2. Suppose the key for round 0 in AES consists of 128 bits, each of which is 1.
a. Show that the key for the first round is W(4), W(5), W(6), W(7), where
$\begin{pmatrix} 00010111 \ 00010110 \ 00010110 \ 00010110 \ \end{pmatrix}$,
W(5) = W(7) =
$\begin{pmatrix} 11101000 \ 11101001 \ 11101001 \ 11101001 \ \end{pmatrix}$.
W(4) = W(6) =
Note that W(5) = \overline{W(4)} = the complement of W(5) (the complement can be
obtained by XORing with a string of all 1s).
b. Show that W(10) = \overline{W(8)} and that W(11) = \overline{W(9)} (HINTS: W(5) \oplus W(6) is a
string of all 1s. Also, the relation A \oplus B = \overline{A} \oplus \overline{B} might be useful.)
