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Attack–Defense Trees Attack–Defense Trees Patrick Schweitzer Supervisor: Prof. Dr. Sjouke Mauw (University of Luxembourg) Daily advisor: Dr. Barbara Kordy (University of Luxembourg) © 2013 Patrick Schweitzer The author was employed at the University of Luxembourg and received support from the Fonds National de la Recherche, Luxembourg (PHD-09-167) in the project “Security Analysis through Attack–Defense Trees”. PhD-FSTC-2013-28 The Faculty of Sciences, Technology and Communication DISSERTATION Presented on 8 November 2013 in Luxembourg to obtain the degree of DOCTEUR DE L’UNIVERSITÉ DU LUXEMBOURG EN INFORMATIQUE by Patrick SCHWEITZER Born on 25 January 1980 in Saarbrücken–Dudweiler (Germany) ATTACK–DEFENSE TREES Dissertation defense committee Dr. Barbara Kordy, vice-chairman Université du Luxembourg Dr. Sjouke Mauw, dissertation supervisor Professor, Université du Luxembourg Dr. Christian W. Probst, member Assistant Professor, The Technical University of Denmark Dr. Yves Le Traon, chairman Professor, Université du Luxembourg Dr. Jan Willemson, member Cybernetica, Estonia Summary The advent of the information age has notably amplified the importance of security. Unfortunately security considerations still widely occur as an afterthought. For many companies, security is not a requirement to conduct business and is therefore readily neglected. However the lack of security may obstruct, impede and even ruin an otherwise flourishing enterprise. Only when internal computer networks shut down, web portals are inaccessible, mail servers are attacked, or similar incidents affect the day to day business of an enterprise, security enters into the field of vision of companies. As such, security by design is only slowly becoming accepted practice. Amongst security researchers, there is no dispute that a reasonable approach to- wards uninterrupted business activities includes security measures and controls from the beginning. To support these efforts, many security models have been developed. Graphical security models are a type of security model that help illus- trate and guide the consideration of security throughout the lifecycle of a product, system or company. Their visual properties are especially well-suited to elucidate security requirements and corresponding security measures. During the last four years, we have developed a new graphical security model called attack–defense trees. The new framework, presented in this thesis, generalizes the well-known attack trees model. Attack–defense trees formally extend attack trees and enhance them with defenses. To be able to deploy attack–defense trees as a security support tool, we have equipped them with three different syntaxes: A visually appealing, graph-based syntax that is dedicated to representing security problems, an algebraic, term-based syntax that simplifies correct, formal and quantitative analysis of security scenarios and a textual syntax that is a compromise between succinct, visual representation and easy, computerized input. We have also equipped attack–defense trees with a variety of semantics. This became necessary, since different applications require different interpretations of attack–defense trees. Besides the very specific and problem oriented propositional, De Morgan and multiset semantics, we have introduced equational semantics. The latter semantics is, in fact, an alternative, unified presentation of semantics based on equational theory. We have expressed the propositional and the multiset seman- tics in terms of the equational semantics. This facilitates algorithmic treatment since the two different semantics have a unified formal foundation. To be able to perform quantitative security analysis, we have introduced the notion of an attribute for attack–defense trees. To guarantee that the evaluation of an attribute on two or more semantically equal attack–defense trees results in the same I II Summary value, we have introduced the notion of a compatibility condition between semantics and attributes. We have also provided usability guidelines for attributes. These guidelines help a user to specify security-relevant questions that can unambiguously be answered using attributes. We have performed several case studies that allowed us to test and improve the attack–defense tree methodology. We have provided detailed explanations for our design choices during the case studies as well as extensive applicability guidelines that serve a prospective user of the attack–defense tree methodology as a user manual. We have demonstrated the usefulness of the formal foundations of attack–defense trees by relating attack–defense terms to other scientific research disciplines. Con- cretely, we have shown that attack–defense trees in the propositional semantics are computationally as complex as propositional attack trees. Moreover, we have described how to merge Bayesian networks with attack–defense trees and have il- lustrated that attack–defense trees in the propositional semantics are equivalent to a specific class of games frequently occurring in game theory. Concluding the thesis, we have related the attack–defense tree methodology to other graphical security models in an extensive literature overview over similar methodologies. Acknowledgments Writing a thesis is, like life, a never-ending learning process. Moments of joy are equally part of the experience as failures and setbacks. Besides having to pull myself (and the horse I was sitting on) out of the self-induced chaos by my own hair, I was frequently helped and supported by numerous people all of whom I wish to thank. First, I want to mention my daily advisor, Barbara Kordy. I cherish the unwaivering endurance that she showed throughout the years. Her devotion to teach me the precise and intelligible writing is admirable. Next, I wish to extend my gratitude to Sjouke Mauw. It was a great pleasure to be part of his research group. His enthusiasm for and capability to inspire individuals to perform theoretical research continues to fascinate me. I appreciate the many valiant conversational attempts to enlighten me in aspects of Dutch humor, which unfortunately still remain a mystery to me. I would also like to thank the members of my defense committee, Christian W. Probst, Yves Le Traon and Jan Willemson. I am grateful for the time and effort they spent on improving the quality of my research results. Furthermore, I would like to thank Björn Ottersten for valuable advice given as a member of my thesis supervisory committee. Many members of SaToSS as well as SnT made life in Luxembourg extremely enjoyable. In particular, I would like to acknowledge Xihui Chen, Ton van Deursen, Naipeng Dong, Hugo Jonker, Piotr Kordy, Jean Lancrenon, Matthijs Melissen, Tim Muller, Marc Pouly, Saša Radomirović and Miguel Urquidi for scientific discussions, memorable Xmas parties and extended aquatic sessions. I am honored to have such great friends as André Berthe, Johannes Hess and Se- bastian Reißmann who managed to, time and again, show me different perspectives on life and unerringly urged me to go on. I’d like to extend my special appreciation to Matty McConchie for thoroughly proofreading the entire manuscript. I give heartfelt thanks to my parents, my Bomi, Annette and Renate for their never-ending moral support. Moreover, I wish to thank Tamaris Zwickler for always lending me a shoulder to cry on and for never complaining about the long hours that it took to compose this thesis. I want to express my deepest gratitude to my brother Pascal, who not only fought his way through the first draft of this thesis but also encouraged me to wake up an hour earlier than him every morning. Finally, I wish to acknowledge my Volk III IV Acknowledgments for always smiling not matter what the circumstances. Patrick Schweitzer Luxembourg, November 2013 Contents 1 Introduction 1 1.1 Graphical Security Modeling ............................ 2 1.2 Formal Security Modeling .............................. 3 1.3 The Research Question ................................ 4 1.4 Contribution ....................................... 7 1.5 Thesis Structure ..................................... 7 1.6 Further Research .................................... 10 2 Syntax and Definitions 13 2.1 ADTrees .......................................... 13 2.1.1 Defining ADTrees ............................... 13 2.1.2 An Introductory Example ......................... 14 2.1.3 A Running Example ............................. 17 2.1.4 A Formal Definition of ADTrees .................... 17 2.2 ADTerms .......................................... 19 2.3 Transformations between ADTrees and ADTerms ............. 20 2.4 Textual Syntax ...................................... 21 2.5 Design Choices ...................................... 26 3 Semantics 29 3.1 Propositional Semantics (≡P ) ........................... 30 3.2 Semantics Induced by a De Morgan Lattice .................. 34 3.3 Multiset Semantics (≡M) .............................. 38 3.4 Equational Semantics ................................. 40 3.5 Axiomatization of Semantics for ADTerms .................. 41 3.5.1 The Notion of a Complete Set of Axioms .............. 42 3.5.2 A Complete Set of Axioms for ≡P ................... 44 3.5.3 A Complete Set of Axioms for ≡M .................. 49 4 Quantitative Analysis 55 V VI Contents 4.1 Historical Overview of Attributes ......................... 55 4.1.1 Attributes for Attack Trees ........................ 56 4.1.2 Attributes for Defensive Aspects .................... 56 4.1.3 Value Domains ................................ 56
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