1. (20 points) Key Exchange. Consider the Diffie-Hellman Key Exchange protocol where the group used is Z 11 and the generator is g = 2. Suppose Alice and Bob want to establish a secret key using this protocol. (a) (3 points) If Alice chooses a = 4 as her private exponent, what does she send to Bob? (b) (3 points) If Bob sent gb 3( mod p) to Alice, what is Bobs secret exponent b? (c) (3 points) Compute the secret shared key that Alice and Bob will share at the end of the protocol. (d) (5 points) Explain how the shared key can be used to encrypt and decrypt using the ElGamal scheme. (e) (6 points) Explain how Eve can use a Man-in-the-Middle attack to impersonate Alice to Bob.