Authenticated key exchange (AKE) ⇒ KE
Statement
Every authenticated key exchange (AKE) protocol is, unchanged, a key exchange protocol secure against eavesdroppers — folklore. The AKE security game additionally gives the adversary control of the network and requires the parties to authenticate each other.
Sketch
A KE eavesdropper is run as an AKE adversary that relays one honest session’s messages faithfully and tests that session’s key.