factorization algorithm
1Factorization — This article is about the mathematical concept. For other uses, see Factor and Integer factorization. A visual illustration of the polynomial x2 + cx + d = (x + a)(x + b) where… …
2Integer factorization — In number theory, integer factorization is the way of breaking down a composite number into smaller non trivial divisors, which when multiplied together equal the original integer.When the numbers are very large, no efficient integer… …
3Dixon's factorization method — In number theory, Dixon s factorization method (also Dixon s random squares method[1] or Dixon s algorithm) is a general purpose integer factorization algorithm; it is the prototypical factor base method, and the only factor base method for which …
4Pollard's rho algorithm — is a special purpose integer factorization algorithm. It was invented by John Pollard in 1975. It is particularly effective at splitting composite numbers with small factors.Core ideasThe rho algorithm is based on Floyd s cycle finding algorithm… …
5Continued fraction factorization — In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general purpose algorithm, meaning that it is suitable for factoring any integer n, not depending on special form or properties.… …
6Williams' p + 1 algorithm — In computational number theory, Williams p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic group factorisation algorithms. It was invented by Hugh C. Williams in 1982. It works well if the number N to be… …
7Index calculus algorithm — In group theory, the index calculus algorithm is an algorithm for computing discrete logarithms. This is the best known algorithm for certain groups, such as mathbb{Z} m^* (the multiplicative group modulo m ).Dubious|date=April 2008 Description… …
8Pollard's p - 1 algorithm — Pollard s p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special purpose algorithm, meaning that it is only suitable for integers with specific types of factors; it is the simplest …
9Bruun's FFT algorithm — Bruun s algorithm is a fast Fourier transform (FFT) algorithm based on an unusual recursive polynomial factorization approach, proposed for powers of two by G. Bruun in 1978 and generalized to arbitrary even composite sizes by H. Murakami in 1996 …
10Shor's algorithm — Shor s algorithm, first introduced by mathematician Peter Shor, is a quantum algorithm for integer factorization. On a quantum computer, to factor an integer N, Shor s algorithm takes polynomial time in log{N}, specifically O((log{N})^3),… …
