Re: Call for participation
pleyland_at_microsoft.com
Date: 11/16/03
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Date: 16 Nov 2003 16:07:27 +0000
"Tom St Denis" <tomstdenis@iahu.ca> writes:
> <pleyland@microsoft.com> wrote in message
>
> > our effort to a record-breaking factorization of the 239-digit
> > cofactor of 2^811-1, aka M811 in GIMPS terms or 2,811-.c239 to the
> > Cunningham project.
>
> First off, heads up to anyone trying Bob's code. It won't build with GCC
> [afaik] and he has win32 binaries only... BOO!
> [btw this is why I go out of my way to write portable code that
> while a tad slower than the "best" will build ANYWHERE not just on
> Bob's Win32 C compiler....].
We (NFSNET) try hard to make our code portable. We know it runs on
Windows >= W95, x86 FreeBSD (v4.x and 5.x), x86 Linux, Sparc Solaris
and Mac OSX. Other architectures on request, assuming we can find a
system to build on.
> As for NFSNET... WHY OH WHY? Who cares what the factors of 2^811 -
> 1 are? Does this mean you can factor say RSA keys of the same
> length with the same effort? [I know for a fact you can't....].
Mathematicians care. Some cryptographers care.
> As far as math is concerned those factors are useless. As far as
> crypto is concerned it's useless too.
You know a different set of mathematicians from the set with which I
correspond. For instance, Richard Brent is interested in the factors
of Mersenne numbers because, inter alia, they form the basis of a
class of long-period random number generators, themselves of interest
to some designers of stream ciphers. Go explore Brent's site at
http://web.comlab.ox.ac.uk/oucl/work/richard.brent/index.html and see
whether you still believe these numbers are of no interest to either
mathematicians or cryptographers. Please report back on your
findings.
> Unless you can directly map your work to a GNFS attack there is
> little merit... e.g. you may say "Oh but NFSNET factored a 800 bit
> integer" and I'll say "That was with the SNFS which can't be used
> against RSA so I don't care."
It is well known by now, or should be if you have been paying
attention, that SNFS can factor integers close to 1.5 times as long as
can GNFS for a comparable effort. If you divide 811 by 1.5 you will
discover that a 540-bit general integer could be factored with very
nearly the same effort.
The advantage of SNFS is that we don't have to muck around trying to
find good polynomials (though that is an interesting subject in its
own right) and there is a good collection of integers with a simple
mathematical description available on which to develop our algorithms.
> Just my two cents...
>
> Tom
Likewise.
Paujl
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