Suppose that in the Fiat-Shamir protocol in Figure 9.32 we have N = 63 and v = 43. Recall that Bob accepts an iteration of the protocol if he verifies that y 2 = x . v e mod N a. In the first...

Suppose that in the Fiat-Shamir protocol in Figure 9.32 we have N = 63 and v = 43. Recall that Bob accepts an iteration of the protocol if he verifies that y²
= x . v^e
mod N

a. In the first iteration of the protocol, Alice sends x = 37 in message one, Bob sends e = 1 in message two, and Alice sends y = 4 in message three. Does Bob accept this iteration of the protocol? Why or why not?

b. In the second iteration of the protocol, Alice sends x = 37, Bob sends e = 0, and Alice sends y = 10. Does Bob accept this iteration of the protocol? Why or why not?

c. Find Alice's secret value S. Hint: 10^_1
= 19 mod 63.