🚀 go-pugleaf

In article <19122.Aug2700.12.0192@virtualnews.nyu.edu> brnstnd@nyu.edu (D. J. Bernstein) writes:
:In article <1992Aug26.132003.5928@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
:> Actually, estimating how long the general number field sieve
:> will take with respect to the quadratic sieve CAN be done without factoring
:> any numbers with GNFS.
:
:Of course---that's exactly what you and Adleman have been doing. The
:problem is that you haven't been doing it *accurately*. Here, for the
:benefit of sci.crypt readers, I'll run through the inaccuracies in the
:above article.
 
All you are doing is gainsaying my data without posting data of your own.

:Your general statement about 6-7 digits corresponding to a 2x speedup
:for 130-digit numbers is not accurate; even a casual analysis of
:Dickman's rho function (why do you call that ``the Knuth-Schroeppel
:function''? Dickman is the one who defined it) would show that the
 
you are confusing the two functions. go ask Arjen about the 
Knuth-Schroeppel function.

:speedup is more than 5. Why are you trying to discourage people from
:entering the RSA-129 contest, Bob?

Now this last accusation really is obnoxious, because it puts words
in my mouth that I have never said.

:You say that ``if many small primes split completely in the extension
:field, this is beneficial to factoring the algebraic side''---but the
:truth is that *any* small prime splitting *at all* in the extension
:field provides a noticeable speedup. *Complete* splitting is rare.

Not that rare. the frequency is 1 over the degree of the Galois closure
of the field.
 
So, Dan, if you can do better, why don't you display your obviously
superior knowledge of such things by giving us your data and estimates.
--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"