Impersonation attempt

We use two intruders to attack each protocol. The intruder $I$_I tries to impersonate the initiator $A$, and the other intruder $I$_R attempts to impersonate the responder $B$. Both intruders have the public keys of all the principals in their initial information. If symmetric encryption is used, the intruders certainly do not obtain any of the secret keys. Then, $I$_I tries to start a session with $B$ impersonating as $A$. If $I$_I can get $B$ to finish his session believing it is talking to $A$, then the protocol is simply broken. Similarly we can check whether $I$_R can impersonate as $B$ to finish a session with $A$. The purpose for this attack is simply to check whether correct and necessary encryptions are used. It does not involve any replay attack and multiple protocol run and hence is very efficient.