I would appreciate it if you could please explain how in the following example the mod by f(x) results in the suggested answer (orange frame). Example at the top of page 3, https://eprint.iacr.org/2019/1090.pdf.
2026-05-05 14:45:12.1777992312
Matrix representation of multiplication of elements in Galois Field
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If $x^3+x+1=0$ in characteristic $2$, then $x^3=x+1$ and $x^4=x^2+x$.
Can you take it from there?