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Proving Resistance Against Invariant Attacks: How to Choose the Round Constants

  • Christof Beierle
  • Anne Canteaut
  • Gregor Leander
  • Yann Rotella
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10402)

Abstract

Many lightweight block ciphers apply a very simple key schedule in which the round keys only differ by addition of a round-specific constant. Generally, there is not much theory on how to choose appropriate constants. In fact, several of those schemes were recently broken using invariant attacks, i.e., invariant subspace or nonlinear invariant attacks. This work analyzes the resistance of such ciphers against invariant attacks and reveals the precise mathematical properties that render those attacks applicable. As a first practical consequence, we prove that some ciphers including Prince, Skinny-64 and \(\textsf {Mantis}_{\mathsf {7}}\) are not vulnerable to invariant attacks. Also, we show that the invariant factors of the linear layer have a major impact on the resistance against those attacks. Most notably, if the number of invariant factors of the linear layer is small (e.g., if its minimal polynomial has a high degree), we can easily find round constants which guarantee the resistance to all types of invariant attacks, independently of the choice of the S-box layer. We also explain how to construct optimal round constants for a given, but arbitrary, linear layer.

Keywords

Block cipher Nonlinear invariant Invariant subspace attack Linear layer Round constants Mantis Midori Prince Skinny LED 

Notes

Acknowledgements

This work was partially supported by the DFG Research Training Group GRK 1817 Ubicrypt and the French Agence Nationale de la recherche through the BRUTUS project under contract ANR-14-CE28-0015.

Supplementary material

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Copyright information

© International Association for Cryptologic Research 2017

Authors and Affiliations

  • Christof Beierle
    • 1
  • Anne Canteaut
    • 2
  • Gregor Leander
    • 1
  • Yann Rotella
    • 2
  1. 1.Horst Görtz Institute for IT SecurityRuhr-Universität BochumBochumGermany
  2. 2.InriaParisFrance

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