a. Let ?? = 111... ... 111 be the DES key consisting of all 1s. Show that if ??_K(P) = C, then ??_K(C) = P, meaning encrypting twice with this key returns the plaintext.

Note: ??_K denotes Encryption function parameterized by a key, ??. ?? denotes plaintext and ?? denotes ciphertext.

[15 marks]

b. Find another key that has the same property as ?? in part (a).

[5 marks]