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There are two users $A$ and $B$ who are in different domain. Let's assume that $A\in KGC_1$ and $B\in KGC_2$. If they want to establish secure session, then they must run an identity-based authenticated key exchange protocol to get a shared secret key.

To users, they can authenticate each other i.e $A$ is assured that only the user $B$ can learn the session key and vice versa. However, as the domain that the user is in can not authenticate each other(Actually I'm not sure about this), so there may exist a malicious KGC(denoted as $KGC_{\mathcal{M}}$) that will attack the session.

My question are :

  1. Is it possible for $KGC_{\mathcal{M}}$ to impersonate $A$ or $B$ to communicate with $B$ or $A$ ?
  2. Is there any practical meaning to consider the attack of a malicious KGC?

P.S As a matter of fact, recently I'm doing something research about this aspect, so I will really appreciate that if someone could do me a favor or offer me some related literature to read further.

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