Projective Aspects of the AES Inversion

Wen-Ai Jackson and S.Murphy

Abstract

We consider the nonlinear function used in the Advanced Encryption
Standard (AES).  This nonlinear function is essentially inversion in
the finite field $\GF (2^8)$, which is most naturally considered as a
projective transformation.  Such a viewpoint allows us to demonstrate
certain properties of this AES nonlinear function.  In particular, we
make some comments about the group generated by such transformations,
and we give a characterisation for the values in the AES 
{\em Difference} or XOR {\em Table} for the AES nonlinear function and
comment on the geometry given by this XOR Table.