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Re: [Full-disclosure] Rapid integer factorization = end of RSA?

from [Stanislaw Klekot] Network Security [Permanent Link]
Subject: Re: [Full-disclosure] Rapid integer factorization = end of RSA?
Date: Thu, 26 Apr 2007 13:07:45 +0200 
On Thu, Apr 26, 2007 at 03:04:39PM +0400, Eugene Chukhlomin wrote:

#v+
gap> p;
163473364580925384844313388386509085984178367003309231218111085238933310010450\
8151212118167511579
gap> q;
190087128166482211312685157393541397547189678996851549366663853908802710380210\
4498957191261465571
gap> n := p * q;
310741824049004372135075003588856793003734602284272754572016194882320644051808\
150455634682967172328678243791627283803341547107310850191954852900733772482278\
3525742386454014691736602477652346609
gap> (p * (n - q)) mod n;
0
gap> 
#v-

What is it supposed to proove?


  

My gypothesis: if exists subsets(A1...An) and (B1...Bn) which satisfies 
equality: A1*B1 +...An*Bn =  N = p*q, then exists some of them, which 
satisfies equality A1*(-B1)+...An*(-Bn)=p*q*(q-1)


But what does that proof have to do with your gypothesis? Except that
  p*q * (q-1) = p*q = p*q * (-1) = p*q * (N-1) = 0   (mod N)
what is obvious equality.

-- 
Stanislaw Klekot

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