Modular equations for hyperelliptic curves

Pierrick Gaudry (1) , Eric Schost (2)

1 TANC - Algorithmic number theory for cryptology
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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.

Domaines: Cryptographie et sécurité [cs.CR]

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