I realize something like this would be the holy grail of communications security and have never heard anything to suggest it has been done.
Am just wondering. A lot of mathematicians and computer scientists spend time doing proofs for theoretical situations. Has anyone done a proof to rule out the possibility of ever doing a key-exchange (or some other encryption setup) over an open or already compromised line?
To be clear I mean : A and B are communicating while C has the potential to be listening (ideally C is not listening in real time and is only logging A&B for action later). Is it impossible for A and B to ever exchange information over the compromised line to setup a new encrypted line that C can't immediately crack?
Last Clarification : I'm realizing public key may technically satisfy the problem by not transferring the whole method of encryption over the line. Is there anything else you do, even if only theoretical? This feels like more of a loophole than directly solving things.