Projective aspects of the AES inversion

Authors:
Wen-Ai Jackson;S. Murphy
Affiliations:
Department of Mathematics, University of Adelaide, Adelaide, Australia 5005;Information Security Group, Royal Holloway, University of London, Egham, UK TW20 0EX
Venue:
Designs, Codes and Cryptography
Year:
2007

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Abstract

We consider the nonlinear function used in the Advanced Encryption Standard (AES). This nonlinear function is essentially inversion in the finite field GF(28), 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 Difference or XOR Table for the AES nonlinear function and comment on the geometry given by this XOR Table.