Ed Carp says:

If I understand D-H right, both sides generate public keys from their private keys, then just exchange public keys. Is that right? Or is there something I'm missing?

Yes. Thats not the algorithm at all. D-H is based on the difficulty of the discrete log problem, that is, the problem of inverting an exponentiation modulo a large prime. Its been a while, so I might be forgetting something here or misstating -- someone correct me if I am wrong. Suppose we have a field Z_p, where p is a prime. Suppose g is a generator of the field. Alice generates a random number a. Bob generates a random number b. Bob tells alice g^b, Alice tells Bob g^a. Alice knows a and g^b, and thus generates g^(ab) trivially. Similarly, Bob knows g^a and b, and trivially generates g^(ab). An interceptor only knows g^a and g^b, and because the discrete log problem is hard cannot get a or b easily, and thus cannot generate g^(ab). g^(ab) is now a shared secret of Alice and Bob. Perry