Re: Breaking Large Composite Numbers...???

On Dec 17, 5:44�pm, user923005 <dcor...@xxxxxxxxx> wrote:
On Dec 17, 2:21�pm, Pubkeybreaker <pubkeybrea...@xxxxxxx> wrote:

Irrelevant, since such information is not protected by public-key
methods.

It was an example of possible valuable information. �I assume that you
can


public key methods are NOT used for encryption. They are used for
dig. sig. and key exchange.



�Or are you saying that
public key encryption should not be used for that type of
information. �If so, that would mean that you do not believe it is an
effective deterrent.

Non sequitur. The strength of public key algorithms has nothing
to do with whether one uses it for encryption of sensitive
intelligence
or military information.


to make you feel fully
comfortable, knowing that for a few thousand dollars you can get a 1
TFlop machine that runs off of a stack of graphics cards?

Since NFS does not use floating point, such a machine is also
irrelevant. �As are its graphic cards. �And even if such machines
were
suitable, you will �need at least several hundred thousand of them
for
just the sieve phase. �You have no appreciation for the amount
of arithmetic required.

I am sure that you realize that floating point units can also process
integer math and that floating point units can perform fft algorithms
to perform arbitrary precision arithmetic faster than any other known
method.

NFS *sieving* is not 'integer math'. And it does not require
extended precision arithmetic. Do you know anything about
the algorithm at all????

And fft's perform extended precision MULTIPLICATION
faster than other methods for large enough integers. They do
not perform general extended precision arithmetic faster
than other methods.

But since NFS does not require multiplication of large
operands, their ability to perform fft's quickly is irrelevant.

These machines have the wrong ARCHITECTURE to perform
well on NFS.

And you would STILL �be unable to do the LA. Didn't you
get that message????

I am not convinced.

Irrelevant. You don't know enough about the problem to
have an informed opinion. You have never implemented NFS,
and you have no experience with solving large sparse matrices
over a finite field.


�All I see is handwaving. �What citation do you
offer to show the infeasibility?

I am the citation, by itself. I am one of the world's
leading experts on factoring algorithms, and QS and
NFS in particular.

I suggest you read:
R. Silverman Optimal Parameterization of SNFS.
J. Math. Cryptology, Jan 2008 for a starter.

I suggest you go read the many discussions in the
Mersenneforum from people who have extensive experience
in writing and executing the LA software required by NFS.


Sometimes I wonder why I bother giving information at all.

I guess that you just aren't a very good teacher. �If you gave the
information and it was clear and unambiguous and it was read and
understood, then I imagine a person of moderate intelligence would not
make posts that create your ranting follow-ups.

Discussion of any subject requires that the reader has
the necessary prerequisites to understand the discussion.
You clearly lack those prerequisites. Others in this discussion
have had no problem understanding what I have said.

And your use of 'ranting follow-ups' shows that you have
nothing to say except resorting to a personal attack.

May I suggest that you actually STUDY this subject before
prattling again????

What reference should I consult

Repeat after me: Google is my friend.
.

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