Alice and Bob are communicating using the Elgamal cryptosystem with prime p = 23 and primitive root alpha = 7. a) Bob creates his public key by choosing a = 5. What is Bobs public key? b) Alice wants to send the message "3" to Bob. Demonstrate how Alice encrypt the message. c) Bob receives the encrypted message (r,t) = (9, 6) from Alice. What is her plaintext message? Suppose A chooses El Gamal signature scheme with p = 17, alpha = 5 and a = 23. What is the public key? What is the private key? Encrypt the message x = 12 for A using as a random number k = 4. Suppose B receives the ciphertext (y_1, y_2) = (35, 49). Find the plaintext x. Let p = 31, alpha = 3, beta = 25 be Bob's public El Gamal key. Alice uses it to generate ciphertext [(17, 20), (17, 07), (17, 27), (17, 27), (17, 09)]. Determine corresponding plaintext x = x_1 x_2 x_3 x_4 x_5 if Bob's private key is a = 10