1. Given a plaintext block P and a round key K0 with the following values:
   • P=000102030405060708090A0B0C0D0E0F
   • K0=00102030405060708090A0B0C0D0E0F0

391424. would the internal state be after the initial AES AddRoundKey layer?

2. The AES byte substitution layer can be defined using the following table:

• |00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f --|----------------------------------------------- 00|63 7c 77 7b f2 6b 6f c5 30 01 67 2b fe d7 ab 76 10|ca 82 c9 7d fa 59 47 f0 ad d4 a2 af 9c a4 72 c0 20|b7 fd 93 26 36 3f f7 cc 34 a5 e5 f1 71 d8 31 15 30|04 c7 23 c3 18 96 05 9a 07 12 80 e2 eb 27 b2 75 40|09 83 2c 1a 1b 6e 5a a0 52 3b d6 b3 29 e3 2f 84 50|53 d1 00 ed 20 fc b1 5b 6a cb be 39 4a 4c 58 cf 60|d0 ef aa fb 43 4d 33 85 45 f9 02 7f 50 3c 9f a8 70|51 a3 40 8f 92 9d 38 f5 bc b6 da 21 10 ff f3 d2 80|cd 0c 13 ec 5f 97 44 17 c4 a7 7e 3d 64 5d 19 73 90|60 81 4f dc 22 2a 90 88 46 ee b8 14 de 5e 0b db a0|e0 32 3a 0a 49 06 24 5c c2 d3 ac 62 91 95 e4 79 b0|e7 c8 37 6d 8d d5 4e a9 6c 56 f4 ea 65 7a ae 08 c0|ba 78 25 2e 1c a6 b4 c6 e8 dd 74 1f 4b bd 8b 8a d0|70 3e b5 66 48 03 f6 0e 61 35 57 b9 86 c1 1d 9e e0|e1 f8 98 11 69 d9 8e 94 9b 1e 87 e9 ce 55 28 df f0|8c a1 89 0d bf e6 42 68 41 99 2d 0f b0 54 bb 16
  • The row headings represent the first four bits of the input byte while the column headings represent the last four bits of the input byte.
  • The entries in the table are the corresponding output bytes for an input byte whose first four bits match the row heading and whose last four bits match the column heading.
  • For example, the input byte b4 would translate to the entry in row b0 and column 04, which is 8d.

2896778. the resulting internal state that you computed in the previous problem, what would be the result after the SubBytes layer from the first round?

3. Given the internal state that you computed in the previous problem, what would be the result after the ShiftRows layer from the first round?
4. Given a plaintext P' which is identical to P except that one of the bytes is different, answer the following questions.
   1. How many bytes would be different in the result you computed over the previous three problems, if you had started with P'?
   2. How many bytes would be different after the first round MixColumn layer for each plaintext?
   3. How many bytes would be different after the first round AddRoundKey layer for each plaintext?
5. 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 and a key K with the following values:
   • P=badbadbadbad
   • K=2b

1391350370. the plaintext using the following modes of operation:
            1. Electronic codebook (ECB) mode.
            2. Cipher block chaining (CBC) mode with initial value of IV=d8 (assume padding is not used).
            3. Counter (CTR) mode with a four-bit nonce N=1001 and a four-bit counter that starts at zero.
            4. List three reasons why this cipher is insecure.

6. Assuming you are using a 64-bit (8-byte) block cipher in CBC mode. Show the results of padding the following plantexts so they can fit into an even number of blocks using the padding scheme discussed in class.
   1. 0f8353c2 8e1ff6
   2. 8c521e
   3. c1
   4. 9f6bef2c 902fe4ba