Practice Problem 2

Recall the encryption mode CBC$ we studied in class. The scheme uses a random IV and is based on a blockcipher E. In class we saw that CBC$ is IND-CPA assuming E is a PRF, and it is never IND-CCA. Your colleague suggests the following encryption scheme CBCH in an effort to make it IND-CCA. The only difference is that in place of IV the encryption algorithm uses H(M), where H is a public, keyless hash with n-bit outputs and M is the message to encrypt. The decryption algorithm decrypts M as usual but also checks that the IV is H(M). If not, it rejects and outputs . The colleague claims that CBCH is IND-CCA assuming E is a PRF.

Show that the colleague is wrong and prove that CBCH is not IND-CCA secure.