Computing Rijndael's S-Box?

I'm a newbie when it comes to cryptography and currently I'm hooked on
Rijndael. I know most of the implementations of it have the S-box
hard-coded into the app for speed gain, but I would like to compute
that s-box myself.

You probably know it is defined by the finite field mapping in GF(2^8)
onto its inverse, and then it is transformed by a certain matrix (i
have that one) and then 0x63 is added.

Can someone help me to compute that first mapping of GF(2^8) onto its
inverse? How do you compute the inverse?

Thanx !
Received on Thu Sep 29 21:51:23 2005