AES

Yayu Wang included in category Cryptography

2023-05-27 2023-06-18 425 words 2 minutes

Contents

AES (Advanced Encryption Standard)

The Advanced Encryption Standard is symmetric encryption specification

Key

keys could be 128, 192, and 256 bits
The repetition go through 10, 12 or 14 rounds

Block

16 bytes
a 4x4 matrix holds the data in a single block

Round

Each round consists of 4 steps
1. applying a key - addRoundKey()
2. substituting bytes - subBytes()
3. shifting rows - shiftRows()
4. mixing columns - mixColumns()

S-Box

Substitution Box

Add Round Key

A bit-wise XOR between the 16-byte state and the appropriate 16-bytes of the expanded key.
You pass the block data stored in the state array through an XOR function with the first key generated (K0). It passes the resultant state array on as input to the next step.

\begin{align*} & \begin{bmatrix} block_{1,1} & block_{1,2} & block_{1,3} & block_{1,4} \\ block_{2,1} & block_{2,2} & block_{2,3} & block_{2,4} \\ block_{3,1} & block_{3,2} & block_{3,3} & block_{3,4} \\ block_{4,1} & block_{4,2} & block_{4,3} & block_{4,4} \\ \end{bmatrix} \bigoplus \begin{bmatrix} key_{1,1} & key_{1,2} & key_{1,3} & key_{1,4} \\ key_{2,1} & key_{2,2} & key_{2,3} & key_{2,4} \\ key_{3,1} & key_{3,2} & key_{3,3} & key_{3,4} \\ key_{4,1} & key_{4,2} & key_{4,3} & key_{4,4} \\ \end{bmatrix} \\ = & \begin{bmatrix} block_{1,1} \bigoplus key_{1,1} & block_{1,2} \bigoplus key_{1,2} & block_{1,3} \bigoplus key_{1,3} & block_{1,4} \bigoplus key_{1,4} \\ block_{2,1} \bigoplus key_{2,1} & block_{2,2} \bigoplus key_{2,2} & block_{2,3} \bigoplus key_{2,3} & block_{2,4} \bigoplus key_{2,4} \\ block_{3,1} \bigoplus key_{3,1} & block_{3,2} \bigoplus key_{3,2} & block_{3,3} \bigoplus key_{3,3} & block_{3,4} \bigoplus key_{3,4} \\ block_{4,1} \bigoplus key_{4,1} & block_{4,2} \bigoplus key_{4,2} & block_{4,3} \bigoplus key_{4,3} & block_{4,4} \bigoplus key_{4,4} \\ \end{bmatrix} \end{align*}

Sub Bytes

replace each bytes in the block with the values in S-Box

\begin{align*} \begin{bmatrix} block_{1,1} & block_{1,2} & block_{1,3} & block_{1,4} \\ block_{2,1} & block_{2,2} & block_{2,3} & block_{2,4} \\ block_{3,1} & block_{3,2} & block_{3,3} & block_{3,4} \\ block_{4,1} & block_{4,2} & block_{4,3} & block_{4,4} \\ \end{bmatrix} \rightarrow \begin{bmatrix} S-Box(block_{1,1}) & S-Box(block_{1,2}) & S-Box(block_{1,3}) & S-Box(block_{1,4}) \\ S-Box(block_{2,1}) & S-Box(block_{2,2}) & S-Box(block_{2,3}) & S-Box(block_{2,4}) \\ S-Box(block_{3,1}) & S-Box(block_{3,2}) & S-Box(block_{3,3}) & S-Box(block_{3,4}) \\ S-Box(block_{4,1}) & S-Box(block_{4,2}) & S-Box(block_{4,3}) & S-Box(block_{4,4}) \\ \end{bmatrix} \end{align*}

Shift Rows

Mix Column

Matrix production in Galois field

\begin{align*} \begin{bmatrix} 2 & 3 & 1 & 1 \\ 1 & 2 & 3 & 1 \\ 1 & 1 & 2 & 3 \\ 3 & 1 & 1 & 2 \end{bmatrix} \times \begin{bmatrix} block_{1,1} & block_{1,2} & block_{1,3} & block_{1,4} \\ block_{2,1} & block_{2,2} & block_{2,3} & block_{2,4} \\ block_{3,1} & block_{3,2} & block_{3,3} & block_{3,4} \\ block_{4,1} & block_{4,2} & block_{4,3} & block_{4,4} \\ \end{bmatrix} \end{align*}