you can start [url="https://openaccess.leidenuniv.nl/handle/1887/14567"]here[/url], which is a fairly in-depth treatment of your question.

[QUOTE=jasonp;259463]you can start [URL="https://openaccess.leidenuniv.nl/handle/1887/14567"]here[/URL], which is a fairly in-depth treatment of your question.[/QUOTE]

I already printed "Optimal Parameterization of SNFS" by R.D Silverman, that one will be next. Thank you.

[QUOTE=Andi47;259447]I just downloaded SVN 413 from Jeff's page. Is it intended, that the 15e binary says that it is SVN 406?
[/QUOTE]

Not sure about the endless loop, but the SVN 406 seems to be correct. The source file gnfs-lasieve4e.c that it is built from was last modified with SVN revision 406.

Jeff.

Attached an excel-table (updated today) which gives estimations for SNFS difficulty from 126 up to 252, based on factorizations I have done and factorizations that have been done by others.

[QUOTE=em99010pepe;260814]Attached an excel-table (updated today) which gives estimations for SNFS difficulty from 126 up to 252, based on factorizations I have done and factorizations that have been done by others.[/QUOTE]

My paper on optimal parameterization gives additional data.

Note that trying to fit a polynomial (and a fairly high degree one)
to a function known [b]NOT[/b] to be polynomial makes very little
sense. It would be much better to fit the o(1) term in the known
asymptotic run time. I gave a rump session talk on this at crypto
back in the late 90's.

[QUOTE=R.D. Silverman;260859]My paper on optimal parameterization gives additional data.

Note that trying to fit a polynomial (and a fairly high degree one)
to a function known [B]NOT[/B] to be polynomial makes very little
sense. It would be much better to fit the o(1) term in the known
asymptotic run time. I gave a rump session talk on this at crypto
back in the late 90's.[/QUOTE]

I printed your paper and it's been very helpful. At the beginning I was concentrated on chapter 4 but when I get more free time I will read the rest.

I know the polynomial fit makes almost no sense at all, I was just playing around with the variables.

Today I received more data to include on the excel-table, as soon as I get some free time I will share it (updated) on google pages.

[QUOTE=em99010pepe;260905]I printed your paper and it's been very helpful. At the beginning I was concentrated on chapter 4 but when I get more free time I will read the rest.

I know the polynomial fit makes almost no sense at all, I was just playing around with the variables.

Today I received more data to include on the excel-table, as soon as I get some free time I will share it (updated) on google pages.[/QUOTE]Note that a polynomial fit might actually be quite useful in practice for [b]interpolation[/b] between well-characterized data points, as long as it is a reasonably low-degree polynomial. To that extent it makes sense, especially if it is much easier to implement than something more justified by theory. Using it for [b]extrapolation[/b] is very likely to lead you astray.

Paul

[QUOTE=xilman;260916]Note that a polynomial fit might actually be quite useful in practice for [b]interpolation[/b] between well-characterized data points, as long as it is a reasonably low-degree polynomial. To that extent it makes sense, especially if it is much easier to implement than something more justified by theory. Paul[/QUOTE]

Once you fit the o(1) term in the exponent for L(N, c) extrapolation
becomes quite easy on a hand calculator. You can ALSO fit an
extrapolation function for the factor base size, since it is just L(N, c/2)
with a different o(1) term.

[QUOTE=R.D. Silverman;260917]Once you fit the o(1) term in the exponent for L(N, c) extrapolation
becomes quite easy on a hand calculator. You can ALSO fit an
extrapolation function for the factor base size, since it is just L(N, c/2)
with a different o(1) term.[/QUOTE]Agreed.

It's the fitting that might be a little more difficult in practice. It's trivial to fit a polynomial to data in Excel or its Open Office counterpart. If you have a decent stats tool available, fitting other curves is fairly straightfoward but many people wouldn't want to track down, install and learn how to use such a tool when they already have Excel to hand. To be honest, I can't say I blame them if all they want is a one-off solution to a one-off problem.

Paul

Attached an excel-table (updated today) which gives estimations for SNFS difficulty from 126 up to 252, based on factorizations I have done and factorizations that have been done by others
You can send me yours to em99010pepe at gmail dot com.

The file is available here: [url]https://sites.google.com/site/em99010pepe/snfs[/url]