On the Structure of Secret Key Exchange Protocols

Modern cryptography is fundamentally concerned with the problem of secure private communication. Suppose two parties, Alice and Bob, wish to communicate privately over a public channel (for instance, a telephone line with an eavesdropper). If Alice and Bob are able to meet, privately, beforehand, and agree on some common secret key, then it becomes easy for them to achieve such private communication. But Alice and Bob might not be able to first meet in private and agree on a key. In this case, we ask under what assumptions they can still agree on a common secret key, where their conversation is conducted entirely in public.