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JSH: Upside down situation
Posted:
Mar 14, 2008 8:06 PM
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For those who missed it, a poster who has routinely critiqued my
factoring research made a post noting that my latest research gave an
algorithm better than Fermat's and I guess that was cool of that
person to admit.
I am currently working on my own practical implementation of what I
call surrogate factoring that follows from the latest theory, and it
is pleasingly fast, while I still have to work at getting it to factor
really big numbers to my satisfaction. Oh, my stated goal is the
ability to factor an RSA encryption sized number in under 10 minutes
on a standard desktop.
Now there is no doubt that I've discovered a new factoring method
then. And that factoring method at its heart relies on the use of two
congruences where mathematicians have traditionally used one:
x^2 = y^2 mod p
and
z^2 = y^2 mod T
where T is your target composite to factor and p is what I call a
helper prime, as it is just there to help you factor, and otherwise
does nothing. So it's just kind of like your buddy. There to help
you, then kind of wander off, other things to do...
There are rules for p though, as, with T factored into two positive
factors, p must be LESS than the smaller factor or p minus the smaller
factors must be less than it, which will make more sense later with
the congruence relations for those factors modulo p.
But incredibly, as in monster math that just kind of boggles the mind,
surrogate factoring tells you that there is a deeper structure to z,
where
z = (1 + 2?^2)k/(2?)
where
k^2 = (1 + ?^2)^{-1}(nT) mod p
and 'n' is a helper variable allowing you to shift things around when
needed, and ? is found such that k exists.
And finally, with f_1*f_2 = nT:
f_1 = ?k mod p
and
f_2 = ?^{-1}(1 + ?^2)k mod p.
So there is this whole zoo of new relations for the classical
difference of squares that follow from just adding one more
congruence!!! And it just gets better.
It turns out that for solutions in all integers, k will be near what I
call k_0, where k_0 is the value of k such that
abs(nT - (1 + ?^2)k_0)
is a minimum. Which is just one of the most beautiful pieces of
mathematics that you will ever see, and it helps a lot.
So you can factor T, modulo p, where to find p you look for big primes
that are not too big, and solve for k modulo p, and then find a k with
that residue near k_0 and then you can look for the k that will factor
modulo p.
Great!!! Easy!!! Factoring made easy!!! Pushing the easy button on
factoring!!!
So why am I still babbling on newsgroups about this and math society
isn't hollering to the public about it?
Because we are in an upside down situation.
I liken it to if Olympic runners faced races with people who were
unethical actors who fantasized at being Olympic runners, who were in
the stands, and were the judges and were everywhere, so that when the
Olympic runner ran the race and won, they'd just say he didn't and
award the gold medal to one of their own.
You see, I have other major discoveries. Math people just lie about
them. And call me names. Nasty names, like crackpot and crank. And
even NASTIER names.
They can get away with this as they have what I call, critical mass.
MOST mathematicians around the world are like those wannabe runners.
So they can just as a group, lie, and who can challenge them then?
Only factoring can which is where this situation gets really, really,
really strange, as hey, if the surrogate factoring theory is correct,
then quite a few people around the world can now, um, probably, um,
factor really huge numbers, but if math people ARE wannabes like I
say, they have NO INCENTIVE to tell the truth, except being decent
human beings, but I digress.
So game theory says they will lie and claim that nothing has changed,
nothing is wrong, nothing to see here, and will explain any security
breaches if they happen, away, and will do so indefinitely.
So game theory says they will do their best to collapse human
civilization as we know it, and we are traveling down that scenario
now.
End of this tale, may be that history is being ended now. The front
story to troubles with stock markets will carry things so far, but
eventually, oh, eventually civilization as we know it will just
collapse, people will turn to endless wars, there will be mass
starvation, disease, lots of nasty flies and things, Armageddon and
all that stuff, but...
Yes, there is a but. I didn't like that end to the story.
So I changed it.
Oh, but I had to lose two countries.
James Harris
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