The transformation MixColumn

The transformation MixColumn is crucial to the kind of our special implementation. The transformation MixColumn operates on the columns of a state separately. To each column a fixed linear transformation is applied. To do so, bytes are interpreted as elements in the field $\mathbb{F}_{2^{8}}$. As is usually done, we will denote elements in this field in hexadecimal notation. Hence $01,02$ and $03$ correspond to the bytes $00000001,00000010$, and $00000011$, respectively. Now MixColumn applies to each row of a state the linear transformation defined by the following matrix

$$\left[\begin{array}{cccc} 02 & 03 & 01 & 01\\ 01 & 02 & 03 & 01\\ 01 & 01 & 02 & 03\\ 03 & 01 & 01 & 02 \end{array}\right].$$ (1)

One complete round of the AES encryption procedure is schematically shown in figure 2.

Figure 2: AES round description, cf. [Sa].