The purpose of Diffie-Hellman key exchange algorithm is to enable two users to exchange a key securely that can be used for subsequent encryption of message.For example, if Alice and Bob agree on a public prime p and primitive root g modulo p, the algorithm tells (The notation is a bit different from the text) . Alice chooses a random value x and sends gx mod p to Bob 2. Bob chooses a random value y and sends gry mod p to Alice 3. Alice computes gx) mod p as (gAy mod px mod p to get the shared secret Bob computes g (xy) mod p as (gx mod p) y mod p to get the same secret Suppose the prime number p- 11 and a primitive root of p is g-2. (As you know, in reality, p and g are more complicated than that) Do the following. Show your work to get points. (a) If Alice choose its private key x- 5, what is Alice's public key? (b) If Bob choose a private key y-7, what is Bob's public key? (c) What is the shared secret key