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. ZASLAVSKYIPart 1. Mathematical Models and Methods for Risk Mitigation and Defending Critical Infrastructure 1Introduction to Part 1 3Pavel S. KNOPOV and Vladimir I. NORKINChapter 1. Three Approaches to Decision-making Under Risk and Uncertainty for the Critical Infrastructure Protection 5Vladimir S. KIRILYUK1.1. Introduction 51.2. Decision-making in stochastic conditions of risk and uncertainty 71.3. Some traditional risk assessments and worst-case analysis 191.4. Adversarial risk analysis in conditions of terrorist threat 261.5. Conclusion 281.6. Acknowledgments 291.7. List of abbreviations 291.8. References 29Chapter 2. Models of Anti-Terrorist Protection 33Vladimir I. NORKIN2.1. Area control tasks 332.2. Simulation of attack and passive defense 372.3. Modeling attack on a market: a linear programming model 392.4. A probabilistic version of the problem of attacking the objective function 412.5. Modeling an attack on resources of optimal systems 422.6. Modeling an attack on the transport system 422.7. Models of protection of transport and information networks 442.8. Stochastic models of passive protection of transport and information networks 472.9. Acknowledgments 492.10. References 49Chapter 3. Allocation of Resources for the Critical Infrastructure Protection 53Vladimir I. NORKIN, Alexei A. GAIVORONSKI, Pavel S. KNOPOV and Volodymyr A. ZASLAVSKYI3.1. The hierarchical dynamic programming 533.2. Examples of resource allocation problems 603.3. Conclusion 643.4. Acknowledgments 643.5. References 64Chapter 4. Simulation of the Defender-Attacker Game for Critical Objects Protection 67Vladimir I. NORKIN4.1. Introduction 674.2. A simple strategic attacker-defender game 704.3. Generalizations 764.4. Further generalization 774.5. Conclusion 774.6. Acknowledgments 784.7. References 78Chapter 5. Making Decisions and Motion Control in Conditions of Conflict 81Arkadii CHIKRII5.1. Introduction 815.2. Problem statement 825.3. Pontryagin’s first direct method 845.4. Schemes of the method of resolving functions 865.5. Scheme with fixed points of the terminal set solid part 965.6. Connection of the first direct method with the method of resolving functions 985.7. Conclusion 1035.8. Acknowledgments 1035.9. References 104Chapter 6. Contemporary Stochastic Quasi-gradient Algorithms 107Vladimir I. NORKIN, Alexei A. GAIVORONSKI, Pavel S. KNOPOV and Anton KOZYRIEV6.1. Introduction 1076.2. A stochastic optimization problem 1096.3. Stochastic approximation 1096.4. Application of stochastic quasi-gradient algorithms in machine learning 1106.5. Stochastic gradient methods 1116.6. Conclusion 1236.7. Acknowledgments 1236.8. References 123Chapter 7. Two Classes of Optimization Problems for Arcs Capacities Modernization for Fault-tolerant Networks 127Petro STETSYUK, Viktor STOVBA and Volodymyr ZHYDKOV7.1. Basic concepts for a fault-tolerant network 1277.2. Basic LP-problems A and P 1317.3. Boolean problems A and P 1347.4. Convex problems A and P: decomposition algorithms 1387.5. Software: programs SolverA and SolverP 1427.6. Acknowledgements 1457.7. References 145Part 2. Cyber Security of Critical Infrastructure Facilities 147Introduction to Part 2 149Alexei A. GAIVORONSKI and Volodymyr A. ZASLAVSKYIChapter 8. Digital Authentication of the Type "friend-or-foe" by Means of One-time Signatures 151Anatoly ANISIMOV8.1. Introduction 1518.2. Coalition group 1538.3. Authentication in public-key cryptography 1558.4. Authentication through digital signatures and sigma protocols 1568.5. A general description of a "friend-or-foe" authentication protocol using OTSs 1628.6. References 171Chapter 9. Main Directions and Basic Mathematical Ideas of Cryptographic Information Security 175Lyudmila KOVALCHUK and Mikhail SAVCHUK9.1. Introduction 1759.2. Problems and aspects of information security, basic concepts of cryptographic information security. 1759.3. Classification of cryptosystems 1799.4. Symmetric cryptography 1809.5. Asymmetric cryptography: public key cryptosystems 1959.6. Conclusion 2089.7. References 209Chapter 10. Cybersecurity Investments in Networks 211Vasyl GORBACHUK, Maksym DUNAIEVSKYI and Seit-Bekir SULEIMANOV10.1. Introduction 21110.2. Cybersecurity in SCNs 21210.3. Numerical experiments for networks 21910.4. Critical and risky SCNs 22610.5. Acknowledgements 23110.6. References 231List of Authors 235Index 239Summary of Volume 1 243

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. ZASLAVSKYIPart 1. Mathematical Models and Methods for Risk Mitigation and Defending Critical Infrastructure 1Introduction to Part 1 3Pavel S. KNOPOV and Vladimir I. NORKINChapter 1. Three Approaches to Decision-making Under Risk and Uncertainty for the Critical Infrastructure Protection 5Vladimir S. KIRILYUK1.1. Introduction 51.2. Decision-making in stochastic conditions of risk and uncertainty 71.3. Some traditional risk assessments and worst-case analysis 191.4. Adversarial risk analysis in conditions of terrorist threat 261.5. Conclusion 281.6. Acknowledgments 291.7. List of abbreviations 291.8. References 29Chapter 2. Models of Anti-Terrorist Protection 33Vladimir I. NORKIN2.1. Area control tasks 332.2. Simulation of attack and passive defense 372.3. Modeling attack on a market: a linear programming model 392.4. A probabilistic version of the problem of attacking the objective function 412.5. Modeling an attack on resources of optimal systems 422.6. Modeling an attack on the transport system 422.7. Models of protection of transport and information networks 442.8. Stochastic models of passive protection of transport and information networks 472.9. Acknowledgments 492.10. References 49Chapter 3. Allocation of Resources for the Critical Infrastructure Protection 53Vladimir I. NORKIN, Alexei A. GAIVORONSKI, Pavel S. KNOPOV and Volodymyr A. ZASLAVSKYI3.1. The hierarchical dynamic programming 533.2. Examples of resource allocation problems 603.3. Conclusion 643.4. Acknowledgments 643.5. References 64Chapter 4. Simulation of the Defender-Attacker Game for Critical Objects Protection 67Vladimir I. NORKIN4.1. Introduction 674.2. A simple strategic attacker-defender game 704.3. Generalizations 764.4. Further generalization 774.5. Conclusion 774.6. Acknowledgments 784.7. References 78Chapter 5. Making Decisions and Motion Control in Conditions of Conflict 81Arkadii CHIKRII5.1. Introduction 815.2. Problem statement 825.3. Pontryagin’s first direct method 845.4. Schemes of the method of resolving functions 865.5. Scheme with fixed points of the terminal set solid part 965.6. Connection of the first direct method with the method of resolving functions 985.7. Conclusion 1035.8. Acknowledgments 1035.9. References 104Chapter 6. Contemporary Stochastic Quasi-gradient Algorithms 107Vladimir I. NORKIN, Alexei A. GAIVORONSKI, Pavel S. KNOPOV and Anton KOZYRIEV6.1. Introduction 1076.2. A stochastic optimization problem 1096.3. Stochastic approximation 1096.4. Application of stochastic quasi-gradient algorithms in machine learning 1106.5. Stochastic gradient methods 1116.6. Conclusion 1236.7. Acknowledgments 1236.8. References 123Chapter 7. Two Classes of Optimization Problems for Arcs Capacities Modernization for Fault-tolerant Networks 127Petro STETSYUK, Viktor STOVBA and Volodymyr ZHYDKOV7.1. Basic concepts for a fault-tolerant network 1277.2. Basic LP-problems A and P 1317.3. Boolean problems A and P 1347.4. Convex problems A and P: decomposition algorithms 1387.5. Software: programs SolverA and SolverP 1427.6. Acknowledgements 1457.7. References 145Part 2. Cyber Security of Critical Infrastructure Facilities 147Introduction to Part 2 149Alexei A. GAIVORONSKI and Volodymyr A. ZASLAVSKYIChapter 8. Digital Authentication of the Type "friend-or-foe" by Means of One-time Signatures 151Anatoly ANISIMOV8.1. Introduction 1518.2. Coalition group 1538.3. Authentication in public-key cryptography 1558.4. Authentication through digital signatures and sigma protocols 1568.5. A general description of a "friend-or-foe" authentication protocol using OTSs 1628.6. References 171Chapter 9. Main Directions and Basic Mathematical Ideas of Cryptographic Information Security 175Lyudmila KOVALCHUK and Mikhail SAVCHUK9.1. Introduction 1759.2. Problems and aspects of information security, basic concepts of cryptographic information security. 1759.3. Classification of cryptosystems 1799.4. Symmetric cryptography 1809.5. Asymmetric cryptography: public key cryptosystems 1959.6. Conclusion 2089.7. References 209Chapter 10. Cybersecurity Investments in Networks 211Vasyl GORBACHUK, Maksym DUNAIEVSKYI and Seit-Bekir SULEIMANOV10.1. Introduction 21110.2. Cybersecurity in SCNs 21210.3. Numerical experiments for networks 21910.4. Critical and risky SCNs 22610.5. Acknowledgements 23110.6. References 231List of Authors 235Index 239Summary of Volume 1 243

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. ZASLAVSKYIPart 1. Mathematical Models and Methods for Risk Mitigation and Defending Critical Infrastructure 1Introduction to Part 1 3Pavel S. KNOPOV and Vladimir I. NORKINChapter 1. Three Approaches to Decision-making Under Risk and Uncertainty for the Critical Infrastructure Protection 5Vladimir S. KIRILYUK1.1. Introduction 51.2. Decision-making in stochastic conditions of risk and uncertainty 71.3. Some traditional risk assessments and worst-case analysis 191.4. Adversarial risk analysis in conditions of terrorist threat 261.5. Conclusion 281.6. Acknowledgments 291.7. List of abbreviations 291.8. References 29Chapter 2. Models of Anti-Terrorist Protection 33Vladimir I. NORKIN2.1. Area control tasks 332.2. Simulation of attack and passive defense 372.3. Modeling attack on a market: a linear programming model 392.4. A probabilistic version of the problem of attacking the objective function 412.5. Modeling an attack on resources of optimal systems 422.6. Modeling an attack on the transport system 422.7. Models of protection of transport and information networks 442.8. Stochastic models of passive protection of transport and information networks 472.9. Acknowledgments 492.10. References 49Chapter 3. Allocation of Resources for the Critical Infrastructure Protection 53Vladimir I. NORKIN, Alexei A. GAIVORONSKI, Pavel S. KNOPOV and Volodymyr A. ZASLAVSKYI3.1. The hierarchical dynamic programming 533.2. Examples of resource allocation problems 603.3. Conclusion 643.4. Acknowledgments 643.5. References 64Chapter 4. Simulation of the Defender-Attacker Game for Critical Objects Protection 67Vladimir I. NORKIN4.1. Introduction 674.2. A simple strategic attacker-defender game 704.3. Generalizations 764.4. Further generalization 774.5. Conclusion 774.6. Acknowledgments 784.7. References 78Chapter 5. Making Decisions and Motion Control in Conditions of Conflict 81Arkadii CHIKRII5.1. Introduction 815.2. Problem statement 825.3. Pontryagin’s first direct method 845.4. Schemes of the method of resolving functions 865.5. Scheme with fixed points of the terminal set solid part 965.6. Connection of the first direct method with the method of resolving functions 985.7. Conclusion 1035.8. Acknowledgments 1035.9. References 104Chapter 6. Contemporary Stochastic Quasi-gradient Algorithms 107Vladimir I. NORKIN, Alexei A. GAIVORONSKI, Pavel S. KNOPOV and Anton KOZYRIEV6.1. Introduction 1076.2. A stochastic optimization problem 1096.3. Stochastic approximation 1096.4. Application of stochastic quasi-gradient algorithms in machine learning 1106.5. Stochastic gradient methods 1116.6. Conclusion 1236.7. Acknowledgments 1236.8. References 123Chapter 7. Two Classes of Optimization Problems for Arcs Capacities Modernization for Fault-tolerant Networks 127Petro STETSYUK, Viktor STOVBA and Volodymyr ZHYDKOV7.1. Basic concepts for a fault-tolerant network 1277.2. Basic LP-problems A and P 1317.3. Boolean problems A and P 1347.4. Convex problems A and P: decomposition algorithms 1387.5. Software: programs SolverA and SolverP 1427.6. Acknowledgements 1457.7. References 145Part 2. Cyber Security of Critical Infrastructure Facilities 147Introduction to Part 2 149Alexei A. GAIVORONSKI and Volodymyr A. ZASLAVSKYIChapter 8. Digital Authentication of the Type "friend-or-foe" by Means of One-time Signatures 151Anatoly ANISIMOV8.1. Introduction 1518.2. Coalition group 1538.3. Authentication in public-key cryptography 1558.4. Authentication through digital signatures and sigma protocols 1568.5. A general description of a "friend-or-foe" authentication protocol using OTSs 1628.6. References 171Chapter 9. Main Directions and Basic Mathematical Ideas of Cryptographic Information Security 175Lyudmila KOVALCHUK and Mikhail SAVCHUK9.1. Introduction 1759.2. Problems and aspects of information security, basic concepts of cryptographic information security. 1759.3. Classification of cryptosystems 1799.4. Symmetric cryptography 1809.5. Asymmetric cryptography: public key cryptosystems 1959.6. Conclusion 2089.7. References 209Chapter 10. Cybersecurity Investments in Networks 211Vasyl GORBACHUK, Maksym DUNAIEVSKYI and Seit-Bekir SULEIMANOV10.1. Introduction 21110.2. Cybersecurity in SCNs 21210.3. Numerical experiments for networks 21910.4. Critical and risky SCNs 22610.5. Acknowledgements 23110.6. References 231List of Authors 235Index 239Summary of Volume 1 243