I have question regarding multiplication in Galois Field.
I know that if we have e.g. $GF(2^m)$ and we have its normal or polynomial basis, we can find matrix representation of the multiplication, however I was not very successful in searching for more details.
Therefore I would like to ask, if you know some good material/document/book regarding this topic, where it is possible to find explanation and clarification of this.
Many thanks for any ideas.
Try this book by Rudolf Lidl and Harald Niederretier. There is an explanation about the representation of $GF(p^m)$ by means of companion matrix. The idea is to construct a (companion) matrix whose characteristic polynomial $p(x)$ is equal to an irreducible polynomial of degree $m$ in $GF(p)[x]$.
I also found this article by William Wardlaw.
However, I haven't found any resource with clear, formal, and rigorous explanation.