Consider an authentication protocol where Alice authenticates herself to Bob. We use
K A−B
​
to denote the symmetric secret key shared by Alice and Bob. Assume Alice and Bob can add more rounds of communications but they can only use the symmetric secret key. Give a new authentication protocol, in which while Alice is authenticating herself to Bob, Bob will also authenticate himself to Alice. Show how to perform a man-in-the-middle attack on the new authentication protocol (i.e., Trudy, pretending to be Alice, can now authenticate herself to Bob as Alice and to Alice as Bob).