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

$\displaystyle r(x) = x^2 + x + \{1000\}_2$ between $\displaystyle GF(2^8)/GF(2^4)$

$\displaystyle s(x) = x^2 + x + \{10\}_2$ between $\displaystyle GF(2^4)/GF(2^2)$

$\displaystyle t(x) = x^2 + x + 1$ between $\displaystyle GF(2^2)/GF(2)$

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

also $\displaystyle (1101110)^2$?

thank you very much!