Mathematical Aspects of Division Property

Phil Hebborn; Gregor Leander; Aleksei Udovenko

Paper 2022/736

Mathematical Aspects of Division Property

Phil Hebborn, Ruhr-Universität Bochum

Gregor Leander

, Ruhr-Universität Bochum

Aleksei Udovenko

, SnT, University of Luxembourg

Abstract

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.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Cryptography and Communications
DOI: 10.1007/s12095-022-00622-2
Keywords: symmetric cryptography Boolean functions algebraic degree integral cryptanalysis division property
Contact author(s): phil hebborn @ rub de
gregor leander @ rub de
aleksei @ affine group
History: 2023-03-05: last of 2 revisions; 2022-06-09: received; See all versions
Short URL: https://ia.cr/2022/736
License: CC BY

BibTeX

@misc{cryptoeprint:2022/736,
      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},
      url = {https://eprint.iacr.org/2022/736}
}