Foundations of Security Week10 Lecture

How it works#

• Key Expansion: The original key (e.g., 128 bits) is expanded into a set of “round keys” used in each step of the encryption. This ensures the key evolves throughout the process, adding complexity.
• Initial Round: The input data (a 16-byte block) is combined with the first round key using a bitwise XOR operation.
• Main Rounds: It applies a series of transformations to the data in multiple rounds (10 rounds for 128-bit keys, 12 for 192-bit, 14 for 256-bit). Each round consists of four steps:
  • SubBytes: Each byte in the block is replaced with another byte according to a predefined substitution table (S-box).
  • ShiftRows: The rows of the data block (visualized as a 4x4 grid) are shifted to the left by different amounts.
  • MixColumns: The columns of the grid are mixed using a mathematical operation, further scrambling the data.
  • AddRoundKey: The current round key is XORed with the block, integrating the key into the process.
• Final Round: The last round skips the MixColumns step but includes SubBytes, ShiftRows, and AddRoundKey to finalize the encryption.

Key Expansion#

• Key Expansion takes the original 128-bit key and expands it into a larger set of keys (called round keys) that AES uses in its encryption rounds. Here we will choose key “cdutobufoscourse”
• For AES-128, which uses 10 rounds of encryption, the process generates 11 round keys (one for the initial round and one for each of the 10 main rounds).
• Each round key is 128 bits (16 bytes), so the total expanded key is 176 bytes (11 rounds $\times$ 16 bytes).

• The original key is 4 words (16 bytes $\div$ 4 = 4 words).
• The total expanded key is 44 words (11 rounds $\times$ 4 words per round).
• So, the Key Expansion generates 44 words (labeled $\textcolor{red}{W_0}$ to $\textcolor{red}{W_{43}}$), where:
  $\textcolor{red}{W_0}$ to $\textcolor{red}{W_3}$ are the original key.
  $\textcolor{red}{W_4}$ to $\textcolor{red}{W_{43}}$ are derived iteratively.

Key Expansion#

Quiz#

What are the steps in a main round?

Waiting…

Main Rounds - SubBytes#

Each byte in the state matrix/array is replaced using the fixed AES S-box (Substitution box).
For example, a byte like 53 is replaced with ED according to the S-box.

Main Rounds - ShiftRows#

It shifts the bytes in each row of the subbytes result to the left by a specific number of positions.

Main Rounds - Mix Columns#

• It transforms each column using matrix multiplication in Galois Field (GF$\textcolor{blue}{(2^8)}$) to ensure that changes to one byte affect all four bytes in the column.
• This multiplication is not traditional matrix multiplication.
• Each column of the state matrix (consisting of 4 bytes) is treated as a 4-byte vector and is multiplied by a fixed 4 $\times$ 4 matrix
• This is done in GF$(2^8)$ using modulo operations with the irreducible polynomial $x^8+x^4+x^3+x+1$