Factoring problem, solved

jstevh_at_msn.com
Date: 01/19/05 

Date: 18 Jan 2005 20:28:00 -0800

I am increasingly certain that I've solved the factoring problem.

That is a bold claim to add to previous bold claims of mine, but here
in THIS post I'll give the underlying theory as it's very basic, and
direct you to a site where you can download a rough, and somewhat
flawed, but still good enough to show the idea, prototype factoring
program, which implements some of the theory.

I'll explain why I say some of the theory in just a bit.

My work boils down to the analysis of a system of equations:

a_1 x + b_1 = f_1
a_2 x + b_2 = f_2

a_1 b_2 + a_2 b_2 = A

a_1 a_2 x^2 + Ax + b_1 b_2 = f_1 f_2

where to match the variables in my initial paper

y = a_1 a_2, T = f_1 f_2, and j^2 = - b_1 b_2.

(Here b_1 b_2 is a negative number so j is still an integer.)

I have a rather complex looking solution in the paper, but remarkably
you can encompass it by solving the first three equations for key
variables:

a_1 = A(b_1 - f_1)/(b_1 f_2 + b_2 f_1 - 2b_1 b_2)

and

x = (b_1 f_2 + b_2 f_1 - 2b_1 b_2)/A

which shows that you can actually factor simply by cycling through the
factors of j and T, while my focus in the program is on cycling
through the factors of T.

All together you then get the factors of your target M, as

M^2 = j^2 + T, so

a_1 a_2 x^2 + Ax + b_1 b_2 = f_1 f_2

is

a_1 a_2 x^2 + Ax - M^2 = 0

so x is a factor of M.

The idea may seem pathetically simple, but that is because you are
programmed to believe that the factoring problem is hard. It is not.

I have just shown you in a few lines how to factor an arbitrary
non-zero positive integer M in polynomial time.

Many of you are programmed to believe that mathematics must be abstruse
and difficult to work. You are wrong. The factoring solution I've
presented here while looking extremely simple can work and is simple
because the PROBLEM is simple.

I have demonstration code, which is rough as I threw something
together, to test out my own theory, and hopefully to be more
convincing. That code implements a VERSION of my own theory, as I
don't factor both j and T, but only T, as j gets background factored by
the mathematics.

If you watch it factoring and spitting out primes (though it also
mislabels some as prime and can't factor some easy numbers...rough
version remember) then you can at least see that something is happening
here worth investigating further.

In the hopes of convincing *someone* willing to help I have put put up
a Yahoo! Group with my paper and some rudimentary code:

http://groups.yahoo.com/group/sufactor/

It is CRITICAL that the information be taken seriously as soon as
possible so that some other method can be used for Internet security,
and quickly implemented.

Time is a factor.

James Harris

Relevant Pages

  • Re: Integer factorization, basics
    ... > The factoring problem concerns itself with finding non-trivial values ... > So the congruence of squares method works by having the square root ... > Being large primes, they are rare. ...
    (sci.math)
  • Re: Proof factoring solution is closed form
    ... >> your proliferation of redundant threads that you don't pay attention ... Remember I'm the inventor of surrogate factoring. ... But are you implying that if Rick were the inventor, ... > the factoring problem as there was every reason to believe that I would ...
    (sci.math)
  • Re: Proof factoring solution is closed form
    ... >> your proliferation of redundant threads that you don't pay attention ... Remember I'm the inventor of surrogate factoring. ... But are you implying that if Rick were the inventor, ... > the factoring problem as there was every reason to believe that I would ...
    (sci.crypt)
  • Re: Factoring problem, solved
    ... > I am increasingly certain that I've solved the factoring problem. ... > That is a bold claim to add to previous bold claims of mine, ... Remember the problem I'm talking about is the factoring problem. ... My program calls the algorithm in order to try and use the algorithm to ...
    (sci.math)
  • Re: JSH: Mystery increases
    ... solution to the factoring problem. ...  Any solution to the factoring problem has ... The mathematics shows that you can factor a composite D, ... The proof shows that one of the combinations of factors of D-1 must ...
    (sci.math)