On Perfect Linear Approximations and Differentials over Two-Round SPNs

Christof Beierle; Patrick Felke; Gregor Leander; Patrick Neumann; Lukas Stennes

Paper 2023/725

On Perfect Linear Approximations and Differentials over Two-Round SPNs

Christof Beierle

, Ruhr University Bochum

Patrick Felke

, University of Applied Sciences Emden Leer

Gregor Leander

, Ruhr University Bochum

Patrick Neumann, Ruhr University Bochum

Lukas Stennes

, Ruhr University Bochum

Abstract

Recent constructions of (tweakable) block ciphers with an embedded cryptographic backdoor relied on the existence of probability-one differentials or perfect (non-)linear approximations over a reduced-round version of the primitive. In this work, we study how the existence of probability-one differentials or perfect linear approximations over two rounds of a substitution-permutation network can be avoided by design. More precisely, we develop criteria on the s-box and the linear layer that guarantee the absence of probability-one differentials for all keys. We further present an algorithm that allows to efficiently exclude the existence of keys for which there exists a perfect linear approximation.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: A major revision of an IACR publication in CRYPTO 2023
Keywords: differential cryptanalysis linear cryptanalysis decomposition boomerang connectivity table weak keys
Contact author(s): christof beierle @ rub de
patrick felke @ hs-emden-leer de
gregor leander @ rub de
patrick neumann @ rub de
lukas stennes @ rub de
History: 2023-05-22: approved; 2023-05-19: received; See all versions
Short URL: https://ia.cr/2023/725
License: CC BY

BibTeX

@misc{cryptoeprint:2023/725,
      author = {Christof Beierle and Patrick Felke and Gregor Leander and Patrick Neumann and Lukas Stennes},
      title = {On Perfect Linear Approximations and Differentials over Two-Round {SPNs}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/725},
      year = {2023},
      url = {https://eprint.iacr.org/2023/725}
}