Finding ECM-friendly curves through a study of Galois properties

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.
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Contributor : Razvan Barbulescu <>
Submitted on : Monday, February 20, 2012 - 9:47:24 AM
Last modification on : Tuesday, December 18, 2018 - 4:18:25 PM
Long-term archiving on : Friday, November 23, 2012 - 4:25:08 PM


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  • HAL Id : hal-00671948, version 1
  • ARXIV : 1202.4285


Razvan Barbulescu, Joppe Bos, Cyril Bouvier, Thorsten Kleinjung, Peter Montgomery. Finding ECM-friendly curves through a study of Galois properties. Algorithmic Number Theory Symposium, University of California, Jul 2012, San Diego, United States. ⟨hal-00671948v1⟩



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