Re: JSH: My view on factoring problem situation

On Nov 4, 11:12 pm, (Gordon Burditt) wrote:
You've blown your credibility.  If you claim that 2+2=4, no first-grade
math student who recognizes you will believe it, even if you say
you have a proof.

We'll see.

Have you admitted yet that "the factoring problem" includes as an
important element the issue of speed of factoring?  If not, well,

I always have.

Then how come none of your proofs mention the speed of the algorithm?

That's a fair question: surrogate factoring factors one number by
factoring another, so its "speed" is dependent both on the ability to
factor the surrogate as well as the efficacy of doing that

So it does not analyze well with Big O notation.

trial division has been around for a long, long time, much longer
than you have been alive.  If you're not going to factor large
numbers, how do you intend to prove that it's fast?  "It's freaking
algebra" doesn't cut it.  Inverting a trillion x trillion matrix

There is no generally accepted method for solving quadratic residues
modulo N.

I've provided such a method: a world's first.

It just so happens that such a thing also solves the factoring

You haven't proved that it works faster than trial division.  For
that matter, you haven't proved that it always works, either.  I
think you did prove that *if* it works, it provides a correct answer,
not necessarily faster than trial division.  That alone is not much
of an accomplishment.

So it's a two-fer.

Not without the missing pieces.

The method connects two factorizations so that factoring one is
connected with factoring the other.

It also proves that EVERY integer factorization is connected to an
infinity of other factorizations--surrogate factorizations.


It is the method for finding quadratic residues modulo N.

And it has been around for around a year now, as I'm sort of
celebrating a belated birthday for the discovery.

Now you can say I don't have credibility but I figure if it works
SOMEONE in the world is probably using it now.

And may have been using it for months.

So what?  I don't buy your doomsday theories that cracking RSA will
cause a world panic.  There are lots easier ways of stealing credit
card numbers than cracking SSL used in e-commerce stores.

Unless people like you have watched exploits and rationalized them
away, deciding that they were "human error".

There are plenty of exploits that don't require cracking SSL, such
as dumpster diving, finding a plaintext file on the server containing
large amounts of credit card info, hacking or social-engineering
the administrator's password, bribing an employee, use of card-number
generators, stealing old backup tapes, etc.  These get maybe hundreds
of thousands of cards at a time.  These have been going on long
before you came up with your method.  (The Egghead breach was at
least 10 years ago, wasn't it?)

Even if you can trivially break SSL, you have to be in a position
where you can tap the traffic to the e-commerce web site (such as
working at their ISP), and that's not very easy, especially if you
are in a different country.  And you only get one card at a time
if you break an SSL connection to an ordinary user buying something,
and only if he enters his card number on that connection (he might
just be checking shipment status).

Ok, so you personally vouch for the safety of the world. Sounds good
to me!!!

I've seen math people do some weird things to go into denial over my

You think I'm a "math people"?  How wrong you are!  I don't even read

IT is unfortunately possible that widespread exploits are commonplace
now, and security experts are explaining them all away.  If so, then
there really is no way to know what the current security situation is.

For all we know at this point, there is no security currently in place
any more.  

As I said, if SSL vanished tomorrow, I doubt it would cause worldwide

After I felt I had a major breakthrough with the factoring problem I
decided to consider the bigger problem of P vs. NP, so I solved TSP,
using a second traveler moving backwards in time to meet himself
moving forward in time, along the optimal path.

So P=NP, so any asymmetric key system can potentially be broken AND
I've talked about the basic way to get to such answers which is by
introducing additional variables like the "backwards Traveler".

The problem here is that the denial by people like you is not rational
so you refuse to accept mathematical proof!!!

But if I'm right it's not necessary for me to factor some large number
at your request.

With hackers worldwide moving into and out of systems, at

Very doubtful that it's being done by SSL.  Remember, even hackers
can get authorized access to most of these servers using their own
accounts (user certificates are not in use).

Hopefully networks are ok, and I find it hard to believe that if there
were serious exploits those would not be noticed and major steps taken
as that's just too weird.

At this point a failure would probably involve the NSA and even the
new US cyber-command. And it would be a MASSIVE intelligence
failure. Possibly the biggest in the history of the world.

I go back and forth with myself on this subject, but I also know that
people can do the darndest things when it comes to rationalization.

The common real world example is Adolph Hitler who refused to accept
that German codes had been broken. That was critical in World War II,
and keeping such information hidden from him was critical to the

If hackers have completely breached world networks then why would they
let you know? But then, how could they NOT let you know?

But that's an endless moot argument around speculation. What is NOT
speculation is that there is not currently accepted a general
probabilistic method for solving quadratic residues modulo N, and I've
given one.

It IS generally accepted I believe that such a thing is also a
solution to the factoring problem.

See? Two different things. So I have a two-fer.

YES! If you wish you can loudly proclaim that solving quadratic
residues modulo N is just boring math that isn't interesting to people
like you!

James Harris