IFP / General integers · heuristic · L(1/3)

Modifications to the Number Field Sieve

Don Coppersmith

Journal of Cryptology 1993

PublishedSource checked

Time bound: L_N[1/3, (92+26 sqrt(13))^1/3/3]
Space bound: Not extracted from the source

Source / version date: Mar 1993
Comparison variant: General integers · heuristic · L(1/3)
Cost scale: L_N[1/3,c]
coefficientExact: (92+26 sqrt(13))^{1/3}/3

Assumptions and source notes

Heuristic many-polynomial/many-number-field variant; includes the first sieve/precomputation in the single-factorization cost. This theoretical asymptotic improvement is distinct from practical two-polynomial GNFS and from the separate factorization-factory regime.

Source location

Section 3, Parameters and Running Time, pp. 176–177
Version: Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08

Primary source ↗

BibTeXDownload .bib

@article{coppersmith93,
  author = {Don Coppersmith},
  title = {{Modifications to the Number Field Sieve}},
  journal = {Journal of Cryptology 6, 169–180},
  year = {1993},
  doi = {10.1007/BF00198464},
  url = {https://research.ibm.com/publications/modifications-to-the-number-field-sieve},
  keywords = {factoring, multiple number fields, number field sieve},
  cr_date = {1993-03-31},
  cr_date_precision = {month},
  cr_status = {published},
  cr_venue = {Journal of Cryptology 6, 169–180},
  cr_author_ids = {don-coppersmith}
}