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7

The point in the question makes senses, especially if one restricts to portable software implementations. But: Small or moderately large constant-time RAM tables are reasonable, efficient, and (thus) common hardware building blocks. They are often used in DPA-protected DES and AES hardware coprocessors. Thus we can't dismiss key-dependent S-tables in ...

1

About the security of your first variation, it is sort of answered here. This is your 1st variation. This is your 2nd variation (your $8 \times 8$ matrix idea is equivalent to apply a permutation). In your first variation, the application of the matrix is useless, one can consider the $S1$ (or $S2$) and the matrix as a single S-box. Hence you have no ...

3

A recent paper presented at FSE'2016 [1] addresses this exact question. In fact, it even provides a bitsliced implementation for the S-Box you are interested in Section 4. In summary: you first encode the existence of a bitsliced implementation as a SAT problem, use an off-th-shelf SAT-solver to solve it and finally retrieve the bitsliced encoding from the ...

1

Try to generate the Algebraic Normal Form (ANF) from the sbox step by step (i.e., with 2 bits and so on) or use something like http://cis.sjtu.edu.cn/index.php/A_Simple_Python_Script_for_Translating_Sbox_to_ANF_Boolean_Functions

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