Finite-field DLP / Small characteristic · heuristic L(1/3)

The Special Function Field Sieve

Oliver Schirokauer

SIAM Journal on Discrete Mathematics 2002

PublishedSource checked

Time bound: L_Q[1/3, (32/9)^1/3], Q=pⁿ
Space bound: Not extracted from the source

Source / version date: 2002
Comparison variant: Small characteristic · heuristic L(1/3)
Cost scale: L_pⁿ[1/3,c]
coefficientExact: (32/9)^{1/3}

Assumptions and source notes

Function-field-sieve modification retaining the same constant while extending the characteristic range to p ≤ n^{o(sqrt(n))}. The analysis is conjectural.

Source location

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

Primary source ↗

BibTeXDownload .bib

@article{schirokauer02,
  author = {Oliver Schirokauer},
  title = {{The Special Function Field Sieve}},
  journal = {SIAM Journal on Discrete Mathematics 16(1), 81–98},
  year = {2002},
  doi = {10.1137/S0895480100372668},
  url = {https://epubs.siam.org/doi/10.1137/S0895480100372668},
  keywords = {discrete logarithms, function field sieve, special primes},
  cr_date = {2002-12-31},
  cr_date_precision = {year},
  cr_status = {published},
  cr_venue = {SIAM Journal on Discrete Mathematics 16(1), 81–98},
  cr_author_ids = {oliver-schirokauer}
}