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.