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

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 Mantis 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.
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https://hal.inria.fr/hal-01631130
Contributor : Yann Rotella <>
Submitted on : Wednesday, November 8, 2017 - 5:03:56 PM
Last modification on : Thursday, May 17, 2018 - 10:34:03 AM
Long-term archiving on: : Friday, February 9, 2018 - 1:53:10 PM

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Christof Beierle, Anne Canteaut, Gregor Leander, Yann Rotella. Proving Resistance Against Invariant Attacks: How to Choose the Round Constants.. Crypto 2017 - Advances in Cryptology, Steven Myers, Aug 2017, Santa Barbara, United States. pp.647--678, ⟨10.1007/978-3-319-63715-0_22⟩. ⟨hal-01631130⟩

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