Special number field sieve (First Category Integer Factoring Integer Factoring)

Time Complexity

$O(exp(({1}+o({1})$)({32}n/{9})^{({1}/{3})}(log n)^{({2}/{3})}) heuristically?

Space Complexity

$O(n^{2/3})$ bits

(http://www.ams.org/notices/199612/pomerance.pdf)

Description

For integers of the form $r^e \pm s$, for r and s relatively small

Approximate?

Exact

Randomized?

No, deterministic

Year

1940