# Does the AES Mixcolum Matrix use a fixed or random matrix?

I understand how work the multiplication but I'm confused if the matrix to use is fixed or variable. The site where I read how mixcolums work is this https://math.stackexchange.com/questions/248456/matrix-multiplication-in-aes-mixcolumns-step Thanks in advance for the replies.

It is fixed.

In the forward direction, it is always:

$$\begin{bmatrix} 02 & 03 & 01 & 01 \\ 01 & 02 & 03 & 03 \\ 01 & 01 & 02 & 03 \\ 03 & 01 & 01 & 02 \end{bmatrix}$$

In the reverse direction, it is always:

$$\begin{bmatrix} 0e & 0b & 0d & 09 \\ 09 & 0e & 0b & 0d \\ 0d & 09 & 0e & 0b \\ 0b & 0d & 09 & 0e \end{bmatrix}$$

Note that the multiplication (and additions) done during the matrix multiplication are done using $GF(2^8)$ operations, which are not the same as $\mathbb{Z}_{256}$ (which is what was confusing Frenzy Li)

• Tank you , now it's clear – Dragonfighter Oct 23 '17 at 16:44