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Permutation rotation-symmetric S-boxes, liftings and affine equivalence (2203.00778v2)

Published 1 Mar 2022 in math.CO, cs.CR, cs.IT, and math.IT

Abstract: 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 $k\leq n$. These functions generalize the well-known map used in the current Keccak hash function, which is generated via the Boolean function on $3$ variables, $x_1+(x_2+1)x_3$. We provide some general constructions, and also study the affine equivalence between rotation-symmetric S-boxes and describe the corresponding relationship between the Boolean function they are associated with.

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