Projective aspects of the AES inversion

Abstract

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 Difference or XOR Table for the AES nonlinear function and comment on the geometry given by this XOR Table.

The Return of the Cryptographic Boomerang

“…The only nonlinear part of an AES round is the SubBytes phase, which consists of the application of an S-Box to each byte of the 16-byte state, where an S-Box is formally a function S : Z 2 8 ), and there exist many nonzero input byte differences α and output byte differences β such that the differential probability for the AES S-Box is 2 −7 [9], [10]. One such pair of input and output differences for SubBytes is given by α = 02 and β = EE, so we have…”

Multiple Dimensional Fault Tolerant Schemes for Crypto Stream Ciphers

“…People mostly focus on fault tolerance for block ciphers and public-key encryptions [6][7][8][9][10] which employ complex computations that cannot be easily embedded into resource constrained applications. Y. Q. Zhong et al proposed low-cost and high efficiency architecture of AES cryptoengine [11].…”

Multiple Dimensional Fault Tolerant Schemes for Crypto Stream Ciphers

“…In previous research, few efforts were contributed to fault tolerance designed for stream ciphers [5]. People mostly focus on fault tolerance for block ciphers and public-key encryptions [6][7][8][9][10] which employ complex computations that cannot be easily embedded into resource constrained applications. Y. Q. Zhong et al proposed low-cost and high efficiency architecture of AES cryptoengine [11].…”