The cryptosystem parameters are $E_{11}(1,7)$ and $G=(3,2).$ B$\text{'}$s private key is $n_B=7.$

a$)$ Find B$\text{'}$s public key $P_B.$

b$)$ User A wishes to encrypt the message $P_m=(10,7)$ and chooses the random value $k=5.$ Determine the ciphertext $C_m.$

c$)$ Show the calculation by which B recovers $P_m$ from $C_m.$