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Paper 2012/070
Finding ECM-Friendly Curves through a Study of Galois Properties
Razvan Barbulescu and Joppe W. Bos and Cyril Bouvier and 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)
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Elliptic Curve Method (ECM)Edwards curvesMontgomery curvestorsion propertiesGalois groups
- Contact author(s)
- joppe bos @ epfl ch
- History
- 2012-02-23: received
- Short URL
- https://ia.cr/2012/070
- License
-
CC BY