3. Sam and Peter want to collaboratively write the solutions for the 376 nal exam, while keeping them secret from the students. As a rst step, they decide to use the DifeHellman protocol with a large prime p and generator 9 of Z; = {1, . . . ,p 1} to establish a shared key that is known only to them. Peter chooses a secret, uniformly random 0. E Z; and sends A = 9\" mod p to Sam; similarly, Sam chooses a secret, uniformly random 5 E Z; and sends B = 9" mod p to Peter. Then, they each compute k = gab modp as their shared key, in the usual way. However, unbeknownst to them, a mischievous student, Malcolm, is able to both eavesdrop on and also modify (or replace) all the data Sam and Peter send to each other, including the values A,B. (Call this a \"Malcolm in the middle\" attack.) Specically, Malcolm chooses an exponent c E Z; and replaces both A and B with C = 96 mod p. (a) (b) (C) After Malcolm performs the above substitutions, what is the key computed by Peter? What is the key computed by Sam? Show how Malcolm can eieiently compute both of these keys. To privately collaborate, Peter and Sam plan to encrypt and send their workinprogress to each other, using (what they believe to be) their shared key in an encryption scheme.2 Such a scheme consists of an encryption algorithm Em: and a decryption algorithm Dec. The encryption algorithm takes a key and message, and outputs a ciphertext. The decryption algorithm takes a key and a ciphertext, and outputs a message. The two algorithms satisfy the following correctness property: for all keys k and messages m, Dec(k:, Enc(k, 721)) = m. Describe how Malcolm can read Peter and Sam's ongoing work on the solutions, without being detected. That is, Peter and Sam should be under the impression that they are communicating privately with each other, with nothing appearing out of the ordinary. The week before the exam, Peter and Sam wake up early to doublecheck the exam solutions they have written. It just so happens that Malcolm is still asleep, so he is not able to intercept and modify Peter's and Sam's messages. Will they be able to meaningfully communicate in same way that they have been doing so? Why or why not