International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: A Geometric Approach to Linear Cryptanalysis

Tim Beyne , imec-COSIC, ESAT, KU Leuven
DOI: 10.1007/978-3-030-92062-3_2
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Presentation: Slides
Conference: ASIACRYPT 2021
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.
Video from ASIACRYPT 2021
  title={A Geometric Approach to Linear Cryptanalysis},
  author={Tim Beyne},