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


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.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Elliptic Curve Method (ECM)Edwards curvesMontgomery curvestorsion propertiesGalois groups
Contact author(s)
joppe bos @ epfl ch
2012-02-23: received
Short URL
Creative Commons Attribution


      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},
      note = {\url{}},
      url = {}
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