Suppose that in the Fiat-Shamir protocol in Figure 9.32 we have N = 77 and v = 53. a. Suppose that Alice sends x = 15 in message one, Bob sends e = 1 in message two, and Alice sends y = 5 in message...

Suppose that in the Fiat-Shamir protocol in Figure 9.32 we have N = 77 and v = 53.

a. Suppose that Alice sends x = 15 in message one, Bob sends e = 1 in message two, and Alice sends y = 5 in message three. Show that Bob accepts this iteration of the protocol.

b. Suppose Trudy knows in advance that Bob will select e = 1 in message two. If Trudy selects r = 10, what can she send for x in message one and y in message three so that Bob accepts this iteration of the protocol? Using your answer, show that Bob actually accepts this iteration. Hint: 53_ 1 = 16 mod 77.