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

Tron Omland; Pantelimon Stanica

Paper 2022/279

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

Tron Omland

, National Security Authority

Pantelimon Stanica, Naval Postgraduate School

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.

Note: revised version where several inaccuracies have been fixed and a few new observations added

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: boolean functions S-boxes rotation-symmetric liftings affine equivalence circulant matrices
Contact author(s): tron omland @ gmail com
pstanica @ nps edu
History: 2022-08-19: revised; 2022-03-02: received; See all versions
Short URL: https://ia.cr/2022/279
License: CC BY

BibTeX

@misc{cryptoeprint:2022/279,
      author = {Tron Omland and Pantelimon Stanica},
      title = {Permutation rotation-symmetric S-boxes, liftings and affine equivalence},
      howpublished = {Cryptology ePrint Archive, Paper 2022/279},
      year = {2022},
      note = {\url{https://eprint.iacr.org/2022/279}},
      url = {https://eprint.iacr.org/2022/279}
}