CSCI $4613/5613-$ Assignment $3$

The AES internal state consists of $16$ bytes $b_0$ through $b_{15}$ arranged in a $4$ by $4$ grid:

Given $16-$byte plaintext blocks $P$ and $P^{\text{'}}$ that are identical except for byte $b_9,$ answer

the following questions about AES encryption. $(2$ points each$)$

$($a$)$ Let A and $A^{\text{'}}$ be the result of putting $P$ and $P^{\text{'}}$ through the initial

AddRoundKey operation. Which bytes are different between A and $A^{\text{'}}?$

$($b$)$ Let $B$ and $B^{\text{'}}$ be the result of putting A and $A^{\text{'}}$ through the first$-$round

SubBytes and ShiftRows operations. Which bytes are different between $B$

and $B^{\text{'}}?$

$($c$)$ Let $C$ and $C^{\text{'}}$ be the result of putting $B$ and $B^{\text{'}}$ through the first$-$round

MixColumns and AddRoundKey operations. Which bytes are different

between $C$ and $C^{\text{'}}?$

$($d$)$ Let $D$ and $D^{\text{'}}$ be the result of putting $C$ and $C^{\text{'}}$ through the second$-$round

SubBytes and ShiftRows operations. Which bytes are different between $D$

and $D^{\text{'}}?$

$($e$)$ Let $E$ and $E^{\text{'}}$ be the result of putting $D$ and $D^{\text{'}}$ through the second$-$round

MixColumns and AddRoundKey operations. Which bytes are different

between $E$ and $E^{\text{'}}?$

Consider a block cipher where the block size is one byte and the encryption $($and

decryption$)$ algorithm is XORing the plaintext block with a one$-$byte key. Given a

plaintext $P=$badb ad ba $db$ ad and a key $K=2b.$ Encrypt the plaintext using the

following modes of operation: $(2$ points each$)$

$($a$)$ Electronic codebook $($ECB$)$ mode.

$($b$)$ Cipher block chaining $($CBC$)$ mode with initial value of $IV=d8($assume

padding is not used$).$

$($c$)$ Counter $($CTR$)$ mode with a four$-$bit nonce $N=1001$ and a four$-$bit counter

that starts at zero.