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An anonymous key exchange protocol $P$ is pair of probabilistic machines $(A,B)$ that sends messages to each other and at the end, both $A$ and $B$ will share the same key $k$.

The attacker can see the protocol transcript $T_P$ of $P$, that is, the sequence of messages exchanged between the parties in one execution of $P$.

How can a computationally unbounded attacker break an anonymous key exchange protocol?

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    $\begingroup$ An unbounded attacker can just run the protocol for all initial states of A and B and for all randomness coin results and stop when the given configuration yields a transcript that matches the given transcript (and then because they have the randomness results and the initial states, they have the key) $\endgroup$ – SEJPM Jun 23 '18 at 11:44

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