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

The inverse of this cipher is shown below.

Note that the block size is $8$ bits, which is one byte $($and one ASCII character$).$ We will work with the fixed key $008.$

We now decrypt various ciphertexts using modes for this cipher. In every case in which the mode requires an IV$,$ the IV will be $0$xAA. In the case of CTR

mode, we use a $($nonce $||$ counter$)$ arrangement in which the nonce is the left $5$ bits of $0AA$ 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 $"314$C$23$FAA$3"$ using $CFB$ mode. Please enter your answer in ASCII characters $($aka words$).$

d$)$ Decrypt the ciphertext $"8$ADF$9821F4"$ using $CBC$ mode. Please enter your answer in ASCII characters $($aka words$).$

e$)$ Decrypt the ciphertext $"3$BD$5693953"$ using OFB mode. Please enter your answer in ASCII characters $($aka words$).$