Please answer question number 5 from the following, the answer should be briefly explained:

4) Bob uses RSA and chooses the pair (N=713,e=7) as his public key. Using this public key, encrypt the message M=59. Show your work step-by-step. [4 marks] Using the public key in part (4), Alice has encrypted a message (we do not know what was the original message), and sends it to Bob through a public channel. Assume the encrypted message sent by Alice is 16. Eve also has the Bob's public key and receives the encrypted message (sent by Alice). Eve claims that using a simple program (as shown in the following) can find the prime numbers p and q which are used by RSA to calculate N (i.e. N=p.q ), thus the original message is 35. Check the program and verify her claim? [2 marks] Show your work step-by-step. What is the output of the program? [2 marks] Explain how she decrypted the message without having Alice's private key? [2 marks] i=2 N=713 while i<>