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From the sound of your questions, it almost appears that you have some confusion between the CBC-MAC key and the CBC-MAC tag. The CBC-MAC algorithm takes the message (in this case, most likely the ciphertext) and a secret key; it outputs a tag (which can be public). The security property of CBC-MAC is that someone who does not know the key cannot generate ...


As additional detail, while the two keys need to be distinct and secret, you can derive the CBC-MAC key and the CBC encryption key from the same master key. Generate a random master key, then use any key derivation algorithm with two different salts to derive the authentication and encryption keys. For example, $K(m, \text{'auth'})$ and $K(m, \text{'enc'})$ ...

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