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Modular equations for hyperelliptic curves

Pierrick Gaudry 1 Eric Schost 2
1 TANC - Algorithmic number theory for cryptology
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : We define modular equations describing the l-torsion subgroups of the Jacobian of a hyperelliptic curve. Over a finite base field, we prove factorization properties that extend the well-known results used in Atkin's improvement of Schoof's genus 1 point counting algorithm.
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https://hal.inria.fr/inria-00000627
Contributor : Pierrick Gaudry <>
Submitted on : Thursday, November 10, 2005 - 11:21:35 AM
Last modification on : Thursday, March 5, 2020 - 6:21:26 PM
Long-term archiving on: : Friday, April 2, 2010 - 6:53:46 PM

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  • HAL Id : inria-00000627, version 1

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Pierrick Gaudry, Eric Schost. Modular equations for hyperelliptic curves. Mathematics of Computation, American Mathematical Society, 2005, 74, pp.429-454. ⟨inria-00000627⟩

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