20050419, 15:11  #1 
"William"
May 2003
New Haven
2^{3}·5·59 Posts 
Guidelines for ECM Before Other Methods
I have seen guidelines that say that before using GNFS, you should do ECM to 1/3 of the digits. And before doing SNFS, you should do ECM to 2/9 of the digits. For smaller numbers MPQS is better, but I haven't seen any guidelines for how much ECM to do first.
Do people generally agree on the first two guidelines, and what do people recommend for QS? 
20050419, 15:58  #2  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10100100001010_{2} Posts 
Quote:
I use the 1/3 guideline for MPQS too. These days it doesn't make much sense to use QS much above 100 digits and those take a short time with modern implementations on modern hardware. All the above assume you know nothing about the factors, other than that there are at least two and that they have not yet been found by trial division and ECM. If you know more about the factors (that they are of comparable size, as in RSA public moduli ,for instance) you need to take that additional information into account. Paul 

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