This problem performs elliptic curve encryption/decryption using the scheme outlined in Section 10.4. The cryptosystem parameters are \(\mathrm{E}_{11}(1,6)\) and \(G=(2,7)\). B's secret key is \(n_{B}=7\).

a. Find B's public key \(P_{B}\).

b. A wishes to encrypt the message \(P_{m}=(10,9)\) and chooses the random value \(k=3\). Determine the ciphertext \(C_{m}\).

c. Show the calculation by which B recovers \(P_{m}\) from \(C_{m}\).