## Standard – composite field conversion

Have just read this and this is all I understand about the paper:

1. There are various way to represent the element of $GF(2^k)$ depending on the choice of the basis or the particular construction method. If $k$ is the product of two integers as $k=m.n$, then it is possible to derive a different representation method by defining $GF(2^k)$ over the ground field $GF(2^n)$. An extension field defined over a subfield of $GF(2^k)$ other than the prime field $GF(2)$ is know as the composite field. We will use $GF((2^n)^m)$ to denote the composite field. Since there is only one field with $2^k$ elements, both the binary and the composite fields refer to this same field. However, their representation methods are different, and it is possible to obtain one representation from the other.
2. For $GF(2^8)$, $A=(a_7\alpha^7, a_6\alpha^6, ..., a1\alpha,a_0)$ where the composite field representation in $GF((2^n)^m)$ is ${\bar{A}={\bar{a}_{00},\bar{a}_{01},\bar{a}_{10},\bar{a}_{11},\bar{a}_{20},\bar{a}_{21},\bar{a}_{30},\bar{a}_{31}}}$