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Recall the Fiat-Shamir public-key digital signature scheme we dis- cussed in class. In this problem, you'll do a toy example of that scheme over the multiplicative group Zii = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Note that the generator for this group is g = 2. Assume that Alice has private-key x = 2 and public key y = 24. Let the random target (or commitment) chosen by Alice be t = 57 = 7 (mod 11), and let the random challenge chosen by Bob be c= 2. (a) What is the correct response, r that Alice will choose such that g'y = t, and how does she compute it? (b) When the group size is large, what makes it hard for someone else to find the correct value for r? (c) If Alice wants to prove she knows x without relying on Bob, how should she choose c? Recall the Fiat-Shamir public-key digital signature scheme we dis- cussed in class. In this problem, you'll do a toy example of that scheme over the multiplicative group Zii = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Note that the generator for this group is g = 2. Assume that Alice has private-key x = 2 and public key y = 24. Let the random target (or commitment) chosen by Alice be t = 57 = 7 (mod 11), and let the random challenge chosen by Bob be c= 2. (a) What is the correct response, r that Alice will choose such that g'y = t, and how does she compute it? (b) When the group size is large, what makes it hard for someone else to find the correct value for r? (c) If Alice wants to prove she knows x without relying on Bob, how should she choose c