HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

ECM and the Elliott-Halberstam conjecture for quadratic fields

Razvan Barbulescu 1
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Contributor : Razvan Barbulescu Connect in order to contact the contributor
Submitted on : Friday, December 17, 2021 - 11:50:51 AM
Last modification on : Wednesday, May 25, 2022 - 3:47:03 AM
Long-term archiving on: : Friday, March 18, 2022 - 6:53:21 PM


Files produced by the author(s)


  • HAL Id : hal-03485435, version 1



Razvan Barbulescu. ECM and the Elliott-Halberstam conjecture for quadratic fields. 2021. ⟨hal-03485435v1⟩



Record views


Files downloads