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| HAL: hal-00671948, version 1 |
| arXiv: 1202.4285 |
| See detailed view |  BibTeX,EndNote,... |
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| Algorithmic Number Theory Symposium, San Diego : United States (2012) |
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| Available versions | v1 (2012-02-20) | v2 (2012-09-04) |
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| Finding ECM-friendly curves through a study of Galois properties |
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| Razvan Barbulescu 1Joppe W. Bos 2 |
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| (2012-02-20) |
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| 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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| 1: | CARAMEL (INRIA Nancy - Grand Est / LORIA) |
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INRIA – CNRS : UMR7503 – Université de Lorraine |
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| 2: | Laboratory for Cryptologic Algorithms (LACAL) |
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École Polytechnique Fédérale de Lausanne |
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| 3: | Microsoft Research [Redmond] |
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Microsoft |
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| CARAMEL |
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| Domain | : | Computer Science/Cryptography and Security Computer Science/Computer Arithmetic Mathematics/Number Theory |
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| Elliptic Curve Method (ECM) – Edwards curves – Montgomery curves – torsion properties – Galois groups |
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| hal-00671948, version 1 | |
| http://hal.inria.fr/hal-00671948 | |
| oai:hal.inria.fr:hal-00671948 | |
| From: Razvan Barbulescu | |
| Submitted on: Monday, 20 February 2012 09:47:24 | |
| Updated on: Friday, 20 April 2012 17:21:03 | |
