Finding ECM-friendly curves through a study of Galois properties
Overview & Synopsis
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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hal.science)
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Document Information
| Document Title | Finding ECM-friendly curves through a study of Galois properties |
|---|---|
| Author / Organization | Razvan Barbulescu, Joppe W. Bos, Cyril Bouvier, Thorsten Kleinjung, Peter L. Montgomery |
| Subject & Discipline | Multidisciplinary Academic Open Research |
| Categories | Science & Mathematics |
| Publication Year | 2012 |
| License / Rights | Open Access / Creative Commons |
| Resource Verification | Listed PDF (Verification Pending) |
| Original Host Website |
HAL Open Science
(hal.science)
|
| File Format | application/pdf (Portable Document Format) |
| Language | EN |
| Catalog ID | DOC-22939 |
| Original Source Link | Visit Source Page on hal.science » |