$(1$ point$)$ This question concerns block cipher modes. We will use a simple affine cipher, which can be expressed in $C$ as follows.

char cipher$($unsigned char block, char key$)$

$\{$

return $($key$+11*$block$)\%256$;

$\}$

The inverse of this cipher is shown below.

char inv$\_$cipher$($unsigned char block, char key$)$

$\{//163$ is the inverse of $11$ mod $256$

return $($block$-$key$+256))\%256$;

$\}$

Note that the block size is $8$ bits, which is one byte $($and one ASCII character$).$ We will work with the fixed key $0$x$08.$

We now decrypt various ciphertexts using modes for this cipher. In every case in which the mode requires an IV$,$ the IV will be OxAA. In the case of CTR mode, we use a $($nonce $|$ counter$)$ arrangement in which the nonce is the left $5$ bits of OxAA and the counter is a $3$ bit counter that begins at $0.$ In all of the problems given below, one character is one block. Each character of the plaintext should be regarded as its corresponding ASCII code. The ciphertext is given in hexadecimal.

a$)$ Decrypt the ciphertext $"22273709"$ using $CTR$ mode. Please enter your answer in ASCII characters $($aka words$).$

b$)$ Decrypt the ciphertext $"3$EAC$3380"$ using ECB mode. Please enter your answer in ASCII characters $($aka words$).$

c$)$ Decrypt the ciphertext $"C_{23\text{F}\text{A}\text{A}3}"$ using $CFB$ mode. Please enter your answer in ASCII characters $($aka words$).$