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Stochastic Modeling and Optimization Methods for Critical Infrastructure Protection is a thorough exploration of mathematical models and tools that are designed to strengthen critical infrastructures against threats - both natural and adversarial. Divided into two volumes, this first volume examines stochastic modeling across key economic sectors and their interconnections, while the second volume focuses on advanced mathematical methods for enhancing infrastructure protection.
The book covers a range of themes, including risk assessment techniques that account for systemic interdependencies within modern technospheres, the dynamics of uncertainty, instability and system vulnerabilities. The book also presents other topics such as cryptographic information protection and Shannon's theory of secret systems, alongside solutions arising from optimization, game theory and machine learning approaches.
Featuring research from international collaborations, this book covers both theory and applications, offering vital insights for advanced risk management curricula. It is intended not only for researchers, but also educators and professionals in infrastructure protection and stochastic optimization.
Alexei A. Gaivoronski is Professor at the Norwegian University of Science and Technology, Norway. His research focuses on risk theory, and its applications in finance, energy, telecommunications and stochastic optimization.
Pavel S. Knopov is Head of Department at V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine. His research focuses on statistical decision theory, stochastic optimal control and stochastic optimization.
Vladimir I. Norkin is Leading Researcher at V.M. Glushkov Institute of Cybernetics, Ukraine. His research focuses on operations research.
Volodymyr A. Zaslavskyi is Professor at the Taras Shevchenko National University of Kyiv, Ukraine. His research focuses on systems analysis, risk and the reliability of critical systems.
Preface xiAlexei A. GAIVORONSKI, Pavel S. KNOPOV, Vladimir I. NORKIN and Volodymyr A. ZASLAVSKYI
Part 1. Mathematical Models and Methods for Risk Mitigation and Defending Critical Infrastructure 1
Introduction to Part 1 3Pavel S. KNOPOV and Vladimir I. NORKIN
Chapter 1. Three Approaches to Decision-making Under Risk and Uncertainty for the Critical Infrastructure Protection 5Vladimir S. KIRILYUK
1.1. Introduction 5
1.2. Decision-making in stochastic conditions of risk and uncertainty 7
1.3. Some traditional risk assessments and worst-case analysis 19
1.4. Adversarial risk analysis in conditions of terrorist threat 26
1.5. Conclusion 28
1.6. Acknowledgments 29
1.7. List of abbreviations 29
1.8. References 29
Chapter 2. Models of Anti-Terrorist Protection 33Vladimir I. NORKIN
2.1. Area control tasks 33
2.2. Simulation of attack and passive defense 37
2.3. Modeling attack on a market: a linear programming model 39
2.4. A probabilistic version of the problem of attacking the objective function 41
2.5. Modeling an attack on resources of optimal systems 42
2.6. Modeling an attack on the transport system 42
2.7. Models of protection of transport and information networks 44
2.8. Stochastic models of passive protection of transport and information networks 47
2.9. Acknowledgments 49
2.10. References 49
Chapter 3. Allocation of Resources for the Critical Infrastructure Protection 53Vladimir I. NORKIN, Alexei A. GAIVORONSKI, Pavel S. KNOPOV and Volodymyr A. ZASLAVSKYI
3.1. The hierarchical dynamic programming 53
3.2. Examples of resource allocation problems 60
3.3. Conclusion 64
3.4. Acknowledgments 64
3.5. References 64
Chapter 4. Simulation of the Defender-Attacker Game for Critical Objects Protection 67Vladimir I. NORKIN
4.1. Introduction 67
4.2. A simple strategic attacker-defender game 70
4.3. Generalizations 76
4.4. Further generalization 77
4.5. Conclusion 77
4.6. Acknowledgments 78
4.7. References 78
Chapter 5. Making Decisions and Motion Control in Conditions of Conflict 81Arkadii CHIKRII
5.1. Introduction 81
5.2. Problem statement 82
5.3. Pontryagin's first direct method 84
5.4. Schemes of the method of resolving functions 86
5.5. Scheme with fixed points of the terminal set solid part 96
5.6. Connection of the first direct method with the method of resolving functions 98
5.7. Conclusion 103
5.8. Acknowledgments 103
5.9. References 104
Chapter 6. Contemporary Stochastic Quasi-gradient Algorithms 107Vladimir I. NORKIN, Alexei A. GAIVORONSKI, Pavel S. KNOPOV and Anton KOZYRIEV
6.1. Introduction 107
6.2. A stochastic optimization problem 109
6.3. Stochastic approximation 109
6.4. Application of stochastic quasi-gradient algorithms in machine learning 110
6.5. Stochastic gradient methods 111
6.6. Conclusion 123
6.7. Acknowledgments 123
6.8. References 123
Chapter 7. Two Classes of Optimization Problems for Arcs Capacities Modernization for Fault-tolerant Networks 127Petro STETSYUK, Viktor STOVBA and Volodymyr ZHYDKOV
7.1. Basic concepts for a fault-tolerant network 127
7.2. Basic LP-problems A and P 131
7.3. Boolean problems A and P 134
7.4. Convex problems A and P: decomposition algorithms 138
7.5. Software: programs SolverA and SolverP 142
7.6. Acknowledgements 145
7.7. References 145
Part 2. Cyber Security of Critical Infrastructure Facilities 147
Introduction to Part 2 149Alexei A. GAIVORONSKI and Volodymyr A. ZASLAVSKYI
Chapter 8. Digital Authentication of the Type "friend-or-foe" by Means of One-time Signatures 151Anatoly ANISIMOV
8.1. Introduction 151
8.2. Coalition group 153
8.3. Authentication in public-key cryptography 155
8.4. Authentication through digital signatures and sigma protocols 156
8.5. A general description of a "friend-or-foe" authentication protocol using OTSs 162
8.6. References 171
Chapter 9. Main Directions and Basic Mathematical Ideas of Cryptographic Information Security 175Lyudmila KOVALCHUK and Mikhail SAVCHUK
9.1. Introduction 175
9.2. Problems and aspects of information security, basic concepts of cryptographic information security. 175
9.3. Classification of cryptosystems 179
9.4. Symmetric cryptography 180
9.5. Asymmetric cryptography: public key cryptosystems 195
9.6. Conclusion 208
9.7. References 209
Chapter 10. Cybersecurity Investments in Networks 211Vasyl GORBACHUK, Maksym DUNAIEVSKYI and Seit-Bekir SULEIMANOV
10.1. Introduction 211
10.2. Cybersecurity in SCNs 212
10.3. Numerical experiments for networks 219
10.4. Critical and risky SCNs 226
10.5. Acknowledgements 231
10.6. References 231
List of Authors 235
Index 239
Summary of Volume 1 243
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