4. Diffie-Hellman key exchange (15 Points) Recall that in a Diffie-Hellman key exchange, there are values a, b, g and p. Alice computes g mod p and Bob computes g mod p. (a) [3 Points] Which of these values (al b, g, and p) are publicly known and which must be kept private? (b) [4 Points] Mallory can eavesdrop, intercept, and modify everything sent between Alice and Bob. Alice and Bob perform Diffie-Hellman to agree on a shared symmetric key k. After the exchange, Bob gets the feeling something went wrong and calls Alice. He compares his value of k to Alice's and realizes that they are different. Explain what Mallory has done. (c) [4 Points] Alice and Bob want to prevent Mallory from tampering with their keys by attaching a hash to each message (ie. Alice sends (g. H(g@)) and Bob sends (ghi, H(gb.))). Does this successfully stop Mallory? (d) [4 Points] Alice and Bob want to prevent Mallory from tampering with their keys by using a MAC. Assume they hold a shared symmetric key k and attach a MAC to each message (ie, Alice sends (g*. MACK(g.)) and Bob sends (gh, MACk(gb))). Does this successfully stop Mallory? Assume Mallory can observe multiple, unique key exchanges between Alice and Bob before attempting an attack