20060312, 09:02  #1 
Sep 2005
UGent
111100_{2} Posts 
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 welldefined answer, but at least it would help to have an algorithm which is not completely stupid. 
20060312, 09:49  #2 
Jun 2003
3·5·107 Posts 
ECM would be the fastest.

20060312, 12:10  #3  
"William"
May 2003
Near Grandkid
3·7·113 Posts 
Quote:
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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