Fast computation of hyperelliptic curve isogenies in odd characteristic

Elie Eid (1, 2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LFANT - Lithe and fast algorithmic number theory

Let p be an odd prime number and g ≥ 2 be an integer. We present an algorithm for computing explicit rational representations of isogenies between Jacobians of hyperelliptic curves of genus g over an extension K of the field of p-adic numbers Qp. It relies on an efficient resolution, with a logarithmic loss of p-adic precision, of a first order system of differential equations.

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

Elie Eid. Fast computation of hyperelliptic curve isogenies in odd characteristic. International Symposium on Symbolic and Algebraic Computation — ISSAC 2021, Jul 2021, Virtual event, Russia. pp.131-138. ⟨hal-02948514⟩