Question: 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).

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 $C_{m}$.

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