Cryptology ePrint Archive: Report 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.

Category / Keywords: secret-key cryptography / Linear cryptanalysis, Nonlinear cryptanalysis, Piling-up lemma, Correlation matrices, Block cipher invariants

Original Publication (with minor differences): IACR-ASIACRYPT-2021

Date: received 19 Sep 2021

Contact author: tim beyne at esat kuleuven be

Available format(s): PDF | BibTeX Citation

Version: 20210920:115143 (All versions of this report)

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