I am trying to compute the multiplicative inverse of:
$x^4 + x^2 + x$
Using the irreducible polynomial:
$x^8 + x^4 + x^3 + x + 1$
Over $GF(2)=\mathbb{F}_2$.
I tried applying the extended euclidean algorithm but to no avail. At some point during the algorithm I end up with the remainder $169/144$ and am unsure how to proceed from there on. Any help would be greatly appreciated.
Thanks in advance!