A. Determine the order of 4 (ord(4)) in Z*. Show your work. B. If Alice and...

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A. Determine the order of 4 (ord(4)) in Z*₁. Show your work. B. If Alice and Bob wish to arrive at a shared key without actually changing the key using Diffie-Hellman Key exchange, Alice publishes p-7 and a 4. Alice chooses a=3 and Bob chooses b-5. Show the exchange of messages between Alice and Bob and the final shared key that they derive. C. Alice chooses a private key of d-3, and sends the Elgamal public key (11,4,9) to Bob. Bob uses this key to encrypt x-5 and sends it to Alice. Alice decrypts the message and derives x. Show the messages that are exchanged between Alice and Bob and the details of how Alice decrypted Bob's message to arrive at x=5. A. Determine the order of 4 (ord(4)) in Z*₁. Show your work. B. If Alice and Bob wish to arrive at a shared key without actually changing the key using Diffie-Hellman Key exchange, Alice publishes p-7 and a 4. Alice chooses a=3 and Bob chooses b-5. Show the exchange of messages between Alice and Bob and the final shared key that they derive. C. Alice chooses a private key of d-3, and sends the Elgamal public key (11,4,9) to Bob. Bob uses this key to encrypt x-5 and sends it to Alice. Alice decrypts the message and derives x. Show the messages that are exchanged between Alice and Bob and the details of how Alice decrypted Bob's message to arrive at x=5.