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The importance of security metrics can hardly be overstated. Despite the attention that has been paid by the academia, government and industry in the past decades, this important problem stubbornly remains open. In this survey, we present a…

Cryptography and Security · Computer Science 2016-01-25 Marcus Pendleton , Richard Garcia-Lebron , Shouhuai Xu

We provide the first formal foundation of SAND attack trees which are a popular extension of the well-known attack trees. The SAND attack tree formalism increases the expressivity of attack trees by introducing the sequential conjunctive…

Cryptography and Security · Computer Science 2015-03-10 Ravi Jhawar , Barbara Kordy , Sjouke Mauw , Sasa Radomirovic , Rolando Trujillo-Rasua

This paper presents the current state of the art on attack and defense modeling approaches that are based on directed acyclic graphs (DAGs). DAGs allow for a hierarchical decomposition of complex scenarios into simple, easily understandable…

Cryptography and Security · Computer Science 2013-04-01 Barbara Kordy , Ludovic Piètre-Cambacédès , Patrick Schweitzer

CONTEXT. Attack treesare a recommended threat modeling tool, but there is no established method to compare them. OBJECTIVE. We aim to establish a method to compare "real" attack trees, based on both the structure of the tree itself and the…

Cryptography and Security · Computer Science 2025-03-05 Nathan D. Schiele , Olga Gadyatskaya

This paper introduces \textit{measurement trees}, a novel class of metrics designed to combine various constructs into an interpretable multi-level representation of a measurand. Unlike conventional metrics that yield single values,…

Artificial Intelligence · Computer Science 2025-10-01 Craig Greenberg , Patrick Hall , Theodore Jensen , Kristen Greene , Razvan Amironesei

In this paper, we present a proof theory for attack trees. Attack trees are a well established and useful model for the construction of attacks on systems since they allow a stepwise exploration of high level attacks in application…

Cryptography and Security · Computer Science 2018-05-16 Florian Kammüller

Security metrics present the security level of a system or a network in both qualitative and quantitative ways. In general, security metrics are used to assess the security level of a system and to achieve security goals. There are a lot of…

Cryptography and Security · Computer Science 2021-05-19 Simon Yusuf Enoch , Jin B. Hong , Mengmeng Ge , Dong Seong Kim

We provide an overview of three different query languages whose objective is to specify properties on the highly popular formalisms of fault trees (FTs) and attack trees (ATs). These are BFL, a Boolean Logic for FTs, PFL, a probabilistic…

Logic in Computer Science · Computer Science 2024-01-30 Stefano M. Nicoletti , Milan Lopuhaä-Zwakenberg , E. Moritz Hahn , Mariëlle Stoelinga

Model-based evaluation in cybersecurity has a long history. Attack Graphs (AGs) and Attack Trees (ATs) were the earlier developed graphical security models for cybersecurity analysis. However, they have limitations (e.g., scalability…

Cryptography and Security · Computer Science 2022-01-05 Simon Yusuf Enoch , Mengmeng Ge , Jin B. Hong , Dong Seong Kim

Embedded Systems (ES) development has been historically focused on functionality rather than security, and today it still applies in many sectors and applications. However, there is an increasing number of security threats over ES, and a…

Cryptography and Security · Computer Science 2021-12-13 Ángel Longueira-Romero , Rosa Iglesias , David Gonzalez , Iñaki Garitano

The ADTool is free, open source software assisting graphical modeling and quantitative analysis of security, using attack-defense trees. The main features of the ADTool are easy creation, efficient editing, and automated bottom-up…

Cryptography and Security · Computer Science 2013-06-12 Barbara Kordy , Piotr Kordy , Sjouke Mauw , Patrick Schweitzer

Attack graphs are a tool for analyzing security vulnerabilities that capture different and prospective attacks on a system. As a threat modeling tool, it shows possible paths that an attacker can exploit to achieve a particular goal.…

Recently, the evolution of deep learning has promoted the application of machine learning (ML) to various systems. However, there are ML systems, such as autonomous vehicles, that cause critical damage when they misclassify. Conversely,…

Cryptography and Security · Computer Science 2023-12-29 Yuki Yamaguchi , Toshiaki Aoki

Advanced Persistent Threats (APTs) pose a significant security risk to organizations and industries. These attacks often lead to severe data breaches and compromise the system for a long time. Mitigating these sophisticated attacks is…

Cryptography and Security · Computer Science 2025-08-04 Ehsan Hallaji , Roozbeh Razavi-Far , Mehrdad Saif

In security analysis, attack trees are a major tool for showing the structural decomposition of attacks and for supporting the evaluation of the quantitative properties (called attributes) of the attacks. However, the validities of…

Cryptography and Security · Computer Science 2022-04-14 Hideaki Nishihara , Yasuyuki Kawanishi , Daisuke Souma , Hirotaka Yoshida

The landscape of cyber threats grows more complex by the day. Advanced Persistent Threats carry out attack campaigns - e.g. operations Dream Job, Wocao, and WannaCry - against which cybersecurity practitioners must defend. To prioritise…

Cryptography and Security · Computer Science 2026-01-23 Stefano M. Nicoletti , Milan Lopuhaä-Zwakenberg , Mariëlle Stoelinga , Fabio Massacci , Carlos E. Budde

This paper is devoted to measuring the security of cyber networks under advanced persistent threats (APTs). First, an APT-based cyber attack-defense process is modeled as an individual-level dynamical system. Second, the dynamic model is…

Cryptography and Security · Computer Science 2017-07-13 Lu-Xing Yang , Pengdeng Li , Xiaofan Yang , Luosheng Wen , Yingbo Wu , Yuan Yan Tang

We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…

Probability · Mathematics 2014-05-06 Rudolf Grübel

Advanced persistent threats (APT) combine a variety of different attack forms ranging from social engineering to technical exploits. The diversity and usual stealthiness of APT turns them into a central problem of contemporary practical…

Cryptography and Security · Computer Science 2022-05-03 Stefan Rass , Sandra König , Stefan Schauer

Tree-width is an invaluable tool for computational problems on graphs. But often one would like to compute on other kinds of objects (e.g. decorated graphs or even algebraic structures) where there is no known tree-width analogue. Here we…

Combinatorics · Mathematics 2022-06-22 Benjamin Merlin Bumpus , Zoltan A. Kocsis