Surrogate factoring, random is better?

jstevh_at_msn.com
Date: 02/17/05 

Date: 17 Feb 2005 15:27:09 -0800

I keeps seeing posters claiming that my surrogate factoring method is
worse than even chance or at best only as good as a chance method for
factoring.

There are several problems with their assertion.

That is, I suggest that they are lying. Here's why.

The base equations are

yx^2 + Ax - M^2 = 0

yz^2 + Az - j^2 = 0

and

T = M^2 - j^2

from which you can easily find

Ax= Az(-Az +/- sqrt((Az - 2M^2)^2 - 4TM^2))/(2j^2 - 2Az)

Az= Ax(-Ax +/- sqrt((Ax - 2j^2)^2 + 4Tj^2))/(2M^2 - 2Ax)

where I've basically wrapped up all the unknowns.

You give M, as it's the target, and j, as it's some picked integer, and
then everything else gets determined.

Well you have *two* base equations showing x, y, z and A are the
unknowns, and then I susbstitue out y and wrap A up with x and z, so
you have Ax, and Az as unknowns.

Substituting out y, gives you the two equations defining Ax and Az,
where the final constraint is the rationality of the square roots.

Now from the first equations square root there MUST be a rational Az
that factors M, so there must exist Ax, and Az such that M is factored.

That's a crucial point, and the first clue that posters must be lying,
as now you have a system where the factorization of M, the target, must
exist, for some solution.

I noted that Ax an integer doesn't usually work, as that's the basic
approach I tried before, and I agree that it gives a low probability of
success, but first thing to note, which CANNOT be disagreed with, there
is a rational Ax that MUST work.

So now you have an issue with the value of that Ax, as you might have

Ax = n/m

where n and m are integers.

Well, suddenly you have *two* more variables, in a system that up until
now has been fully constrained, as you had three unknowns with two
equations, where the final constraint is a rationality of square roots
constraint.

So guess what?

If posters claiming my method doesn't work are right, then m is
basically a random number.

My method then would be the world's first perfect non-quantum random
number generator.

If m is NOT random, then there is some mathematical reason or
constraint that governs the value of m, and then that can be determined
and if you figure it out, then you have a solution to the factoring
problem.

So, either I've found the world's first perfect, non-quantum, random
number generator, or there's a way to make this method work.

I suggest to you that posters are not so dumb as to not realize the
constraints and reality here, but are actually deliberately lying about
what follows mathematically, for their own reasons.

Now I did the analysis that shows that in fact the denominator of Ax IS
in fact determined so that it contains prime factors of T.

The math is not hard proving this fact.

Now then, I would be curious if any poster might reply explaining how
there is some other possibility than I mentioned:

1. A perfect random number generator

2. A method that must work in some deterministic fashion.

If and when they dodge those possibilities, trot out crap to try and
explain why that is not valid, without giving anything *mathematical*
then you will know that yes, they are indeed, lying.

James Harris

Relevant Pages

  • Surrogate factoring, random is better?
    ... I keeps seeing posters claiming that my surrogate factoring method is ... where the final constraint is the rationality of the square roots. ... That's a crucial point, and the first clue that posters must be lying, ...
    (sci.crypt)
  • JSH: Extraodinary to supposedly ordinary
    ... Basically no matter what I discover, ... Now, supposedly, surrogate factoring is just some random, or, ... The reality is that I show extraordinary mathematics, and posters work ...
    (sci.math)
  • JSH: Extraodinary to supposedly ordinary
    ... Basically no matter what I discover, ... Now, supposedly, surrogate factoring is just some random, or, ... The reality is that I show extraordinary mathematics, and posters work ...
    (sci.crypt)
  • Surrogate factoring, theory versus implementation
    ... the surrogate factoring method is itself being called to ... Now the discussions can go on indefinitely as posters who reply to me ... It's in its failures that my primary interest lies. ...
    (sci.crypt)
  • Surrogate factoring, theory versus implementation
    ... the surrogate factoring method is itself being called to ... Now the discussions can go on indefinitely as posters who reply to me ... It's in its failures that my primary interest lies. ...
    (sci.math)