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A normal security notion for MAC's is that of unforgeability. So given some set of message,tag pairs $(m_0,t_0),\ldots,(m_k,t_k)$ is should be hard to create a tag for a new message not among the $\{m_0,\ldots,m_k\}$, stated informally. In your case, you could just use $E_k(m_0)$ with the secret MAC key $k$ ($H_0$ in your notation); no need for the extra ...


The MAC is NOT redundant. As alluded to by PaĆ­lo Ebermann's comment, the word authentication has a different meaning in the two scenarios you mentioned. In the key exchange phase of SSH, the purpose of authentication is to ensure to both parties that they are indeed talking to the right peer (if using mutual authentication). Typically, the server ...

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