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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.)

          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.)

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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
< p m a t r i x >,
W(5) = W(7) =
< p m a t r i x >.
W(4) = W(6) =
Note that W(5) = 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) = W(8) and that W(11) = W(9) (HINTS: W(5) ⊕W(6) is a
string of all 1s. Also, the relation A ⊕B = A ⊕B might be useful.)

Added by Rhonda M.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

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Solved by Expert Florencia Cuzmar

Step 1

- The key for round 0 consists of 128 bits, each of which is 1. This means the key is a string of 128 ones: \[ \text{Key}_0 = \underbrace{1111 \ldots 1111}_{128 \text{ bits}} \] Show more…

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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 W(5) = W(7) = [00010111 00010110 00010110 00010110], W(4) = W(6) = [11101000 11101001 11101001 11101001]. Note that W(5) = 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) = W(8) and that W(11) = W(9) (HINTS: W(5) + W(6) is a string of all 1s. Also, the relation A + B = A + B might be useful.) 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 [00010111 00010110] W(5) = W(7) = [00010110 00010110] [11101000 11101001] W(4) = W(6) = [11101001 11101001] Note that W(5) = 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) = W(8) and that W(11) = W(9) (HINTS: W(5) - W(6) is a string of all 1s. Also, the relation A - B = A - B might be useful.)

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