I was presented with this seemingly paradoxical information, and am hoping someone can explain what I'm missing here.
I have an encrypt-and-mac scheme here.If I want to transmit message m to Bob, I'd first Enc_k1(m) = c, MAC_k2(m) = t, and then send c||t over to Bob. So far, I understand that this scheme provides no integrity on the cipher-text itself, since the tag only verifies the original message and nothing else.
However, I am also presented with that Enc_k1 is CCA secure.
And then I was told that the Enc-and-MAC scheme is NOT CCA secure.
How can this be? If the encryption itself is CCA secure, the only way the scheme is not CCA secure is if and only if the MAC is not CCA insecure, but I have no idea if that even makes sense.
If it is possible, how can an attacker provide a possible CCA attack?