Authenticated Diffie-Hellman with no proofs that each one keys are the right keys. Is it possible?

Question

Let's suppose that Bob has only Alice's IP and no more information about Alice's key, nor the digest of Alice's key.

They exchange keys and need proof that the received keys are the same keys that were sent.

How Bob and Alice can know that the key received is the right key?

Also, I read about Sigma protocol:

The general idea is that Alice and Bob do an unauthenticated Diffie-Hellman (D-H) key exchange to set up an encrypted channel, and then do mutual authentication inside that channel.

Would this protocol work for this scenario?

Answer 1

If what you are describing were possible, then we wouldn't need certificate authorities.

The paper you've linked to uses a technique that only works if Alice and Bob already know each other's long-term public keys.