Re: Prime magnitude and keys...a ?

[Jim choate <ravage@bga.com>]

> 
> 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 only found a single set of factors for your public key (ie 3,8 also work)
and if I had asked "is the number 6?" as my first question then I would have 
had it in 1 single guess which does *NOT* qualify as factoring your key.


> You may not think that you are talking about factoring, but factoring is a
> subset of what you are discussing.
>
the fact it is a subset of what I am talking about means that there are some
issues (and possibly an algorithm or two) that are outside of the purvue of
a discussion limited to simply factoring. The horizon has been expanded.