Paper 2022/736

Mathematical Aspects of Division Property

Phil Hebborn, Ruhr-Universität Bochum
Gregor Leander, Ruhr-Universität Bochum
Aleksei Udovenko, SnT, University of Luxembourg

This work surveys mathematical aspects of division property, which is a state of the art technique in cryptanalysis of symmetric-key algorithms, such as authenticated encryption, block ciphers and stream ciphers. It aims to find integral distinguishers and cube attacks, which exploit weakness in the algebraic normal forms of the output coordinates of the involved vectorial Boolean functions. Division property can also be used to provide arguments for security of primitives against these attacks. The focus of this work is a formal presentation of the theory behind the division property, including rigorous proofs, which were often omitted in the existing literature. This survey covers the two major variants of division property, namely conventional and perfect division property. In addition, we explore relationships of the technique with classic degree bounds.

Note: Preprint. Added DOI.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. Cryptography and Communications
symmetric cryptographyBoolean functionsalgebraic degreeintegral cryptanalysisdivision property
Contact author(s)
phil hebborn @ rub de
gregor leander @ rub de
aleksei @ affine group
2023-03-05: last of 2 revisions
2022-06-09: received
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Creative Commons Attribution


      author = {Phil Hebborn and Gregor Leander and Aleksei Udovenko},
      title = {Mathematical Aspects of Division Property},
      howpublished = {Cryptology ePrint Archive, Paper 2022/736},
      year = {2022},
      doi = {10.1007/s12095-022-00622-2},
      note = {\url{}},
      url = {}
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