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Computing isogenies between Jacobian of curves of genus 2 and 3

Abstract : We present a quasi-linear algorithm to compute isogenies between Jacobians of curves of genus 2 and 3 starting from the equation of the curve and a maximal isotropic subgroup of the l-torsion, for l an odd prime number, generalizing the Vélu's formula of genus 1. This work is based from the paper Computing functions on Jacobians and their quotients of Jean-Marc Couveignes and Tony Ezome. We improve their genus 2 case algorithm, generalize it for genus 3 hyperelliptic curves and introduce a way to deal with the genus 3 non-hyperelliptic case, using algebraic theta functions.
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https://hal.archives-ouvertes.fr/hal-01589683
Contributor : Enea Milio <>
Submitted on : Monday, August 26, 2019 - 6:20:41 PM
Last modification on : Wednesday, August 28, 2019 - 1:01:50 AM

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Enea Milio. Computing isogenies between Jacobian of curves of genus 2 and 3. 2019. ⟨hal-01589683v2⟩

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