Rijndael Mix Columns

MixColumns

The MixColumns step can be performed by multiplying a coordinate vector of four numbers in Rijndael's Galois field by the following circulant MDS matrix:

$\begin{bmatrix}r_0\\r_1\\r_2\\r_3\end{bmatrix} = \begin{bmatrix} 2&3&1&1 \\ 1&2&3&1 \\ 1&1&2&3 \\ 3&1&1&2 \end{bmatrix} \begin{bmatrix}a_0\\a_1\\a_2\\a_3\end{bmatrix}$

This can also be seen as the following:

Since this math is done in Rijndael's Galois field, the addition above is actually an exclusive or operation, and multiplication is a complicated operation.

Read more about this topic: Rijndael Mix Columns

Rijndael Mix Columns - MixColumns