Q$2.$ Answer the following questions.

$2+4=6$

$($a$)$ Is Playfair cipher secure against brut$-$force attack? Justify your answer.

$($b$)$ Assume that the following ciphertext is created using the Affine Cipher. Find the encryption key $K=(k_1,k_2).$

OINRF HORXH ONAPF VHLHM NZOFU OINAN GRLZI PYNJL

HOINM KVBLY GMKVB SFLAG LAALY BNRNY OVHNG SXPO

Q$3.$ Answer the following questions.

$3+3=6$

$($a$)$ Prove that $\{Z_{14}^{**},x\}$ is a cyclic group. Find a generator $g$ of $\{Z_{14}^{**},x\}.$ Also find the order of the generator.

$($b$)$ Compute all the subgroups of the cyclic group $\{Z_{14}^{**},\}.$