Class Invariants by the CRT Method

Andreas Enge; Andrew V.  Sutherland

Paper 2010/031 Original: eprint.iacr.org/2010/031 ↗

Class Invariants by the CRT Method

Andreas Enge

Andrew V. Sutherland

Abstract

We adapt the CRT approach to computing Hilbert class polynomials to handle a wide range of class invariants. For suitable discriminants D, this improves its performance by a large constant factor, more than 200 in the most favourable circumstances. This has enabled record-breaking constructions of elliptic curves via the CM method, including examples with |D| > 10^{15}.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2010-01-22: last updated; 2010-01-22: published
Short URL: https://ia.cr/2010/031
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2010/031,
      author = {Andreas Enge and Andrew V.  Sutherland},
      title = {Class Invariants by the CRT Method},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/031},
      year = {2010},
      url = {https://eprint.iacr.org/2010/031}
}