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 2006-11-25, 22:13 #1 roger     Oct 2006 22×5×13 Posts A beginners question about ECM In regard to Alpertrons ECM applet, Why is it that factors are found at different curves while the size of the factor remains the same? Clearer : I have found a factor P33 at curve 722, and another P33 at curve 2231. Is there any specific reason for this? Thanks, Roger
 2006-11-26, 04:58 #2 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts ECM is a randomized algorithm. Whether a given factor is found with a curve depends on that curve's sigma value and the B1 and B2 values. Since we don't know which sigma values are going to be lucky in finding factors (because we don't know what the factors are!), implementations of ECM select the sigma value at random. Alex
2006-11-27, 16:13   #3
R.D. Silverman

Nov 2003

11101001001002 Posts

Quote:
 Originally Posted by roger In regard to Alpertrons ECM applet, Why is it that factors are found at different curves while the size of the factor remains the same? Clearer : I have found a factor P33 at curve 722, and another P33 at curve 2231. Is there any specific reason for this? Thanks, Roger
I would be happy to give a complete explanation. Before I do so,
it would be useful if you could tell me what you already know about
the ECM algorithm and what you know about Lagrange's Theorem and
elementary group theory. If you know nothing about the latter, explaining
the algorithm will be impossible.

 2006-11-29, 22:36 #4 roger     Oct 2006 22·5·13 Posts Thanks, anyway RD Silverman, I just wanted an overview, and am quite content with Akruppa's reply. Thanks for replying, Roger PS : no, I don't have any background in those topics, though I will google them.

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