ECM And The Elliott-Halberstam Conjecture For Quadratic Fields
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | BARBULESCU, Razvan | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JOUVE, Florent | |
| dc.date | 2024 | |
| dc.date.accessioned | 2024-04-04T02:36:25Z | |
| dc.date.available | 2024-04-04T02:36:25Z | |
| dc.date.created | 2023-01 | |
| dc.date.issued | 2024 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190717 | |
| dc.description.abstractEn | The complexity of the elliptic curve method of factorization (ECM) is proven under the celebrated conjecture of existence of smooth numbers in short intervals. In this work we tackle a different version of ECM which is actually much more studied and implemented, especially because it allows us to use ECM-friendly curves. In the case of curves with complex multiplication (CM) we replace the heuristics by rigorous results conditional to the Elliott-Halberstam (EH) conjecture. The proven results mirror recent theorems concerning the number of primes p such thar p − 1 is smooth. To each CM elliptic curve we associate a value which measures how ECM-friendly it is. In the general case we explore consequences of a statement which translated EH in the case of elliptic curves. | |
| dc.language.iso | en | |
| dc.publisher | Instytut Matematyczny PAN | |
| dc.subject.en | Elliott-Halberstam conjecture | |
| dc.subject.en | Elliptic curve method | |
| dc.subject.en | Number field sieve | |
| dc.title.en | ECM And The Elliott-Halberstam Conjecture For Quadratic Fields | |
| dc.type | Article de revue | |
| dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 2212.11724 | |
| bordeaux.journal | Acta Arithmetica | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03485435 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03485435v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Acta%20Arithmetica&rft.date=2024&rft.au=BARBULESCU,%20Razvan&JOUVE,%20Florent&rft.genre=article |
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