Comparison of conversion matrices for a compact AES–CTR defined over an isomorphic field

AES is a widely used block cipher that adopts inverse operation over
$\mathbb{F}_{2^{8}}$
in the nonlinear operation, called SubBytes. The inverse operation is usually implemented by a lookup table considering its time-consuming nature. In this paper, the authors introduce an isomorphic field
$\mathbb{F}_{(2^{4})^{2}}$
and compare several conversion matrices by counting the number of required logic gates (AND and XOR) to reduce the circuit size.