IFP / General integers · heuristic · L(1/2)

Factoring integers with elliptic curves

Hendrik W. Lenstra Jr.

Annals of Mathematics 1987

PublishedSource checked

Time bound: L_N[1/2, 1]
Space bound: Not extracted from the source

Source / version date: Nov 1987
Comparison variant: General integers · heuristic · L(1/2)
Cost scale: L_N[1/2,c]
derivation: Substitute log p = (1/2+o(1)) log N into sqrt(2 log p log log p).

Assumptions and source notes

For balanced semiprimes p ≍ sqrt(N), the conjectured ECM bound becomes the displayed L_N[1/2,1] bound. This is a direct parameter specialization of the paper’s small-factor expression.

Source location

Abstract; balanced-factor specialization
Version: Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08

Primary source ↗

BibTeXDownload .bib

@article{lenstra87,
  author = {Hendrik W. Lenstra Jr.},
  title = {{Factoring integers with elliptic curves}},
  journal = {Annals of Mathematics 126(3), 649–673},
  year = {1987},
  doi = {10.2307/1971363},
  url = {https://annals.math.princeton.edu/1987/126-3/p09},
  keywords = {factoring, elliptic curve method, small prime factors},
  cr_date = {1987-11-30},
  cr_date_precision = {month},
  cr_status = {published},
  cr_venue = {Annals of Mathematics 126(3), 649–673},
  cr_author_ids = {hendrik-w-lenstra-jr}
}