Re: Surrogate factoring ideas to ponder

From: fred fish (fred_at_fish.com)
Date: 03/22/05 

Date: Wed, 23 Mar 2005 05:27:25 +0800

On 21 Mar 2005 15:26:37 -0800, jstevh@msn.com wrote:

[snip][snip][snip]

I REALLY tried to understand all of this by creating a program
following all the step by step instructions.

Yes I can solve "yz^2 - Az + j^2 = 0" for all instances of 'j' from 2
to 9 except 7 with min 3 and max 100 for all values.

Adding T to the equation and answer is absolutely superfluous.

equ = ans

and

equ + T = ans + T

==========

I actually made a function to solve (a_1 z + b_1)(a_2 z + b_1) = T but
did not run it, did not save it. Reading ahead to understand where a1,
a2 and b1 are leading.

Using the above formula, f1 and f2 can be calculated which are two
factors of M. Forgive me if I am wrong but I see not direct
calculation to solve the function. Is it a matter of try and test for
all a1, a2 and b1 values?

Let me get this straight: a1 z+b1 and a2 z+b1 are two factors of T?

A*B=T simple factor equation.

(A*n) (B*n)=T means A and B are 1/n times smaller than they should be.
Solution is to multiply by Z. Additionally, A and B are b1 less than
what they should be.

Random sample numbers for experimentation:

T = 190
F1=10
F2=19

(F1-4)/3=2
(F2-4)/3)=5

So for a T of 190, A1 and A2 equal 2 and 5 respectively.

Perhaps this is a typing error but where is B2 come from?

a_2 z + b_2 = f_2

Regardless of the error (funct1)(funct2)=T is still a factor problem.
And on top of that it's J^2 less than M^2 of what we wanted to find in
the first place!

Unless J is greater than M, you are trying to factor a value larger
than the target value. That takes us back to examining the initial
equation of yz^2 - Az + j^2 = 0

It becomes evident that predicting the result of a large J is not
worth the effort as there is no indicatin of what Y or A are supposed
to represent.

It is at this point I may understand what you are trying to achieve,
but it is 5:15am indicating I am not thinking clearly. Are you
attempting to factor a small A*B=C and scale it up solve a large
factorization of a big M? Initially this seems like a valid approach
but then I recall many people commenting on the difficulty of
factorizing an RSA PQ value, being composed of two primes. Roughly
guessing, there cannot be a scaled down version of PQ because they are
prime?

Maybe you will have better luck with examining the raw potential of
the following:

PQ - ( (P-1) (Q-1) ) = P + Q - 1

Now that is a remarkable formula!

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