Re: Surrogate factoring and the k/T ratio

On Mar 2, 9:12�pm, jst...@xxxxxxxxx wrote:
On Mar 2, 6:10 pm, rossum <rossu...@xxxxxxxxxxxx> wrote:





On 2 Mar 2007 14:02:18 -0800, jst...@xxxxxxxxx wrote:

Probability is by k.

Now I can guess you're not very bright so I'll explain it to you
carefully:

Let's say you have a target T that is an RSA number that you wish to
factor so that you can break some computer encryption and you're using
surrogate factoring.

If you know with 100% certainty that a particular k will factor your
target T with one of the combinations for the surrogates, but there
are 1000 combinations, is your factoring percentage 100% or 1/1000th?

I have said repeatedly and consistently that your methods work, so I
agree with your figure of 100% success.  My tests showed that your
method factored all 500 of the target numbers with zero errors.

What I showed was that for each k you have to try out a number of
possible factors.  The number of possible factors depends on the
factorisation of the surrogate derived from k.  Each of those possible
factors takes some time to test.  If there are a lot of possible
factors to try then they will take a lot of time to test.

Trial factorisation will find factors with 100% certainty.  The
problem with trial factorisation is that you have to try a large
number of non-factors before you find a factor.  Your methods are
similar, you have to try a lot of non-factors before you find a
factor.  That make the method slow because of all the work testing
non-factors.  I was trying to show you why your method is slow.

Your posting indicates you think it'd be 1/1000th when there is a
guarantee of factoring the target T, which is, well, just stupid.

I agree that your method guarantees finding a factor of any composite
T.  What is at issue is that your method is slower than existing
methods that also guarantee finding a factor of T.  Given a choice
between a faster guaranteed method and a slower guaranteed method then
the faster method is going to be the method of choice.

We know that your method can find factors, you need to work on
speeding it up so that it finds factors *quickly*.

rossum

If surrogate factoring works then it works one way, and in a way that
is entirely meant to solve the factoring problem, as it means that if
you have a hard to factor target T, you can get as many other
surrogates to factor as you wish, to attack it.

So you turn factoring one number into instead factoring other numbers,
like a conversion kind of thing.

So if some person picks a hard to factor number that has only 2 prime
factors, you can turn to surrogate factoring and face numbers that
have more than 2 prime factors that while still quite large, are
hopefully easier to factor, and the theory I'm looking at puts your
odds at very high by k.

Which goes back to my point that if you know a particular k, will
work, like with

2k^2 - T

as you could use 2k^2 - 2T or in general 2k^2 + wT, where w is a non-
zero integer, then if you know that to factor T, you can just factor
2k^2 - T, do you really care that you may loop through a lot of
combinations of the factors of 2k^2 - T?

And I think people may get the wrong idea there as well, as you can
stupidly pick k, and w, and you can intelligently pick them, to give
yourself easier numbers to factor, and maybe even few combinations.

One of my examples from my math blog gives some sense of the
potential:

T = 732367903, k=24412263

y=-170273672118069/2 and x=170273623293557/2

so, x+y=-24412256, which has 223 as a factor.

T = 732367903 = (223)(3284161)

Iterations: 1

Surrogate:

1191915704826532 = ( 2^2 )( 7 )( 73 )( 583129014103 )

f_1=7/2
f_2=170273672118076/2

Here readers can see that factoring the surrogate factored the target
with just one iteration, not just of k, but through combinations of
factors of the surrogate as well.

The theory says that could happen with an RSA number.

Now if you are insane, yes, you can explain away mathematicians
ignoring this research as them being highly intelligent, yes,
brilliant in some way that you with your more meager mind can't
comprehend.

Or if you are a rational adult you can worry why these people are
quiet now, when just a few years back the merest hint of something
related to factoring drew huge headlines when a group of
mathematicians proved that checking if a number is prime is in P.

They let headlines happen then because it helps their con.

They will not talk about my research because it does not.

They are protecting themselves in a highly coordinated way that leaves
no doubt what they are doing--if you are willing to quit being a patsy
for mathematicians who are not really brilliant and who often just
lie.

I have quite a few major mathematical results, including ones that
prove that modern "pure math" techniques are bogus, so the
mathematicians you trust don't want people to accept my research to
protect themselves.

These cons are working to block legitimate mathematical research to
protect their bogus research, so they are working to block the
advancement of the human species to protect themselves.

Wake up!  I picked factoring deliberately.

I have HUGE mathematical research that the cons are blocking.

I picked factoring deliberately to try and get some leverage against
these con artists who have taken over much of the mathematical field.

They are blocking out real research.  They are con artists.

NOTHING they are doing is of real value to humanity.

They are cons!!!

James Harris- Hide quoted text -

- Show quoted text -

Ok, I finally figured out what you meant by your suggestion
to use a known factor of T to see how k, F1, F2, and A-B
work together. Now I can generate values that work starting
with the factor of T and various k's that force one of F1 or
F2 to have small factors. Still debugging the routines, not
ready to look at that k/T ratio yet.

Enrico

.

Relevant Pages

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