Randomized authentication primitive problem in key exchange with strong security

Security proofs are invaluable formal criteria in assuring practitioners on the security properties of protocols. However, one could obtain various security results while proving the considered protocol in different security models. We notice that there are some security proof problems caused by randomized authentication primitives (RAP) in the recent authenticated key exchange (AKE) protocols. Those RAP problems would simply invalidate the security result of such protocols in the corresponding security models. Unfortunately, we figure out that some previous AKE protocols overlooked the RAP problem in their security analysis. We also introduce general solution ideas and concrete examples to avoid RAP problem.