The system of factoring congruences I found give two basic paths to
getting a factorization with them, where I've debated which one is
easier. Now at least I can describe them better:

Reiterating what the result is, with

z^2 = y^2 + nT

where T is the target to factor and n is some nonzero integer you
pick, with p a prime you pick:

z = (2a)^{-1} (1 + 2a^2)k mod p,

k^2 = (a^2+1)^{-1}(nT) mod p

and

y = (1+2a^2)^{-1} z mod p

as I realized that the second solution I usually give is redundant.

The best case is with n=1, as then if p>sqrt(T), you only have the
trivial factorization or the non-trivial one to switch between but
that necessitates a search solving for k, where

k^2 = (a^2+1)^{-1}(T) mod p

For some really ancient discussion of this, there are documents about
Kerberos in ftp://athena-dist.mit.edu/pub/ATHENA/kerberos/doc

It says here the Kerberos model for authentication and authorization
is based on the Needham and Schroeder key distribution protocols,
modified with the addition of timestamps. "Their paper ... describes
the basic protocol; a tutorial paper by Voydock and Kent provides a
broader introduction to the topic and explains the timestamp
modifications"

The Needham and Schroeder paper is "Using Encryption for Authentication
in Large Networks of Computers" CACM 21:12 (Dec 1978) pp 993-999.

The Voydock and Kent paper is "Security Mechanisms in High-Level
Network Protocols", Computing Surveys 15:2 (June 1983) pp 135-171.

The paper I'm quoting from is in the above FTP site and directory
with the title techplan.PS

First off, I did find a proof of Fermat's Last Theorem, but did so
with methods that did show an error in "core" mathematics. The
journal that published my introductory paper did the right thing, and
the mathematics within it clearly shows there is something big there.
But the massive failures began when they collapsed under pressure, and
withdrew my paper, possibly puzzled themselves to finally learn that
their field was corrupt, and that's when I also learned just how
corrupt the math field had become.

As I looked for various ways to get my research accepted I tried
multiple avenues, so I have my Class Viewer open source project, and
lately I even came up with a business plan for YouTube as it was
bugging me that Google wasn't doing anything with it that made serious
money.

Nothing worked though to break the impasse.

Years back I concluded that one option was to solve the factoring
problem, as it was a non "pure math" area where denial was impossible.

Seemed brilliant to me, but as I've come closer to the solution I
realized there were problems with the idea.

On Jan 14, 11:24 pm, hbdere gmx.net> wrote:

I mathematically proved that the factoring congruences solve the
factoring problem.

And it's an easy proof.

On Jan 16, 8:40 pm, Enrico aol.com> wrote:

Thanks for all replies!

It's already implemented and 100%% working. I've just learn a little
bit more today :)

Cheers

1) Senator McConnell should read this story in the NYT, Dec.24,07 :"
In Kentucky's teeth,toll of poverty and neglect" were we find out
that Kentucky State has the highest level of toothless people,from
chewing tobaco ,lack of hygiene, lack of Health Insurance and
Education,
hundreds of thousands of Kentucky's citizens spend their whole lifes
without a denture, without a simple "flipper" worth 100 dollars to
let them chew and look like normal human beens, in the USA in
2008 !!!
and while the
Senator sends 12 billion dollars a month to Iraq and Afghanistan to
feed the
Military and Security Contractors and his Hedge-Funds ( ....and the
100 Pentagon Generals that retired to Senior VP positions in the War
Contracting Business, and that's another story to COURT MARTIAL,
because will the young officers in the Pentagon expose the corrupt
ones pushing the war to go on for more contracts ? SHAME ON THE
PHONY PATRIOTS !!!! ) .....anyway, going back to Senator
McConnell , his people are toothless, how can he let his own people
down like that ? how ? ...

Condradulations on you sucess James!

The foundation of the National Security Agency is based on highly advanced
mathematics. Currently, we are the largest employer of mathematicians in the
country. In order to remain a world leader in cryptologic methods in the
future, we must continue to explore, understand, and exploit the power of
advanced mathematics. This will also enable us to keep U.S. communications
secure and maintain the country's ability to exploit new, advanced foreign
communications systems.

In the world of the NSA, the language is mathematics and the tools are
high-performance supercomputers. Technical problems are often stated in
abstract terms, so mathematics is the natural language for precise
expression. Many of the advanced techniques that have resulted from this
research have potential applications to physical phenomena outside the
national security realm.

"JSH" gmail.com> wrote in message
news:e394c0aa-e4b1-46e3-9be8-fe30925f61f1@e23g2000prf.googlegroups.com...

We have in place all academic blocks, and node blocks, and have re-notified
the industrial military complex of this JSH threat, proper action is
currently underway by the AOC "association of old crows" and will conclude
with re-institutional confinement by this weekend.

On 14 Jan, 21:12, orangata...@googlemail.com wrote: