The State Matrix

AES operates on a fixed 128-bit (16-byte) block, organized as a 4×4 matrix of bytes:

input bytes:  s00 s10 s20 s30 s01 s11 ... s33

state matrix (column-major):
  | s00 s01 s02 s03 |
  | s10 s11 s12 s13 |
  | s20 s21 s22 s23 |
  | s30 s31 s32 s33 |

Note the layout: the FIRST four bytes are the FIRST COLUMN. AES is column-major. This matters for the operations later.

The block size is FIXED at 16 bytes regardless of key size. Key sizes vary:

• AES-128: 10 rounds
• AES-192: 12 rounds
• AES-256: 14 rounds

Each round transforms the state via four operations:

1. SubBytes (S-box substitution)
2. ShiftRows (cyclic shift)
3. MixColumns (matrix multiplication in GF(2^8))
4. AddRoundKey (XOR with round key)

The first round skips MixColumns; the last round skips MixColumns. Otherwise all rounds apply all 4.

You'll implement each transformation, then assemble. The math is dense but each piece is small.