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Finding ECM-friendly
curves through a study of Galois properties
Razvan Barbulescu, Joppe W. Bos, Cyril Bouvier, Thorsten Kleinjung and Peter L. Montgomery |
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Vol. 1 (2013), No. 1, 63–86
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Abstract |
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We prove some divisibility properties of the cardinality of elliptic curve groups 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 behind the proofs help us to find new infinite families of elliptic curves with good division properties increasing the success probability of ECM. |
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Keywords
elliptic curve method (ECM), Edwards curves, Montgomery
curves, torsion properties, Galois groups
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Mathematical Subject Classification 2010
Primary: 14H52
Secondary: 11Y05
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Milestones
Published: 14 November 2013
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Authors |
| Razvan Barbulescu | |
| Université de Lorraine LORIA - Bât. A Équipe CARAMEL Campus Scientifique, BP 239 54506 Vandoeuvre-lès-Nancy France |
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| Joppe W. Bos | |
| Microsoft Research One Microsoft Way Redmond, WA 98052 United States |
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| Cyril Bouvier | |
| ENS Paris and Université de
Lorraine LORIA - Bât. A Équipe CARAMEL Campus Scientifique, BP 239 54506 Vandoeuvre-lès-Nancy France |
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| Thorsten Kleinjung | |
| EPFL Laboratory for Cryptologic Algorithms CH-1015 Lausanne Switzerland |
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| Peter L. Montgomery | |
| Microsoft Research One Microsoft Way Redmond, WA 98052 United States |
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