Q$4.$ Let $E_k$ and $D_k$ denote the encryption and decryption function of the AES. Let $Z_0$ be an

initial value IV$,$ which is any chosen binary string of length $128.$ A new cipher based on

the one$-$key block cipher AES $($called the AES in the output feedback $($OFM$)$ mode$)$ is

built as follows.

The plaintext and ciphertext space of the new cipher are $\{0,1{\}}^{*}.$

The key space of the new cipher is $\{0,1{\}}^{128}$ or $\{0,1{\}}^{192}$ or $\{0,1{\}}^{256}.$

Let $M=M_{t}dots{M}_2{M}_1$ be any padded plaintext according to a padding method,

where $t1$ is a positive message and each $M_i$ is a binary string of length $128.$ The

encryption function of the new cipher is:

$C_i=M_{i}o+Z_i$ for $i1$

where $o+$ denotes the bitwise exclusive$-$or operation, $C_i$ is the ciphertext block corre$-$

sponding to the plaintext block $M_i$ and $k$ is a secret key and $Z_i=E_k(Z_{i-1})$ for each

$i1$

$(4$a$)$ Write down the decryption function of the new cipher without proving its correctness.

$10$ marks

$(4$b$)$ Is this new cipher a stream cipher or block cipher? Justify your answer briefly.