curve. Using his work, we give a complete description of the structure of curves related via rational ℓ-degree isogenies, a structure we call a volcano. We explain how we can travel through this structure using modular polynomials. The computation of the structure is possible without knowing the cardinality of the curve, and that as a result, we deduce information on the cardinality.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Mireille Fouquet
    • 1
  • François Morain
    • 1
  1. 1.Laboratoire d’InformatiqueÉcole PolytechniquePalaiseau CedexFrance