Computing class polynomials for abelian surfaces
Cryptography and Security
2013-12-11 v2 Number Theory
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 - 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.
Cite
@article{arxiv.1305.4330,
title = {Computing class polynomials for abelian surfaces},
author = {Andreas Enge and Emmanuel Thomé},
journal= {arXiv preprint arXiv:1305.4330},
year = {2013}
}