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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2013/299}},
      url = {https://eprint.iacr.org/2013/299}
}
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