## Multiplication in Composite Field Elements

Say element $\{11001010\}_2$ and $\{1101110\}_2$ are both element of composite field $GF(((2^2)^2)^2)$ which is generated using the following irreducible polynomials:

$r(x) = x^2 + x + \{1000\}_2$ between $GF(2^8)/GF(2^4)$
$s(x) = x^2 + x + \{10\}_2$ between $GF(2^4)/GF(2^2)$
$t(x) = x^2 + x + 1$ between $GF(2^2)/GF(2)$

how do I perform multiplication between $\{11001010\}_2$ and $\{1101110\}_2$?

also $(1101110)^2$?

thank you very much!