The multiplicative inverse in AES s-box is transformed using the following affine transformation:
$s = b \oplus (b \lll 1) \oplus (b \lll 2) \oplus (b \lll 3) \oplus (b \lll 4) \oplus 99_{10}$
Where did the number 99 come from? For what purpose is it there?
I'm asking, because I'm trying to generalize it in $GF(2^{128})$. So I would like to find a similar number if we would operating in $GF(2^{128})$.
