Re: RSA not an easy crack

[DSC Siltec <dscpubl@siltec.lt>]

Michael Robinson wrote:
> 
> On Fri, Apr 26, 2002 at 11:18:16AM +0200, DSC Siltec wrote:
> > Now, define this function to be F, and define P to be the product of
> > a whole bunch of functions F.  Now, define that a function F is to be
> > centered at any integer location where the value of the function is 1.
> 
> Consider the case of a 512-bit product of two 256-bit primes.  In this
> case, your "whole bunch of functions" is going to have a cardinality
> (if I read your pseudo-Sieve of Erathostenes idea correctly) on the order
> of P * 2^128 (where P is the fraction of integers that are prime), or
> P * 340,282,366,920,938,463,463,374,607,431,768,211,456 functions F.
> 
> Back to the drawing board, I would say.
> 
>     -Michael Robinson

Actually, the beauty of the Parker Souchacki method is that it would 
allow the simultaneous solution of a system of equations that has one
functional solution.  Which means that you only need one set of
equations,
and it solves for all values at once, 

Which means you might have only about 40 equations to solve, and when
you add the RSA algorithm, perhaps another 10-20.  The algorithm then
starts with a single known point (for example, the value at x=2 is y=1)
and then performs a simple operation on each function, cranking out one
term of the MacLauren series of one function for each simple operation. 
One of those output functions will be a function that is 1 at every
prime, and zero everywhere else.  If done correctly, though, another one
of the functions is y=[Solution key] that means that after 60 simple
math operations you get 1 bit of the solution.  Another 60 operations
yields two more bits.  Another 60 operations yields another 4 bits.  
*Again -- that is if you know the raw data.*

It's that bad.  



However, the double-layered encryption, which always takes a randomly
generated number as its "raw data", does sound secure, because the RNGs
are going to be practically unbreakable (we hope -- and that can be
improved with white-noise CDs recorded from your local waterfall.).  

The thing, then, would be to upgrade all security to double-layer, or
let it be understood that single-layer encryption is fragile -- if
indeed this algorithm works out.

 - Mike


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