Integer factorization algorithms

Special number field sieve

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: 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. (Wikipedia).

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Related pages

Fibonacci number | Integer factorization | Linear algebra | Smooth number | Big O notation | Algebraic number field | Greatest common divisor | Integer factorization records | Sieve of Eratosthenes | Mersenne number | Rational sieve | General number field sieve | Lucas number | Mathematics | Integer | Ring homomorphism | Root of a function | Ring (mathematics) | Number theory | L-notation | Irreducible polynomial | Computational complexity theory | Unique factorization domain | Modular arithmetic | Algorithmic efficiency