We know that perfect secrecy in encryption is possible (one-time pad). Now, the concept of key exchange like Diffie-Hellman is that we can establish a shared key without an interceptor knowing, and with no previous communication.
Obviously, for Diffie-Hellman as such, an interceptor can actually find the shared key; it would just take them ridiculously long. But I'm wondering, is it possible to make it impossible for the interceptor to find out the shared key?
I know that no such key exchange currently exists, but is it proven that it's impossible for such a scheme to exist? Or is there a chance it could be invented?