Critiquing surrogate factoring

jstevh_at_msn.com
Date: 03/30/05 

Date: 29 Mar 2005 17:18:18 -0800

The idea is simple enough, factor one number and use its factorization
to get the factorization of another. The point being taking a number
that is hard to factor, and yet, factoring it, by factoring an easier
number.

I thought it might help to try and write the the gist of it in a
theorem.

Surrogate Factoring Theorem:

Given M, a target natural number to be factored, and j, an integer
chosen such that j^2>M^2, a rational factor b_2 of M is given by

b_2 f_1 = (-(Az - 2M^2)+/- sqrt((Az - 2M^2)^2 - 4TM^2))/2

where T = M^2 - j^2, and f_1 is a rational factor of T, and where Az is
given by

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

where Ax is then given by

Ax = +/- (k_1 + k_2) + 2j^2

where k_1 k_2 = -Tj^2, and k_1 and k_2 are integers.

So the surrogate to be factored is finally seen at the end, as it is

Tj^2

which you factor to get Ax, which gives you Az, which gives you b_2,
and b_2 is a rational factor of M.

(To see the equations above fully derived see my Google Group:

http://groups-beta.google.com/group/Surrogate-Factoring)

Now then, I just say that b_2 is a rational factor of M, as it must be,
but does it factor M?

After all, M/2 is a rational factor of M, but so what?

The answer is, looking at the equations, I don't see anything that says
which rational factor of M you'll get.

I interpret that to mean that you'd get factors of M at random, which
would mean that you'd have a fairly good chance of factoring M,
non-trivially.

But if so, this idea is kind of big, and I've been talking about this
for days, with nothing happening, so I guess maybe I'm missing
something.

Of all my research, this idea may be the hardest to critique in some
ways, and the easiest in others, as you can just program it and see if
it factors, but I'll admit I've so far not had the nerve to test it,
preferring to think about it.

It may be the hardest though, as if it doesn't work, then I don't see
why it wouldn't, and going over the equations repeatedly hasn't shown
me why, so it may be some really deep reason.

So let's get to it.

This thread is for critiquing surrogate factoring.

James Harris

Relevant Pages

  • Proper evaluation of surrogate factoring
    ... Surrogate factoring is just kind of a wild idea that means you have to ... I am being very serious here, modern mathematicians lie a lot. ...
    (sci.crypt)
  • Re: SF: Areas of confusion, infinity
    ... > notably the set of rationals. ... choosing any integer is the same as the probability of any other ... That's what make the factoring problem interesting, i.e., not ... > is naive with the surrogate factoring theorem. ...
    (sci.crypt)
  • Re: What surrogate factoring theory now says
    ... Surrogate factoring theory says that you can turn factoring a hard ... once the engineering is figured out that is achievable. ... Mainly I just added one more congruence to the difference of squares. ...
    (sci.crypt)
  • Re: What surrogate factoring theory now says
    ... Surrogate factoring theory says that you can turn factoring a hard ... once the engineering is figured out that is achievable. ... Mainly I just added one more congruence to the difference of squares. ...
    (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)