Well, if you exchange your keys via DH and start using that key to cipher the communication, you're going to find out very soon if you exchanged the key properly, won't you?
In essence, once you've agreed on a key you won't keep it to yourself (although you could, in theory). But am I missing the point? Are we talking about two different things? I'm talking about ZK from a mathematical point of view, you know, the cavern, the treasure, the two paths... (if you know this layman example about ZK)
Unfortunately I cannot go into details, but what I meant about my preference for DLP is that although I was mathematically more attracted to DLP based algorithms (when it came to asymmetric cryptography) I didn't really have the chance to "play" with them and spent more time with RSA.
So it's probable my knowledge of the DH key exchange algorithm is imperfect and last time I wrote crypto it was very mundane (it was using RC4, that's saying a lot!), so maybe I should just refrain from commenting about crypto.
