Eric Hahn wrote:
>
> If a person runs an ECM test using a B1 of 250,000 with 700
> curves (for up to 30 digits), will they also find any factors
> that they would have found if they had used a B1 of 50,000 with
> 300 curves (for up to 25 digits) ?!?
>
> Eric
If the sigma is the same, then a curve with B1=250000 will find any
factor that a curve with B1=50000 finds.
When you run 700 random curves at B1=250000, you might theoretically
miss a factor that someone else finds with B1=50000, if he gets a lucky
sigma so that the group order is very smooth. But in general, using the
same number of curves, the higher bound should find all the factors that
the lower bound can find.
But dont be tempted into running only a few curves at very high bounds.
The strength of ECM is that you can try curves with different group
orders until a sufficiently smooth one comes along. So "skipping" bound
levels is usually not a good idea unless you have reason to believe the
the number unter attack has only large factors which call for a higher
bound.
Ciao,
Alex.
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