# Math Help - Inverse in Galois field

1. ## Inverse in Galois field

how can one find the inverse of an element over the Galois field, GF(2^8)?

2. Originally Posted by pranay
how can one find the inverse of an element over the Galois field, GF(2^8)?
The 255 elements of G(256) different from the null element can be written as , where $\alpha$ is a 'primitive root' of the field. A basic property is that the are periodic of period 255 so that the inverse element of is :..

... as example we consider the GF(256) generated by the polynomial...

(1)

... one 'primitive root' of which is . We have...

(2)

Observing table (2) we can deduce that the inverse of $x$ is , the inverse of is and so one...

Kind regards

$\chi$ $\sigma$