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

2022/03/01 by Omland, Tron, Stanica, Pantelimon · 1 citation
#Combinatorics (math.CO) #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2203.00778

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≤ 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, x₁+(x₂+1)x₃. 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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