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Old 2003-08-07, 20:49   #12
smh
 
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Quote:
Does anybody know of any other factoring algorithms ?
P+1
Pollard Rho
quidric sieve (mpqs, siqs)
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Old 2003-08-08, 11:35   #13
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Originally Posted by smh
Quote:
Does anybody know of any other factoring algorithms ?
P+1
Pollard Rho
quidric sieve (mpqs, siqs)

There are dozens, if not hundreds. Browsing through some of the standard texts such as Riesel, Crandall&Pomerance, Knuth, Cohen will turn up many more.

SQUFOF, for instance is widely used to factoring double-length integers.

Dixon's algorithm is provably sub-exponential (unlike NFS and QS which are only heuristically so), very easy to program, and completely impractical in real life.

CFRAC to the quadratic sieve. Zhang's Special QS is a neat way of making the QS run faster for numbers of a special form.

Of historical interest are Legendre's and Gauss' algorithms.

An algorithm for finding small factors of a large number of integers is first to form the product of small primes and take GCDs. Yes, this one is used in real life.

Paul
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