Paper 2021/1247

A Geometric Approach to Linear Cryptanalysis

Tim Beyne


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.

Available format(s)
Secret-key cryptography
Publication info
A minor revision of an IACR publication in ASIACRYPT 2021
Linear cryptanalysisNonlinear cryptanalysisPiling-up lemmaCorrelation matricesBlock cipher invariants
Contact author(s)
tim beyne @ esat kuleuven be
2021-09-20: received
Short URL
Creative Commons Attribution


      author = {Tim Beyne},
      title = {A Geometric Approach to Linear Cryptanalysis},
      howpublished = {Cryptology ePrint Archive, Paper 2021/1247},
      year = {2021},
      note = {\url{}},
      url = {}
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