The transformation ByteSub

Given a state $(a_{ij})$, $0\le i<4, 0\le j<$Nb, the transformation ByteSub applies an invertible function $S:\{0,1\}^8\to \{0,1\}^8$ to each state byte $a_{ij}$ separately. The exact nature of $S$ is of no relevance for the implementation described later. We just mention that $S$ is non-linear, and in fact, it is the only non-linear part of the AES encryption process. In practice, $S$ is often realized by a substitution table or S-box.