## Isomorphism

In order to obtain the isomorphic matrix (that map from field $GF(2^8)$ to $GF(((2^2)^2)^2))$, we need a root alpha such that $R(\alpha) = 0$ whereby $R(z) = z^8 +z^4 + z^3 + z + 1$ is a field polynomial of $GF(2^8)$

The representation of $GF(((2^2)^2)^2))$ is generated by

$x^2 + x + {1000}_2$, $x^2 + x + {10}_2$ and $x^2 + x + 1$

so I understand that $\alpha$ range from 0 to 255 and how do I actually test that $R(\alpha) = 0$. how do I actually perform such arithmetic when the element are bind to composite field operations.