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.

Table of Contents:
Preface xi Alexei 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 3 Pavel S. KNOPOV and Vladimir I. NORKIN Chapter 1. Three Approaches to Decision-making Under Risk and Uncertainty for the Critical Infrastructure Protection 5 Vladimir 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 33 Vladimir 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 53 Vladimir 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 67 Vladimir 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 81 Arkadii 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 107 Vladimir 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 127 Petro 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 2 149 Alexei A. GAIVORONSKI and Volodymyr A. ZASLAVSKYI Chapter 8. Digital Authentication of the Type "friend-or-foe" by Means of One-time Signatures 151 Anatoly 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 175 Lyudmila 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 211 Vasyl 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