Prime magnitude and keys...a ?

[Linn Stanton]

In message <199406171835.NAA09573 at zoom.bga.com>you write:
  > I am *NOT* talking about factoring anything. Perhaps this is why you 
  > are having a problem understanding what I am asking. I don't care what
  > the original key is, simply am I above it or below it. I don't see this
  > as a 1 to 1 with factoring large digit numbers.

Lets try a game:

I'm thinking of a number, lets call it my private factor.

I tell you that it is less than some other number, which we'll call my
public key.

For any number you choose, I'll tell you whether your choice is above or
below my private factor.

How long will it take you to guess my factor?

Lets try. my public key is 24.

Is the factor above 10? No.
Is the factor above 5? Yes.
Is the factor above 7? No.
Is it 6? Yes.

And look: 24 / 6 = 4 ! You guessed my private key, and you happen to have factored
my public key at the same time! Wow!

You may not think that you are talking about factoring, but factoring is a
subset of what you are discussing.