Computing class polynomials for abelian surfaces

Andres Enge; Emmanuel Thomé

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): PDF
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

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}
}