How is Diffle Hellman with RSA immune to man in the middle?

Question

Alice and Bob want to exchange keys, Alice sends his half (the public key of the ephemeral key pair) signed with his private key and makes the public key available. Eve is bridging the connection so he intercepts the message uses the public key and verifies the half. He then sends his half to Alice signed and establishes a connection. Now Alice is communicating with Eve and Eve is decrypting the message and sending to Bob.

Isnt this exactly same as the raw Diffie Hellman ? How are we exactly preventing man in the middle attack if Alice thinks the whole time that Eve is Bob ? Is it correct to assume that the message(half key) is not encrypted ? Is a certification authority also required for ephemeral diffie hellman ?

Please correct me if I have misunderstood Ephemeral Diffie Hellman

Answer 1

He [Ed: Eve] then sends his half to Alice signed and establishes a connection. Now Alice is communicating with Eve and Eve is decrypting the message and sending to Bob.

Eve can only sign with her own private key. So your attack only works if Alice accepts the signature from Eve. That means that:

1. Eve's public verification key needs to be trusted and
2. that Alice doesn't check that that public key belongs to the intended party, i.e. Bob.

Some kind of PKI is usually involved, and PKIX is the most common PKI. But you can establish trust by e.g. sending the public key and then validating the fingerprint of it over the phone. I'm not sure if you can call that a PKI because of the simplicity of the protocol and the lack of other participants.

So no, this is not the same as raw Diffie-Hellman - unless the necessary verification steps are missing, of course.