Q22Information System Security

Selected by NIST in 2001 to violently replace the aging DES, AES (Rijndael) is the absolute global standard for symmetric encryption. It is mathematically classified as a Substitution-Permutation Network (SPN). Unlike DES, it completely abandons the Feistel structure; AES violently mathematically processes the ENTIRE 128-bit block in every single round, providing explosive execution speed and impenetrable security.

AES strictly operates on a fixed 128-bit plaintext block. However, it supports three key sizes, which mathematically dictate the number of processing rounds:

• AES-128: 128-bit key $\to$ exactly 10 rounds.
• AES-192: 192-bit key $\to$ exactly 12 rounds.
• AES-256: 256-bit key $\to$ exactly 14 rounds (Military Standard).

The 128-bit data block is mathematically mapped into a $4\times 4$ matrix of bytes (16 bytes total), called the State Array. All transformations violently mutate this State Array.

A single standard AES round executes four highly aggressive mathematical transformations in strict sequence:

1. SubBytes (Non-linear Substitution)

The absolute core of AES security. Every single byte in the State Array is violently replaced with a different byte using a rigid 16x16 mathematical Look-Up Table (The S-Box). The S-Box is constructed using highly complex Galois Field $GF(2^8)$ inverse mathematics. This introduces massive "Confusion", completely destroying linear mathematical relationships between the key and the ciphertext.

2. ShiftRows (Permutation / Diffusion)

A mathematical manipulation of the rows in the $4\times 4$ State Array:

• Row 0: Absolutely unchanged.
• Row 1: Violently cyclically shifted exactly 1 byte to the left.
• Row 2: Cyclically shifted exactly 2 bytes to the left.
• Row 3: Cyclically shifted exactly 3 bytes to the left.

This completely shatters the vertical columns, guaranteeing that data is mathematically spread across the entire matrix (Diffusion).

3. MixColumns (Mathematical Diffusion)

The most computationally violent step. It operates on the columns of the State Array. Each column (4 bytes) is mathematically treated as a polynomial and multiplied by a rigid matrix in Galois Field $GF(2^8)$. This aggressively scrambles the bits, ensuring that a single flipped bit in the input violently alters all 4 bytes in the output column.

4. AddRoundKey (Key Mixing)

The 128-bit State Array is mathematically XORed directly with the 128-bit Subkey generated for this specific round by the Key Schedule. This mathematically fuses the secret key into the chaotic data.

In the absolute final round (Round 10, 12, or 14), the MixColumns step is intentionally and mathematically omitted to allow the decryption algorithm to mirror the encryption architecture flawlessly.