Consider an affine cipher on $Z_{28}$ that work over "ABCD....XYZ$?!"$ where the numerical equivalent of $?$ and $!$ are $26$ and $27,$ respectively. The encryption function to compute ciphertext $C$ is given by $C=a.P+b$ mod $28$ where $P$ is the plaintext, $a=14,$ and $b=3.$

a$)$ Is $14$ a valid choice for $"$a$"?$ Why?

b$)$ Is $3$ a valid choice for $"b"?$ Why?

c$)$ Encrypt the plaintext "AFFINE".

Find the decryption function for an affine cipher over $Z_{28}$ with the encryption function given by $C=9P+2$mod$28.$

Consider the affine cipher $C=aP+b$ mod $26.$ You observed the following plaintextciphertext pairs $(P,C)$:$(1,10)$ and $(2,17).$ Recover the key $(a,b)$ used in the encryption.