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Fast computation of hyperelliptic curve isogenies in odd characteristic

Elie Eid 1, 2
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02948514
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Submitted on : Thursday, September 24, 2020 - 5:01:39 PM
Last modification on : Saturday, December 4, 2021 - 3:43:53 AM
Long-term archiving on: : Thursday, December 3, 2020 - 5:17:56 PM

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  • HAL Id : hal-02948514, version 1

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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⟩

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