Re: Surrogate factoring and the k/T ratio


<jstevh@xxxxxxxxx> wrote in message
news:1172335144.861958.112280@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
For years I've done research on ways you might factor a target
composite T by factoring some other number I call the surrogate, and
after a lot of failed approaches I realized that the idea
mathematically reduced to a couple of very simple relations:

x^2 ? y^2 mod T

and

k^2 ? 2xk mod T

or k ? 2*x mod T

where the first should be familiar enough, while the second is an
addition needed mathematically by the concept of surrogate factoring.

So after a lot of years of fumbling around I found mathematically I
could reduce the idea quite simply to the given relations.

Now using those requires going to explicit equations:

x^2 = y^2 + aT

and

k^2 = 2xk + bT

and I can add one to the other, and complete the square to find:

(x+k)^2 = y^2 + 2k^2 + (a-b)T

I did not get that result,

x^2 + k^2 = y^2 + aT + 2xk + bT

or

x^2 + k^2 = y^2 + 2xk + (a + b)*T

x^2 + k^2 + 2*x*k = y^2 + 2*x*k + (a + b)*T + 2*x*k

or

(x+k) ^2 = y^2 + 4*x*k + (a + b)*T


Looks like you made two mistakes, you should have a 4, and then you have a
sign mistake at b.


.

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