Suppose Bob and Alice want to flip a coin over a network and decide who is the winner. Alice proposes the following protocol.

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