Why do we need extra hashing if we could use simpler scheme?

Lets say that we use init vector IV, key K and HMAC key H. Message is M.

Mode of operation is CBC !!!

We usually encrypt this way:

C = crypt(M,K,IV) #encrypted data
R = C + MAC(C)  # final result and + is for con cat


But we could just use:

R = len + crypt(M + H,K, IV)  # notice M + H


Is there something wrong with such a scheme? It looks much faster to me and requires like half the computation and complexity.

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Yes, it does not give message authenticity and it leaves crypt accessible to chosen-ciphertext attacks. – Ricky Demer Jul 30 '12 at 10:48
If HMAC is too slow for you, I'd look into authenticated encryption modes. They use much faster MAC techniques. – CodesInChaos Jul 30 '12 at 11:36

This scheme is totally insecure. If an attacker modifies any part of the ciphertext except the last block before the ciphertext corresponding to H, your scheme won't catch it.