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Paper 2013/299
Computing class polynomials for abelian surfaces
Andres Enge and 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.
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- number theory
- Contact author(s)
- Emmanuel Thome @ gmail com
- History
- 2013-05-25: received
- Short URL
- https://ia.cr/2013/299
- License
-
CC BY