24. Suppose Bob and Alice want to flip a coin over a network. Alice proposes the following protocol.

(i) Alice randomly selects a value X e {0,1}.

(ii) Alice generates a 256-bit random symmetric key K.

(iii) Using the AES cipher, Alice computes Y = E(X,R,K), where R consists of 255 randomly selected bits.

(iv) Alice sends Y to Bob.

(v) Bob guesses a value Z {0,1} and tells Alice.

(vi) Alice gives the key K to Bob who computes (X, R) = D(Y, K).

(vii) If X = Z then Bob wins, otherwise Alice wins.

This protocol is insecure.

a. Explain how Alice can cheat.

b. Using a cryptographic hash function h, modify this protocol so that Alice cannot cheat.