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It would at first appear we need to perform a guess over 4 bytes instead of 1 byte. This would be a considerably more complicated operation! We can consider writing that last step as an equation:
<blockquote><math>X^{13} &= SBytes^{-1}\left(MixCols^{-1}\left(ShiftRows^{-1}(X^{13} \oplus K^{13})\right)\right)</math>
</blockquote>
The MixCols() operation is a linear function, meaning for example the following applies:
Which means instead of determining the encryption key, we can determine the encryption key modified by the inverse MixCols.
<blockquote><math>X^{13} = SBytes^{-1}\left(MixCols^{-1}\left(ShiftRows^{-1}(X^{13} \oplus K^{13})\right)\right) \\</math><math>X^{13} = SBytes^{-1}\left(MixCols^{-1}\left(ShiftRows^{-1}(C)\right) \oplus Y^{13}\right) \\</math><math>Y^{13} = MixCols^{-1}\left(ShiftRows^{-1}(K^{13})\right) \\</math>
</blockquote>
Once we fully determine the encryption key we can perform the MixCol and ShiftRow operation to determine the correct key.
<blockquote><math>K^{13} = MixCols\left(ShiftRows(Y^{13})\right) \\</math>
</blockquote>
Performing the complete AES-256 side channel analysis attack will thus require the following steps:
