Suppose that in the Fiat-Shamir protocol, as illustrated in Figure 9.32, we have N = 27,331 and v = 7339. a. In the first iteration, Alice sends x = 21,684 in message one, Bob sends e = 0 in message...

Suppose that in the Fiat-Shamir protocol, as illustrated in Figure 9.32, we have N = 27,331 and v = 7339.

a. In the first iteration, Alice sends x = 21,684 in message one, Bob sends e = 0 in message two, and Alice sends y = 657 in the third message. Show that Bob verifies Alice's response in this case.

b. At the next iteration, Alice again sends x = 21,684 in message one, but Bob sends e = 1 in message two, and Alice responds with y = 26,938 in message three. Show that Bob again verifiesAlice's response.

c. Determine Alice's secret S. Hint: 657- 1 = 208 mod 27,331.