i) State the service(s) that can be provided by the architecture. (1 mark) ii) If Abdullah needs to sign the message, write the full function of the ciphertext to be sent. (2 marks) iii) Write the function of decryption. (2 marks) b) Consider the RSA cryptosystem is used to encrypt a message M= 14. Given p= 3,9 = 5, and e = 7, calculate the value of the private key. Show all your workings step by step involved clearly. (7 marks) c) Consider the RSA cryptosystem is used to encrypt a message, M. Given the p= 3,9 = 11, e = 7, and d = 3 . If the public key is used to generate the ciphertext, C = 16, calculate the value of M. Show your workings. (4 marks) d) Consider the RSA cryptosystem is used by Ahmad to authenticate a message, M=7. Given the Ahmad's private key = {3, 22; and the Ahmad's public key = {7, 22}. Proof the ciphertext, C = 13 received by Azizah either is original or not original from the sender and justify your answer. Show your workings. (4 marks) QUESTION 4 (20 marks) (a) Proof either 4 or 6, is/are the primitive root of 13 by constructing a complete primitive root table for those number only. Based on the constructed table, justify your answer. (5 marks) (b) Keys are not actually exchanged in DHKE they are jointly derived." Explain clearly the steps taken to jointly derive the cryptography key in Diffie Hellman Key Exchange (DHKE). Consider the value of g = 8, p = 11, private key for sender is 2 and private key for receiver is 3. By using the cryptography key in Diffie Hellman Key Exchange (DHKE), explain the steps and show all your workings clearly to generate the i) R1 and R2 (8 marks) ii) and the symmetric key, K. (7 marks) i) State the service(s) that can be provided by the architecture. (1 mark) ii) If Abdullah needs to sign the message, write the full function of the ciphertext to be sent. (2 marks) iii) Write the function of decryption. (2 marks) b) Consider the RSA cryptosystem is used to encrypt a message M= 14. Given p= 3,9 = 5, and e = 7, calculate the value of the private key. Show all your workings step by step involved clearly. (7 marks) c) Consider the RSA cryptosystem is used to encrypt a message, M. Given the p= 3,9 = 11, e = 7, and d = 3 . If the public key is used to generate the ciphertext, C = 16, calculate the value of M. Show your workings. (4 marks) d) Consider the RSA cryptosystem is used by Ahmad to authenticate a message, M=7. Given the Ahmad's private key = {3, 22; and the Ahmad's public key = {7, 22}. Proof the ciphertext, C = 13 received by Azizah either is original or not original from the sender and justify your answer. Show your workings. (4 marks) QUESTION 4 (20 marks) (a) Proof either 4 or 6, is/are the primitive root of 13 by constructing a complete primitive root table for those number only. Based on the constructed table, justify your answer. (5 marks) (b) Keys are not actually exchanged in DHKE they are jointly derived." Explain clearly the steps taken to jointly derive the cryptography key in Diffie Hellman Key Exchange (DHKE). Consider the value of g = 8, p = 11, private key for sender is 2 and private key for receiver is 3. By using the cryptography key in Diffie Hellman Key Exchange (DHKE), explain the steps and show all your workings clearly to generate the i) R1 and R2 (8 marks) ii) and the symmetric key, K. (7 marks)