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This has been specified by the standard, steps 4 and 5 of the protocol described in RFC 4253: S generates a random number y (0 < y < q) and computes f = g^y mod p. S receives e. It computes K = e^y mod p, H = hash(V_C || V_S || I_C || I_S || K_S || e || f || K) (these elements are encoded according to their types; see below), ...


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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