Finding ECM-Friendly Curves through a Study of Galois Properties

Razvan Barbulescu; Joppe W.  Bos; Cyril Bouvier; Thorsten Kleinjung; Peter L.  Montgomery

Paper 2012/070

Finding ECM-Friendly Curves through a Study of Galois Properties

Razvan Barbulescu, Joppe W. Bos, Cyril Bouvier, Thorsten Kleinjung, and Peter L. Montgomery

Abstract

In this paper we prove some divisibility properties of the cardinality of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas of the proofs help us to find new families of elliptic curves with good division properties which increase the success probability of ECM.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Elliptic Curve Method (ECM)Edwards curves Montgomery curves torsion properties Galois groups
Contact author(s): joppe bos @ epfl ch
History: 2012-02-23: received
Short URL: https://ia.cr/2012/070
License: CC BY

BibTeX

@misc{cryptoeprint:2012/070,
      author = {Razvan Barbulescu and Joppe W.  Bos and Cyril Bouvier and Thorsten Kleinjung and Peter L.  Montgomery},
      title = {Finding {ECM}-Friendly Curves through a Study of Galois Properties},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/070},
      year = {2012},
      url = {https://eprint.iacr.org/2012/070}
}