ECM bounds

2011-07-17, 10:10

Hi, I would like to know if I have more chance of finding a factor with ECM doing 3 curves on an exponent with B1=1000000 B2=100000000 or doing 1 curve on the same exponent with B1=3000000 B2=300000000 or it is not difference.
Thanks a lot.

xilman · 2011-07-17, 15:37

Quote:

Originally Posted by Unregistered

Hi, I would like to know if I have more chance of finding a factor with ECM doing 3 curves on an exponent with B1=1000000 B2=100000000 or doing 1 curve on the same exponent with B1=3000000 B2=300000000 or it is not difference.
Thanks a lot.

The accurate answer is "it depends". It depends on the size of the factor which may be found.

In practice, and to a first approximation, it rarely matters all that much which of the two alternatives you choose because, for a given size of factor to be found, the work versus B1 curve has a very shallow minimum.

Paul

R.D. Silverman · 2011-07-17, 18:15

Quote:

Originally Posted by Unregistered

Hi, I would like to know if I have more chance of finding a factor with ECM doing 3 curves on an exponent with B1=1000000 B2=100000000 or doing 1 curve on the same exponent with B1=3000000 B2=300000000 or it is not difference.
Thanks a lot.

All of this, and more, is answered in my joint paper with Sam Wagstaff:
A Practical Analysis of ECM, Math. Comp.

c10ck3r · 2011-07-17, 20:11

Quote:

Originally Posted by R.D. Silverman

All of this, and more, is answered in my joint paper with Sam Wagstaff:
A Practical Analysis of ECM, Math. Comp.

Is this paper available online at no cost/low cost?
If so, please add link?

fivemack · 2011-07-17, 20:18

http://www.ams.org/journals/mcom/199...-1122078-7.pdf

2011-07-17, 10:10	#1
Unregistered 6267₁₀ Posts	ECM bounds Hi, I would like to know if I have more chance of finding a factor with ECM doing 3 curves on an exponent with B1=1000000 B2=100000000 or doing 1 curve on the same exponent with B1=3000000 B2=300000000 or it is not difference. Thanks a lot.

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2011-07-17, 20:18	#5
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 3·2,141 Posts	http://www.ams.org/journals/mcom/199...-1122078-7.pdf