5. Public Key Encryption [10 Points] When Alice sends a message M to Bob, she and Bob agree to use the following protocol where [M]Alice refers to Message Mencrypted with thenPrivate Key of Alice {S} Alice refers to Signature S decrypted with the Public Key of Alice (i) Alice computes S= = [M]Alice (ii) Alice sends (M, S) to Bob. (iii) Bob computes V = {S}Alice. (iv) Bob accepts the signature as valid provided V = M. With this protocol it's possible for Trudy to forge Alice's signature on a random "message" as follows. Trudy generates a value R. She then computes N = {R} Alice and sends (N, R) to Bob. a. Is this a feasible attack? That is, does Bob think it is a signed message from Alice? Explain. b. Suppose we modify the protocol as follows: (i) Alice computes S = (F(M)]Alice (ii) Alice sends (M, S) to Bob. (iii) Bob computes V = {S}Alice (iv) Bob accepts the signature as valid provided V F(M). What conditions must the function satisfy so as to prevent this annoying attack