Assume Alice knows Bob's public key and Bob knows Alice's public key. How can thwy use these to perform the Diffie Hellman key exchange while making sure that:

* Eve does not learn any part of the Diffie Hellman key exchange

* Alice can be sure to have exchanged the key with only Bob

* Bob can be sure to have exchanged the key with only Alice

* Only two messages are exchanged between Alice and Bob

Show and explain your steps