Paper 2021/1247
A Geometric Approach to Linear Cryptanalysis
Tim Beyne
Abstract
A new interpretation of linear cryptanalysis is proposed. This 'geometric approach' unifies all common variants of linear cryptanalysis, reveals links between various properties, and suggests additional generalizations. For example, new insights into invariants corresponding to non-real eigenvalues of correlation matrices and a generalization of the link between zero-correlation and integral attacks are obtained. Geometric intuition leads to a fixed-key motivation for the piling-up principle, which is illustrated by explaining and generalizing previous results relating invariants and linear approximations. Rank-one approximations are proposed to analyze cell-oriented ciphers, and used to resolve an open problem posed by Beierle, Canteaut and Leander at FSE 2019. In particular, it is shown how such approximations can be analyzed automatically using Riemannian optimization.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- A minor revision of an IACR publication in ASIACRYPT 2021
- Keywords
- Linear cryptanalysisNonlinear cryptanalysisPiling-up lemmaCorrelation matricesBlock cipher invariants
- Contact author(s)
- tim beyne @ esat kuleuven be
- History
- 2021-09-20: received
- Short URL
- https://ia.cr/2021/1247
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/1247,
author = {Tim Beyne},
title = {A Geometric Approach to Linear Cryptanalysis},
howpublished = {Cryptology ePrint Archive, Paper 2021/1247},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/1247}},
url = {https://eprint.iacr.org/2021/1247}
}
