Cryptology ePrint Archive: Report 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.

Category / Keywords: Elliptic Curve Method (ECM), Edwards curves, Montgomery curves, torsion properties, Galois groups

Date: received 17 Feb 2012

Contact author: joppe bos at epfl ch

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Version: 20120223:132643 (All versions of this report)

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