RE: [PrimeNumbers] Stage 1 / Stage 2 ratios
> There's little formality in the discussions that I've seen regardingThere's a paper by Bob Silverman and at least one co-author, which
> the stage 1 /stage 2 division for the group order based block-GCD
> factoring algorithms such P-1, P+1, ECM, et al.
> The bell curve of opinions puts B2/B1 roughly between 10 and 100,
> with the comment that if you're spending about the same amount of
> time in each stage, then you're not too far out. ECM has a relatively
> faster B2, and so ECM advice is for larger B2s than P-1
> Does anyone know if there have been statistical studies made
> regarding the 'best' ratio or relation between B2 and B1?
examines the choice of parameters in ECM. When Tim Charron, Paul
Zimmermann and I were setting up the ECMNET client/server network I
attempted to read it. I'll be honest: I found it very heavy going and
didn't fully understand it. As it was gross overkill for our
requirements I didn't make a lot of effort to increase my understanding.
However, as I've often found out, one can never have too much overkill
and I now realise I should have tried harder.
I'll see if I can dig out the reference. Some of the paper is probably
relevant to your requirements. As I remember it, it's purely analytical
and reports no experimental testing of the results --- but my memory is
not what it was, or so I believe.