Efficient computation of Cantor's division polynomials of hyperelliptic curves over finite fields

Elie Eid (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Let $p$ be an odd prime number. We propose an algorithm for computing rational representations of isogenies between Jacobians of hyperelliptic curves via-adic differential equations with a sharp analysis of the loss of precision. Consequently, after having possibly lifted the problem in the $p$-adics, we derive fast algorithms for computing explicitly Cantor's division polynomials of hyperelliptic curves defined over finite fields.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Elie Eid. Efficient computation of Cantor's division polynomials of hyperelliptic curves over finite fields. Journal of Symbolic Computation, 2023, 117, pp.68 - 100. ⟨10.1016/j.jsc.2022.10.006⟩. ⟨hal-03588288⟩