We have $A$, $B \in GF(q^k)$
We want to find polynomial $h \in GF(q)[x]$ where
$h(A) = B$
What is the lowest degree of $h$?
How to find $h$ with the lowest degree and what is complexity of this algorithm?
We have $A$, $B \in GF(q^k)$ We want to find polynomial $h \in GF(q)[x]$ where $h(A) = B$ What is the lowest degree of $h$? How to find $h$ with the lowest degree and what is complexity of this algorithm? 

