Suppose that Alice and Bob share a 4-digit PIN number, X. To establish a shared symmetric key, Bob proposes the following protocol: Bob will generate a random key K that he will encrypt using the PIN...

Suppose that Alice and Bob share a 4-digit PIN number, X. To establish a shared symmetric key, Bob proposes the following protocol: Bob will generate a random key K that he will encrypt using the PIN number X, that is, E(K, X). Bob will send E(K, X) to Alice, who will decrypt it using the shared PIN number X to obtain K. Alice and Bob will then use the symmetric key K to protect their subsequent conversation. However, Trudy can easily determine K by a brute force attack on the PIN number X, so this protocol is insecure. Modify the protocol to make it more secure. Note that Alice and Bob only share the 4-digit PIN number X and they do not have access to any other symmetric key or public keys. Hint: Use Diffie-Hellman.