Aes Encryption Round 4De2C3

1. **Problem Statement:** Explain one full encryption round of AES (Advanced Encryption Standard) step by step. 2. **AES Round Overview:** AES operates on a 4x4 byte matrix called the State. One round consists of four operations: AddRoundKey, SubBytes, ShiftRows, and MixColumns. 3. **AddRoundKey:** Each byte of the State is XORed with the corresponding byte of the Round Key. Example: For byte $69_{16}$ XOR $4B_{16}$: $$69_{16} = 0110\ 1001_2$$ $$4B_{16} = 0100\ 1011_2$$ $$0110\ 1001 \oplus 0100\ 1011 = 0010\ 0010 = 22_{16}$$ Resulting State after AddRoundKey: $$\begin{bmatrix} 00 & 3C & 6E & 47 \\ 1F & 4E & 22 & 74 \\ 0E & 08 & 1B & 31 \\ 54 & 59 & 0B & 1A \end{bmatrix}$$ 4. **SubBytes:** Each byte is replaced using the AES S-Box. The first hex digit is the row, the second is the column. Example: $6E \to$ row 6, column E in S-Box $= 9F$ Resulting State after SubBytes: $$\begin{bmatrix} 63 & EB & 9F & A0 \\ C0 & 2F & 93 & 92 \\ AB & 30 & AF & C7 \\ 20 & CB & 2B & A2 \end{bmatrix}$$ 5. **ShiftRows:** Rows shift cyclically left by 0, 1, 2, and 3 positions respectively. Resulting State after ShiftRows: $$\begin{bmatrix} 63 & EB & 9F & A0 \\ 2F & 93 & 92 & C0 \\ AF & C7 & AB & 30 \\ A2 & 20 & CB & 2B \end{bmatrix}$$ 6. **MixColumns:** Each column is multiplied by the fixed matrix in GF(2^8): $$\begin{bmatrix} 02 & 03 & 01 & 01 \\ 01 & 02 & 03 & 01 \\ 01 & 01 & 02 & 03 \\ 03 & 01 & 01 & 02 \end{bmatrix}$$ Multiplication rules: - $1 \times x = x$ - $2 \times x = $ shift left by 1 bit; if overflow bit is 1, XOR with $1B_{16}$ - $3 \times x = (2 \times x) \oplus x$ Worked example for first column $(63, 2F, AF, A2)$: - $2 \times 63 = C6$, $3 \times 63 = A5$ - $2 \times 2F = 5E$, $3 \times 2F = 71$ - $2 \times AF = 45$ (since $5E \oplus 1B = 45$), $3 \times AF = EA$ - $2 \times A2 = 5F$ (since $44 \oplus 1B = 5F$), $3 \times A2 = FD$ Calculate each row of the new column: - Row 1: $C6 \oplus 71 \oplus AF \oplus A2 = BA$ - Row 2: $63 \oplus 5E \oplus EA \oplus A2 = 75$ - Row 3: $63 \oplus 2F \oplus 45 \oplus FD = F4$ - Row 4: $A5 \oplus 2F \oplus AF \oplus 5F = 7A$ Repeat for other columns to get final State: $$\begin{bmatrix} BA & 84 & E8 & 1B \\ 75 & A4 & 8D & 40 \\ F4 & 8D & 06 & 7D \\ 7A & 32 & 0E & 5D \end{bmatrix}$$ 7. **Summary:** The four operations in order are AddRoundKey, SubBytes, ShiftRows, and MixColumns. Starting State and final State after one round are shown side by side. End with "Any questions?"