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  1. No Access

    Chapter and Conference Paper

    Isogeny Volcanoes of Elliptic Curves and Sylow Subgroups

    Given an ordinary elliptic curve over a finite field located in the floor of its volcano of \( \ell \) -isogenies, we ...

    Mireille Fouquet, Josep M. Miret, Javier Valera in Progress in Cryptology - LATINCRYPT 2014 (2015)

  2. No Access

    Chapter and Conference Paper

    Isogeny Volcanoes and the SEA Algorithm

    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 struct...

    Mireille Fouquet, François Morain in Algorithmic Number Theory (2002)

  3. Chapter and Conference Paper

    Finding Secure Curves with the Satoh-FGH Algorithm and an Early-Abort Strategy

    The use of elliptic curves in cryptography relies on the ability to count the number of points on a given curve. Before 1999, the SEA algorithm was the only efficient method known for random curves. Then Satoh...

    Mireille Fouquet, Pierrick Gaudry, Robert Harley in Advances in Cryptology — EUROCRYPT 2001 (2001)

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