Prime magnitude and keys...a ?

[Jim choate]

> 
> If you can get the sign of the difference between RSA(your number) and
> RSA(unknown key), then you can discover (unknown key) in log n time.
> That implies, due to the nature of RSA, that you can factor in log n
> time using whatever algorithm it is that makes the determination of
> the sign of the difference. 

No, again   it will allow you to find the secret key, it will not 
provide any information about the factors of that number. It might
be used for that but as you have pointed out, it takes a long time.

If I can take a cypher-text and look at the periodicity of the mod
function when several false keys are provided  I can narrow down
the guess through a binary search. I am going up, not down (ie finding
the factors which must be smaller than n). I am looking for n, not
its *@$^%# factors.

You are asking the wrong question. I am asking, since I can't factor the
keys is there some periodicity in the mod function that I can attack.