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- Includes bibliographical references and index.Intro; Preface; Acknowledgments; Contents; About the Author; 1 Cyberspace Security and Cryptography; 1.1 Cyber and Cyberspace; Cyber and Cybernetics; Cyberspace; Problems for Sect.1.1; 1.2 Cyberspace Security; Cyberspace Security; UK Cybersecurity Strategy; US and Canada's Cybersecurity Strategies; Australia and New Zealand Cybersecurity Strategies; Problems for Sect.1.2; 1.3 Cybersecurity and Cryptography; Problems for Sect.1.3; 1.4 Conclusions, Notes and Further Reading; References; 2 Mathematical Preliminaries; 2.1 Groups, Rings and Fields; Problems for Sect. 2.1; 2.2 Divisibility Theory.Problems for Sect. 2.22.3 Arithmetic Functions; Problems for Sect. 2.3; 2.4 Congruence Theory; Problems for Sect. 2.4; 2.5 Order, Primitive Root and Index; Problems for Sect. 2.5; 2.6 Theory of Elliptic Curves; Problems for Sect. 2.6; 2.7 Conclusions, Notes and Further Reading; References; 3 Computational Preliminaries; 3.1 Classical Computability Theory; Turing Machines; The Church-Turing Thesis; Decidability and Computability; Problems for Sect. 3.1; 3.2 Classical Complexity Theory; Complexity Classes; The Cook-Karp Thesis; Problems for Sect. 3.2; 3.3 Quantum Information and Computation.Problems for Sect. 3.33.4 Quantum Computability and Complexity; Problems for Sect. 3.4; 3.5 Conclusions, Notes and Further Reading; References; 4 Secret-Key Cryptography; 4.1 Secret-Key vs Public-Key Cryptography; Problems for Sect. 4.1; 4.2 Stream (Bit) Ciphers; Introduction to Stream Ciphers; The Vernam Cipher; Random Bit Generator; Problems for Sect. 4.2; 4.3 Monographic (Character) Ciphers; Caesar Cipher; Shift Transformation Ciphers; Affine Transformation Ciphers; Problems for Sect. 4.3; 4.4 Polygraphic (Block) Ciphers; Problems for Sect. 4.4; 4.5 Exponentiation Ciphers.Residuosity Based CryptographyZero-Knowledge Proof; Problems and Exercises for Sect. 5.2; 5.3 Quantum Attacks of Factoring Based Cryptography; Relationships Between Factoring and Factoring Based Cryptography; Order Finding Problem; Quantum Order Computing; Quantum Integer Factorization; Quantum Algorithm for Breaking RSA; Exercises and Problems for Sect. 5.3; 5.4 Conclusions, Notes and Further Reading; References; 6 Logarithm Based Cryptography; 6.1 Discrete Logarithm Problem; Problems for Sect. 6.1; 6.2 Classic Solutions to Discrete Logarithm Problem; Shanks' Baby-Step Giant-Step Algorithm.This book provides the basic theory, techniques, and algorithms of modern cryptography that are applicable to network and cyberspace security. It consists of the following nine main chapters: Chapter 1 provides the basic concepts and ideas of cyberspace and cyberspace security, Chapters 2 and 3 provide an introduction to mathematical and computational preliminaries, respectively. Chapters 4 discusses the basic ideas and system of secret-key cryptography, whereas Chapters 5, 6, and 7 discuss the basic ideas and systems of public-key cryptography based on integer factorization, discrete logarithms, and elliptic curves, respectively. Quantum-safe cryptography is presented in Chapter 8 and offensive cryptography, particularly cryptovirology, is covered in Chapter 9. This book can be used as a secondary text for final-year undergraduate students and first-year postgraduate students for courses in Computer, Network, and Cyberspace Security. Researchers and practitioners working in cyberspace security and network security will also find this book useful as a reference.