## Cryptology ePrint Archive: Report 2022/279

Permutation rotation-symmetric Sboxes, liftings and affine equivalence

Tron Omland and Pantelimon Stanica

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 $x_1+x_1x_2+x_3$. 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.

Category / Keywords: foundations / boolean functions