Computing isogenies between Jacobian of curves of genus 2 and 3

Enea Milio 1
1 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry, Inria Nancy - Grand Est
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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Submitted on : Monday, September 18, 2017 - 7:41:53 PM
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Enea Milio. Computing isogenies between Jacobian of curves of genus 2 and 3. 2017. ⟨hal-01589683⟩



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