4. Show that it is extremely unlikely that a message such as that described in Exercise 3 can be discovered. Do this by demonstrating that the probability that a message P is not relatively prime to n is 1/p + 1/q - 1/pq, and if p and q are both larger than 10^100, this probability is less than 10^-99. In this exercise, assume that it is equally likely for a message to fall into each residue classes modulo n. 5. What is the ciphertext that is produced when RSA encryption with key (e, n) = (3, 2669) is used to encrypt the message BEST WISHES? 6. What is the ciphertext that is produced when RSA encryption with key (e, n) = (7, 2627) is used to encrypt the message LIFE IS A DREAM? 7. If the ciphertext message produced by RSA encryption with the key (e, n) = (13, 2747) is 2206 0755 0436 1165 1737, what is the plaintext message? 8. If the ciphertext message produced by RSA encryption with the key (e, n) = (5, 2881) is 0504 1874 0347 0515 2088 2356 0736 0468, what is the plaintext message? 9. Encrypt the message SELL NOW using the Rabin cipher C = P(P + 5) (mod 2573).