Welcome to the resource topic for 2013/299
Title:
Computing class polynomials for abelian surfaces
Authors: Andres Enge, Emmanuel Thomé
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.
ePrint: https://eprint.iacr.org/2013/299
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