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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 $K(m, \text{'enc'})$ ...


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 ...

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