Factoring attack against RSA based on Pollard's Rho

[Sandy Harris]

On Mon, Jun 8, 2009 at 11:51 AM, Victor Duchovni
<Victor.Duchovni at morganstanley.com> wrote:
> On Sun, Jun 07, 2009 at 05:41:00PM -0700, Greg Perry wrote:
>
>> The significance of this method is the ability to determine any
>> properties of p and q from a simple operation to n.
>
> To be blunt, I see no significance of any kind...
>
> You have observed that unless N is divisible by 3, p and q are both also
> not divisible by 3. This is not new, and ...

I do not have it to hand, but at one point I had a solution for

   N = pq = (a-b)(a+b) = a^2 - b^2

where I could find unique values for a^2 and b^2 mod 9, mod 16,
or by combining those mod 144. Mod 25, mod 49 et cetera gave
constraints but not unique solutions.

After playing with this a while,  I concluded that it was not
actually useful,

-- 
Sandy Harris,
Quanzhou, Fujian, China

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