Computing isogenies between Jacobians of hyperelliptic curves of arbitrary genus via differential equations
EID, Elie
Institut de Recherche Mathématique de Rennes [IRMAR]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Institut de Recherche Mathématique de Rennes [IRMAR]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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.Read less <
Origin
Hal imported