Attack Tree Metrics are Operad Algebras

Milan Lopuhaa-Zwakenberg

doi:10.1109/CSF61375.2024.00005

Attack Tree Metrics are Operad Algebras

Milan Lopuhaa-Zwakenberg^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Attack Trees (ATs) are a widely used tool for security analysis. ATs can be employed in quantitative security analysis through metrics, which assign a security value to an AT. Many different AT metrics exist, and there exist multiple general definitions that aim to study a wide variety of AT metrics at once. However, these all have drawbacks: they do not capture all metrics, and they do not easily generalize to extensions of ATs. In this paper, we introduce a definition of AT metrics based on category theory, specifically operad algebras. This encompasses all previous definitions of AT metrics, and is easily generalized to extensions of ATs. Furthermore, we show that under easily expressed operad-theoretic conditions, existing metric calculation algorithms can be extended in considerable generality.

Original language	English
Title of host publication	Proceedings - 2024 IEEE 37th Computer Security Foundations Symposium, CSF 2024
Publisher	IEEE
Pages	665-679
Number of pages	15
ISBN (Electronic)	9798350362039
DOIs	https://doi.org/10.1109/CSF61375.2024.00005
Publication status	Published - 20 Sept 2024
Event	37th IEEE Computer Security Foundations Symposium, CSF 2024 - Enschede, Netherlands Duration: 8 Jul 2024 → 12 Jul 2024 Conference number: 37

Publication series

Name	Proceedings - IEEE Computer Security Foundations Symposium
ISSN (Print)	1940-1434

Conference

Conference	37th IEEE Computer Security Foundations Symposium, CSF 2024
Abbreviated title	CSF 2024
Country/Territory	Netherlands
City	Enschede
Period	8/07/24 → 12/07/24

Keywords

2025 OA procedure
category theory
operads
security analysis
Attack trees

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10.1109/CSF61375.2024.00005

Attack_Tree_Metrics_are_Operad_AlgebrasFinal published version, 536 KBLicence: Taverne

Cite this

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title = "Attack Tree Metrics are Operad Algebras",

abstract = "Attack Trees (ATs) are a widely used tool for security analysis. ATs can be employed in quantitative security analysis through metrics, which assign a security value to an AT. Many different AT metrics exist, and there exist multiple general definitions that aim to study a wide variety of AT metrics at once. However, these all have drawbacks: they do not capture all metrics, and they do not easily generalize to extensions of ATs. In this paper, we introduce a definition of AT metrics based on category theory, specifically operad algebras. This encompasses all previous definitions of AT metrics, and is easily generalized to extensions of ATs. Furthermore, we show that under easily expressed operad-theoretic conditions, existing metric calculation algorithms can be extended in considerable generality.",

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AB - Attack Trees (ATs) are a widely used tool for security analysis. ATs can be employed in quantitative security analysis through metrics, which assign a security value to an AT. Many different AT metrics exist, and there exist multiple general definitions that aim to study a wide variety of AT metrics at once. However, these all have drawbacks: they do not capture all metrics, and they do not easily generalize to extensions of ATs. In this paper, we introduce a definition of AT metrics based on category theory, specifically operad algebras. This encompasses all previous definitions of AT metrics, and is easily generalized to extensions of ATs. Furthermore, we show that under easily expressed operad-theoretic conditions, existing metric calculation algorithms can be extended in considerable generality.

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KW - category theory

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Attack Tree Metrics are Operad Algebras

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