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Pré-Publication, Document De Travail Année : 2022

Computing the Canonical Lift of Genus 2 Curves in Odd Characteristics

Résumé

Let A/Fq be an ordinary abelian surface. We explain how to use the Siegel modular polynomials, and if available the Hilbert modular polynomials to compute the canonical lift of A. As an application, if q = p n , we show how to use the canonical lift to count the number of points on A in quasi-quadratic time Õ(n 2), this is a direct extension of Satoh's original algorithm for elliptic curves. We give a detailed description with the necessary optimizations for an efficient implementation.
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Dates et versions

hal-03738314 , version 1 (25-07-2022)

Identifiants

  • HAL Id : hal-03738314 , version 1

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Damien Robert, Abdoulaye Maiga. Computing the Canonical Lift of Genus 2 Curves in Odd Characteristics. 2022. ⟨hal-03738314⟩
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