JSH: Explaining surrogate factoring, again

jstevh_at_msn.com
Date: 01/24/05 

Date: 24 Jan 2005 15:34:56 -0800

Now I figure that many of you don't have a clue about the mathematics
behind what I call surrogate factoring, as you listen to people who
make it their business to try and obscure the mathematics of what I'm
discussing.

These people reply in my posts mostly to distract from what I'm saying
mathematically.

I'm going to explain again.

Surrogate factoring works by factoring a number I call a surrogate in
order to factor the target number.

Two important quadratics in surrogate factoring are

yx^2 + Ax - j^2 = T

and

yz^2 + Az - j^2 = 0

where A, j, and T are integers, and j^2 + T = M^2, which is the target
integer I'm trying to factor.

The aim is to find a *rational* y such that x and z are rationals.

I repeat, these are rationals. They are not necessarily integers.

It is trivial to show that x can be defined by factors of j and T, as
with

b_1 b_2 = - j^2, and f_1 f_2 = T, you have

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

and x is there defined by factors of j and T, but from the first
quadratic

yx^2 + Ax - j^2 = T, which is

yx^2 + Ax - M^2 = 0,

as j^2 + T = M^2, and you have

x(yx + A) = M^2

showing that x is a factor of M.

But x is rational. So you focus on the numerator of x, and whether or
not it gives a prime factor of M.

Now, again, x, while being a factor of M, is defined by factors of j
and T, as

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

where b_1 b_2 = - j^2, and f_1 f_2 = T,

but b_1 and b_2 are *rational* factors of j.

While I deliberately make f_1 and f_2 integer factors, so that there's
some way to get a handle here.

How can I do that?

Well b_1 and b_2 are found for you, given f_1 and f_2.

The mathematics finds them for you, and selects them out of infinity to
give you a special and finite set.

Whether or not your x gives a prime factor of your target M, can be
shown to depend on quadratic residues, such that there's about a 50%
chance for a given rational x solution that it will give you a prime
factor of M.

The full explanations are already worked out, in my paper or on the
group site:

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

In checking b_1 and b_2 for you, the mathematics acts to check *every*
possible rational out of infinity, which is why the method is so
powerful.

It is like quantum factoring methods, but with mathematics instead of
physics, which should make sense to at least some of you.

After all, there were machines built in the past or even today by
hobbyists, which with gears and other mechanical tools could factor
numbers.

But deep down those mechanical tools rely on mathematics. You can
abstract out the mathematics, and build software tools that do the same
things, and more.

Quantum ideas for factoring are like mechanical tools.

If they existed, there had to be mathematical ideas that covered the
same ground.

What I've found is a way to factor that checks through infinity for
solutions.

It doesn't work all the time for mathematical reasons having to do with
quadratic residues.

You don't have to just believe me, check it out for yourself.

That math isn't even all that complicated and you can go through it in
a few hours, from the paper to posts showing the quadratic residue
result:

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

Now I'm sure there will be posters who will reply with nonsense, on a
newsgroup where mathematics is supposed to be what's important.

I give the mathematics.

You can just believe posters who work like mad demons to try and
obscure what I'm saying, or go see the actual math for yourself in a
paper I think is quite good ( I wrote it myself ) and in posts that
step through important math with elementary methods.

And there's even an implementation for those of you who can do a little
Java programming.

Now then, I know that sci.math is full of people who not only are not
interested in mathematics, they aren't the slightest bit interested in
what is the truth, as they post for their own psychological needs.

A lot of these people don't like me for any number of reasons, so they
spend time replying to me.

That's odd. Do you obsessively track people you don't like to
obsessively reply to them, all the while, working to convince others
that they are not worth paying attention to, while you pay attention to
them constantly, obsessively, year after year after year?

Consider the possibility that I am an amateur mathematician with
dramatic results--quite correct--which so challenge people in
mainstream math society that they work to ignore my results, or, some
on sci.math, work to deflect other people from them.

Think of all that energy people. Think of all the time some posters
spend to convince you to ignore me.

And then think. Do people really spend so much time and energy on
something not very important to them?

What could be so important about deflecting people from paying
attention to the actual mathematics presented by someone like me?
James Harris

Relevant Pages

  • Re: SF: Areas of confusion, infinity
    ... One of the problems with surrogate factoring in terms of understanding ... it, is that it utilizes infinite sets, notably the set of rationals. ... Well, the surrogate factoring theorem links rational factorizations, ... The mathematics then gives you factors in exchange. ...
    (sci.crypt)
  • SF: Areas of confusion, infinity
    ... One of the problems with surrogate factoring in terms of understanding ... it, is that it utilizes infinite sets, notably the set of rationals. ... Well, the surrogate factoring theorem links rational factorizations, ... The mathematics then gives you factors in exchange. ...
    (sci.crypt)
  • Re: Surrogate factoring works very well
    ... it you can use surrogate factoring for any size number. ... They decided that humanity had discovered enough mathematics. ... But they are like actors who took over a hospital when no one was ... They killed people to keep that secret. ...
    (sci.crypt)
  • Re: Surrogate factoring works very well
    ... it you can use surrogate factoring for any size number. ... They decided that humanity had discovered enough mathematics. ... But they are like actors who took over a hospital when no one was ... They killed people to keep that secret. ...
    (sci.crypt)
  • Re: Surrogate factoring works very well
    ... it you can use surrogate factoring for any size number. ... discoveries in mathematics because it was inconvenient for them. ... German superiority that he refused to believe that the German codes ... and the will to keep a secret. ...
    (sci.crypt)