In number theory, a branch of mathematics, the special number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from it.
The special number field sieve is efficient for integers of the form re ± s, where r and s are small (for instance Mersenne numbers).
Heuristically, its complexity for factoring an integer is of the form:[1]
in O and L-notations.
The SNFS has been used extensively by NFSNet (a volunteer distributed computing effort), NFS@Home and others to factorise numbers of the Cunningham project; for some time the records for integer factorization have been numbers factored by SNFS.
^Pomerance, Carl (December 1996), "A Tale of Two Sieves" (PDF), Notices of the AMS, vol. 43, no. 12, pp. 1473–1485
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