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wblipp 2005-04-19 15:11

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?

xilman 2005-04-19 15:58

[QUOTE=wblipp]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?[/QUOTE]
As long as you realise that the guide lines are only convenient rules of thumb and [b]not[/b] the output from rigorous optimization calculations, the first two work well in practice.

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 [b]nothing[/b] 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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