Computing class polynomials for abelian surfaces

Andreas Enge 1 Emmanuel Thomé 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
2 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due to Dupont for evaluating ϑ- constants in quasi-linear time using Newton iterations on the Borchardt mean. We report on experiments with our implementation and present an example with class number 17608.
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https://hal.inria.fr/hal-00823745
Contributor : Emmanuel Thomé <>
Submitted on : Friday, May 17, 2013 - 6:32:38 PM
Last modification on : Monday, May 20, 2019 - 2:30:25 PM
Long-term archiving on : Sunday, August 18, 2013 - 4:16:28 AM

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  • HAL Id : hal-00823745, version 1
  • ARXIV : 1305.4330

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Andreas Enge, Emmanuel Thomé. Computing class polynomials for abelian surfaces. 2013. ⟨hal-00823745v1⟩

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