| Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3). |
Navigation
| Topics | Help • Register • News • History • How to • Sequences statistics • Template prototypes |
Difference between revisions of "Special number field sieve"
(restored) |
(shortcut) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | The '''special number field sieve''' | + | {{Shortcut|SNFS|Special number field sieve: special-purpose [[factorization]] algorithm.}} |
| + | The '''special number field sieve (SNFS)''' is a special-purpose [[factorization]] algorithm. The [[general number field sieve]] (GNFS) was derived from it. | ||
The special number field sieve is efficient for integers of the form ''r''<sup>''e''</sup> ± ''s'', where ''r'' and ''s'' are small. In particular, it is ideal for factoring [[Mersenne number]]s. | The special number field sieve is efficient for integers of the form ''r''<sup>''e''</sup> ± ''s'', where ''r'' and ''s'' are small. In particular, it is ideal for factoring [[Mersenne number]]s. | ||
| Line 6: | Line 7: | ||
:<math>\Theta\left(\exp\left( \left(\frac{32}{9}n\right)^{\frac{1}{3}} (\log n)^{\frac{2}{3}} \right)\right).</math> | :<math>\Theta\left(\exp\left( \left(\frac{32}{9}n\right)^{\frac{1}{3}} (\log n)^{\frac{2}{3}} \right)\right).</math> | ||
| − | The SNFS has been used extensively by [[NFSNET]] (a volunteer [[distributed computing]] effort) and others to factorise numbers of the [[Cunningham | + | The SNFS has been used extensively by [[NFSNET]] (a volunteer [[distributed computing]] effort) and others to factorise numbers of the [[Cunningham project]]. |
The first step is the [[SNFS polynomial selection|polynomial selection]]. | The first step is the [[SNFS polynomial selection|polynomial selection]]. | ||
| Line 15: | Line 16: | ||
==External links== | ==External links== | ||
| − | *[[Wikipedia:Special number field sieve|Special number field sieve]] | + | *[[Wikipedia:Special number field sieve|Special number field sieve]] |
*[http://sourceforge.net/projects/ggnfs GGNFS], developed by Chris Monico, containing Kleinjung/Franke polynomial selection and Jens Franke's lattice siever. | *[http://sourceforge.net/projects/ggnfs GGNFS], developed by Chris Monico, containing Kleinjung/Franke polynomial selection and Jens Franke's lattice siever. | ||
*[https://sourceforge.net/projects/msieve Msieve], developed by Jason Papadopoulos, having sophisticated postprocessing. | *[https://sourceforge.net/projects/msieve Msieve], developed by Jason Papadopoulos, having sophisticated postprocessing. | ||
*[http://cado-nfs.gforge.inria.fr/ CADO-NFS] on INRIA. | *[http://cado-nfs.gforge.inria.fr/ CADO-NFS] on INRIA. | ||
[[Category:Factorization]] | [[Category:Factorization]] | ||
Latest revision as of 12:07, 19 February 2019
The special number field sieve (SNFS) is a special-purpose 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. In particular, it is ideal for factoring Mersenne numbers.
Its running time, in asymptotic notation, is conjectured to be:
- [math]\displaystyle{ \Theta\left(\exp\left( \left(\frac{32}{9}n\right)^{\frac{1}{3}} (\log n)^{\frac{2}{3}} \right)\right). }[/math]
The SNFS has been used extensively by NFSNET (a volunteer distributed computing effort) and others to factorise numbers of the Cunningham project.
The first step is the polynomial selection.
See also
External links
- Special number field sieve
- GGNFS, developed by Chris Monico, containing Kleinjung/Franke polynomial selection and Jens Franke's lattice siever.
- Msieve, developed by Jason Papadopoulos, having sophisticated postprocessing.
- CADO-NFS on INRIA.
