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 2009-07-27, 15:36 #1 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 17×251 Posts optimal B1 Which is more efficient: running ECM with a few large B1 increments, (e.g. run some curves at B1=11e3, then more at 5e4, then ...) or incrementing B1 by some optimized amount for each curve? What gives the best optimization for how quickly the minimum expected factor size can grow? Granular B1 increments are certainly more convenient for communicating and calculating work done (it's certainly easier to say, "I've run 2000 curves at B1=11e6" and to calculate the level from that than if it was incremented), but are they more efficient?
2009-07-27, 15:58   #2
R.D. Silverman

Nov 2003

161008 Posts

Quote:
 Originally Posted by Mini-Geek Which is more efficient: running ECM with a few large B1 increments, (e.g. run some curves at B1=11e3, then more at 5e4, then ...) or incrementing B1 by some optimized amount for each curve? What gives the best optimization for how quickly the minimum expected factor size can grow? Granular B1 increments are certainly more convenient for communicating and calculating work done (it's certainly easier to say, "I've run 2000 curves at B1=11e6" and to calculate the level from that than if it was incremented), but are they more efficient?
Read my joint paper with Sam Wagstaff: A Practical Analysis of ECM.

It answers these kinds of questions (and more).

2009-07-27, 17:04   #3
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

426710 Posts

Quote:
 Originally Posted by R.D. Silverman Read my joint paper with Sam Wagstaff: A Practical Analysis of ECM. It answers these kinds of questions (and more).

2009-07-27, 18:26   #4
R.D. Silverman

Nov 2003

11100010000002 Posts

Quote:
 Originally Posted by Mini-Geek Is the paper available for free anywhere? (preferably as a PDF)
I don't know whether this is free:

http://cat.inist.fr/?aModele=afficheN&cpsidt=3769506

You can get a copy from the AMS website, but as they own the
copyright, it costs \$.....

2011-05-27, 12:19   #5
Walter Nissen

Nov 2006
Terra

2·3·13 Posts
key paper from 1993

Quote:
 Originally Posted by Mini-Geek Is the paper available for free anywhere? (preferably as a PDF)
A practical analysis of the elliptic curve factoring algorithm
Robert D. Silverman; Samuel S. Wagstaff
Math. Comp. 61 (1993), 445-462
in .pdf is available free from :
http://www.ams.org/journals/mcom/199...993-1122078-7/

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