i need some help with a product in GF(16), where it is seen as an extension of GF(4)={0, 1, x, x+1} (where $x^2 = x + 1$ ) with the irreducible polynom $f(y) = y^2 + y + x$
So the elements in the fields are: $\{0, 1, x, x+1, y, y + 1, y + x, y + x + 1, xy, ... \}$
I'm try to multiply $((x+1)y + x) * (xy + x + 1)$ and i obtain as result $(x + 1)$
I'm not sure that it is the correct result, can you help me?
Thank you, greetings