Class Invariants by the CRT Method

Andreas Enge; Andrew V.  Sutherland

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Paper 2010/031

Class Invariants by the CRT Method

Andreas Enge and 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: Published elsewhere. Unknown where it was published
Keywords: elliptic curve cryptography complex multiplication
Contact author(s): drew @ math mit edu
History: 2010-01-22: received
Short URL: https://ia.cr/2010/031
License: CC BY

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},
      note = {\url{https://eprint.iacr.org/2010/031}},
      url = {https://eprint.iacr.org/2010/031}
}