# 8.2 The Layers

We now describe the steps in more detail. The 128 input bits are grouped into 16 bytes of eight bits each, call them

These are arranged into a $4\times 4$ matrix

In the following, we’ll occasionally need to work with the finite field $GF({2}^{8})$. This is covered in Section 3.11. However, for the present purposes, we only need the following facts. The elements of $GF({2}^{8})$ are bytes, which consist of eight bits. They can be added by *XOR*. They can also be multiplied in a certain way (i.e., the product of two bytes is again a byte), but this process is more complicated. Each byte $b$ except the zero byte has a ...

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