Permutation rotation-symmetric S-boxes, liftings and affine equivalence

Tron Omland; Pantelimon Stanica

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arXiv · 2203.00778

Permutation rotation-symmetric S-boxes, liftings and affine equivalence

Tron Omland·Pantelimon Stanica

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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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Tron Omland, Pantelimon Stanica. 2022-03-01. Permutation rotation-symmetric S-boxes, liftings and affine equivalence. https://arxiv.org/abs/2203.00778

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