Permutation rotation-symmetric Sboxes, liftings and affine equivalence
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In this paper, we investigate permutation rotation-symmetric (shift-invariant) vectorial Boolean functions on n bits that are liftings from Boolean functions on k bits, for k≤ n. These functions generalize the well-known map used in the current Keccak hash function, which is generated via the Boolean function x_1+x_1x_2+x_3. We provide some general constructions, and also study the affine equivalence between rotation-symmetric Sboxes and describe the corresponding relationship between the Boolean function they are associated with. In the process, we point out some inaccuracies in the existing literature.
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