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Modular equations for hyperelliptic curves

Pierrick Gaudry 1 Eric Schost 2 
1 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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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Contributor : Pierrick Gaudry Connect in order to contact the contributor
Submitted on : Thursday, November 10, 2005 - 11:21:35 AM
Last modification on : Friday, February 4, 2022 - 3:11:33 AM
Long-term archiving on: : Friday, April 2, 2010 - 6:53:46 PM


  • HAL Id : inria-00000627, version 1



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



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