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Old 2006-03-12, 09:02   #1
Jushi
 
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Sep 2005
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Default Algorithms for "small" numbers?

I am looking for algorithms to factor numbers of about 64 to 128 bits in size (20 to 39 decimal digits). I guess I should start with trial factoring with primes up to about 20 or 24 bits, but what would you recommend for the larger factors? The numbers I'm trying to factor are basically random, so they don't have any special form. On the other hand, they shouldn't be particularly hard to factor either.

I realize this question does not have a well-defined answer, but at least it would help to have an algorithm which is not completely stupid.
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Old 2006-03-12, 09:49   #2
Citrix
 
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ECM would be the fastest.
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Old 2006-03-12, 12:10   #3
wblipp
 
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Quote:
Originally Posted by Jushi
I am looking for algorithms to factor numbers of about 64 to 128 bits in size (20 to 39 decimal digits).
As a starting point you can look at what Dario Alpern has done in his java factoring applet at

http://www.alpertron.com.ar/ECM.HTM

He does trial factoring, then a few ECM curves, then SIQS. His ECM parameters and SIQS transition thresholds are described lower on that page.
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