Question: A Fiat-Shamir protocol for entity authentication uses 9 challenge-response rounds to verify the claimant.

Part 1: What is the probability that a dishonest claimant is falsely verified as an authentic entity, i.e., what is the probability that the dishonest claimant responds correctly to all 9 challenges?

Part 2: A Guillou-Quisquater protocol uses an integer challenge c in the range [1, 20] inclusive, i.e., there are 20 different values for c.

What is the minimum value of challenge-response rounds needed so that the probability of falsely verifying a dishonest claimant is equal to or smaller than the probability obtained in part (1) for the Fiat-Shamir protocol?

Part 3: A Guillou-Quisquater protocol uses an integer challenge c in the range [1, K] inclusive. What is the minimum value of K such that only two rounds of the G-Q protocol are needed to get a probability strictly smaller than the probability obtained in part (1) for the Fiat-Shamir protocol?

Answer these parts and show each and every step with example and find the probability.