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This scheme is not worth the name MAC; it is horribly weak. First and foremost, the tag/MAC is unchanged when two blocks of plaintext are exchanged (because of the commutativity and associativity of the $\oplus$ operation). If follows that from any message with at least two different blocks, we can make a different message for which we know the tag/MAC. ...


It seems that all this discussion about the IV is just to confuse the reader. Ignore IV. You just have to do a simple length-extension attack on the CBC-MAC. Yes, one message is enough.

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