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 2006-11-14, 01:52 #1 BWetter246   Aug 2005 1710 Posts ECM Factoring for beginners I was wondering if their are any basic papers/thesis on the internet on how ECM actually works. thanks, brandon
 2006-11-14, 03:05 #2 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts Depends on how deeply you want to understand how it works... could be anything between why sometimes factors pop out any why large B1,B2 values have a higher chance of finding a given factor, to details of elliptic curve arithmetic and curve parameterisation. A starting point is the http://www.mersennewiki.org/index.ph...c_Curve_Method page. A must-read for anyone who wants to implement ECM is Peter Montgomery's thesis, "An FFT extension of the Elliptic Curve Method of Factorization" (ftp://ftp.cwi.nl/pub/pmontgom/ucladissertation.psl.gz). Alex Last fiddled with by akruppa on 2006-11-14 at 03:05
2006-11-14, 14:17   #3
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by akruppa Depends on how deeply you want to understand how it works... could be anything between why sometimes factors pop out any why large B1,B2 values have a higher chance of finding a given factor, to details of elliptic curve arithmetic and curve parameterisation. A starting point is the http://www.mersennewiki.org/index.ph...c_Curve_Method page. A must-read for anyone who wants to implement ECM is Peter Montgomery's thesis, "An FFT extension of the Elliptic Curve Method of Factorization" (ftp://ftp.cwi.nl/pub/pmontgom/ucladissertation.psl.gz). Alex
There is also Peter's "Speeding the Pollard and Elliptic Curve Methods of
Factorization" back in Math. Comp. in the '87 Lehmer issue.

 2006-11-14, 18:18 #4 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts Indeed there is, and without doubt it is a landmark work on the subject. But the style of that paper is very terse and it may not be the best text to read for a newcomer. His thesis spends a little more time on explaining the various ideas so I think it's better for a first read. Alex
2006-11-14, 18:37   #5
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by akruppa Indeed there is, and without doubt it is a landmark work on the subject. But the style of that paper is very terse and it may not be the best text to read for a newcomer. His thesis spends a little more time on explaining the various ideas so I think it's better for a first read. Alex
Newcomer to factoring or newcomer to math beyond the high school level?
The latter will have great difficulty with either paper.

 2006-11-15, 13:19 #6 alpertron     Aug 2002 Buenos Aires, Argentina 25148 Posts In order to program my ECM factoring applet I used Richard Brent's publication Factorization of the tenth Fermat Number and Peter Montogomery's thesis cited above, among other online resources.

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