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Semantics of Attack-Defense Trees for Dynamic Countermeasures and a New Hierarchy of Star-Free Languages

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LATIN 2024: Theoretical Informatics (LATIN 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14579))

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Abstract

We present a mathematical setting for attack-defense trees (adts), a classic graphical model to specify attacks and countermeasures. We equip adts with (trace) language semantics allowing to have an original dynamic interpretation of countermeasures. Interestingly, the expressiveness of adts coincides with star-free languages, and the nested countermeasures impact the expressiveness of adts. With an adequate notion of countermeasure-depth, we exhibit a strict hierarchy of the star-free languages that does not coincide with the classic one. Additionally, driven by the use of adts in practice, we address the decision problems of trace membership, non-emptiness, and equivalence, and study their computational complexities parameterized by the countermeasure-depth.

This work has been partly supported by the F.R.S.- FNRS under grant n\(^{\circ }\)T.0027.21 and a PHC Tournesol project.

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Notes

  1. 1.

    https://www.schneier.com/academic/archives/1999/12/attack_trees.html.

  2. 2.

    Arbitrary regular expressions extended with intersection and complementation.

  3. 3.

    With the convention that 0-Expspace =Pspace.

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Authors and Affiliations

  1. University of Mons, Mons, Belgium

    Thomas Brihaye & Alexandre Terefenko

  2. University of Rennes, Rennes, France

    Sophie Pinchinat & Alexandre Terefenko

Authors
  1. Thomas Brihaye
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  2. Sophie Pinchinat
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  3. Alexandre Terefenko
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Correspondence to Thomas Brihaye .

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Editors and Affiliations

  1. DIM-CMM, Universidad de Chile, Santiago, Chile

    José A. Soto

  2. Technical University of Munich, Munich, Germany

    Andreas Wiese

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Brihaye, T., Pinchinat, S., Terefenko, A. (2024). Semantics of Attack-Defense Trees for Dynamic Countermeasures and a New Hierarchy of Star-Free Languages. In: Soto, J.A., Wiese, A. (eds) LATIN 2024: Theoretical Informatics. LATIN 2024. Lecture Notes in Computer Science, vol 14579. Springer, Cham. https://doi.org/10.1007/978-3-031-55601-2_17

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  • DOI: https://doi.org/10.1007/978-3-031-55601-2_17

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