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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 Connect in order to contact the contributor
Submitted on : Monday, September 3, 2012 - 10:58:27 AM
Last modification on : Friday, November 18, 2022 - 9:28:19 AM
Long-term archiving on: : Friday, December 16, 2016 - 6:56:23 AM


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  • HAL Id : hal-00671948, version 2
  • ARXIV : 1202.4285



Razvan Barbulescu, Joppe W. Bos, Cyril Bouvier, Thorsten Kleinjung, Peter L. Montgomery. Finding ECM-friendly curves through a study of Galois properties. ANTS-X 10th Algorithmic Number Theory Symposium - 2012, University of California, Jul 2012, San Diego, United States. ⟨hal-00671948v2⟩



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