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You misunderstand $(02) \cdot 10000100$; it is not integer multiplication (resulting in a 9 bit integer); instead, it is multiplication in $GF(2^8)$ (which results in an element in $GF(2^8)$, which can be represented in 8 bits). AES uses a polynomial representation of $GF(2^8)$, using the polynomial $x^8 + x^4 + x^3 + x + 1$; what this means is that ...


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AES transformation can be viewed as a sequence of invertible transformations each processing only a small part of the state. All these transformations would be even, and so is the entire AES for any key (see also this question).



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