Computing isogenies between Jacobians of hyperelliptic curves of arbitrary genus via differential equations

Elie Eid (1, 2, 3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LFANT - Lithe and fast algorithmic number theory
3 CANARI - Analyse cryptographique et arithmétique

Let $p$ be an odd prime number and be an integer coprime to $p$. We survey an algorithm for computing explicit rational representations of $(\ell,...,\ell)$-isogenies between Jacobians of hyperelliptic curves of arbitrary genus over an extension $K$ of the field of $p$-adic numbers $\mathbb{Q}_p$. The algorithm has a quasi-linear complexity in $\ell$ as well as in the genus of the curves.

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

Elie Eid. Computing isogenies between Jacobians of hyperelliptic curves of arbitrary genus via differential equations. 2021. ⟨hal-03142205⟩