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RE: [PrimeNumbers] Stage 1 / Stage 2 ratios

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  • Paul Leyland
    ... There s a paper by Bob Silverman and at least one co-author, which examines the choice of parameters in ECM. When Tim Charron, Paul Zimmermann and I were
    Message 1 of 4 , Jun 28, 2002
      > There's little formality in the discussions that I've seen regarding
      > 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
      > recommendations.
      >
      > Does anyone know if there have been statistical studies made
      > regarding the 'best' ratio or relation between B2 and B1?

      There's a paper by Bob Silverman and at least one co-author, which
      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.


      Paul
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