# Dependent keys on Encrypt Then MAC

It is generally bad form to reuse the same key for encryption and authentication in an "encrypt then MAC" scheme. For example, in the naive encrypt then MAC scheme, we use a randomized CBC block cipher and MAC the cipher text but an attacker can pass in all 0 messages to violate the CPA security condition.

However, what if we used dependent but not the same keys?

For example, if the key used for MAC is of the form $k' = k \oplus V$ for some fixed value $V$. Is this still bad form, i.e. would there be an encrypt then MAC scheme which is insecure?

• If something breaks a scheme it is much worse than bad form. Bad form is for the case when something might be bad. – Elias Mar 23 '17 at 17:08
• This is the point where you have to assume your block cipher is secure against certain classes of related-key attacks which is quite a strong assumption usually (even though many iphers pass here). – SEJPM Mar 24 '17 at 16:41

This is indeed best way to do it. As the final $(cbc\oplus cipher)$ encrypted by a different key even if we pass 0 messages it do not reveal any information.
Previously passing on 0 messages gave encrypted cbc (which is later $\oplus$ed encrypted ($cbc\oplus cipher$) to reveal information) now as the key used is different even if the encrypted cbc (on passing 0 messages) is known it wont reveal information.