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Given some intermediate data $x$ as two shares $x=x_1\oplus x_2$ take some fresh random $r$ to calculate new shares $x_1' = ((x_1\oplus r)\oplus x_2)\oplus(n\oplus r)$ [parenthesis indicating the order of evaluation] and $x_2' = n$. Now you can use $x_1'$ ($=x\oplus n$) as input for both tables. The answer to "So how should it be computed?" is not at all. ...
I did not paid attention enough when reading the paper. The figure 2 illustrates the operation: So after the computation of $S'$ and $M$, at the first round, the $\texttt{AddRoundKey}$ step stay the same but in addition, the round key is xored with $n$. So if the block data is $x$, after the first $\texttt{AddRoundKey}$ we get $x \oplus k \oplus N$ (where ...