Paper 2013/299 Original: eprint.iacr.org/2013/299 ↗
Computing class polynomials for abelian surfaces
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)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2013-05-25: last updated
- 2013-05-25: published
- Short URL
- https://ia.cr/2013/299
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2013/299,
author = {Andres Enge and Emmanuel Thomé},
title = {Computing class polynomials for abelian surfaces},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/299},
year = {2013},
url = {https://eprint.iacr.org/2013/299}
}