A Course in Cryptography

Description

Cover Title page Contents Preface Getting Started with SageMath 0.1. Installation 0.2. SageMath Command Line 0.3. Browser Notebooks 0.4. Computations with SageMath Chapter 1. Fundamentals 1.1. Sets, Relations and Functions 1.2. Combinatorics 1.3. Computational Complexity 1.4. Discrete Probability 1.5. Random Numbers 1.6. Summary Exercises Chapter 2. Encryption Schemes and Definitions of Security 2.1. Encryption Schemes 2.2. Perfect Secrecy 2.3. Computational Security 2.4. Indistinguishable Encryptions 2.5. Eavesdropping Attacks 2.6. Chosen Plaintext Attacks 2.7. Chosen Ciphertext Attacks 2.8. Pseudorandom Generators 2.9. Pseudorandom Functions 2.10. Block Ciphers and Operation Modes 2.11. Summary Exercises Chapter 3. Elementary Number Theory 3.1. Integers 3.2. Congruences 3.3. Modular Exponentiation 3.4. Summary Exercises Chapter 4. Algebraic Structures 4.1. Groups 4.2. Rings and Fields 4.3. Finite Fields 4.4. Linear and Affine Maps 4.5. Summary Exercises Chapter 5. Block Ciphers 5.1. Constructions of Block Ciphers 5.2. Advanced Encryption Standard 5.3. Summary Exercises Chapter 6. Stream Ciphers 6.1. Definition of Stream Ciphers 6.2. Linear Feedback Shift Registers 6.3. RC4 6.4. Salsa20 and ChaCha20 6.5. Summary Exercises Chapter 7. Hash Functions 7.1. Definitions and Security Requirements 7.2. Applications of Hash Functions 7.3. Merkle-Damgård Construction 7.4. SHA-1 7.5. SHA-2 7.6. SHA-3 7.7. Summary Exercises Chapter 8. Message Authentication Codes 8.1. Definitions and Security Requirements 8.2. CBC MAC 8.3. HMAC 8.4. Authenticated Encryption 8.5. Summary Exercises Chapter 9. Public-Key Encryption and the RSA Cryptosystem 9.1. Public-Key Cryptosystems 9.2. Plain RSA 9.3. RSA Security 9.4. Generation of Primes 9.5. Efficiency of RSA 9.6. Padded RSA 9.7. Factoring 9.8. Summary Exercises Chapter 10. Key Establishment 10.1. Key Distribution 10.2. Key Exchange Protocols 10.3. Diffie-Hellman Key Exchange 10.4. Diffie-Hellman using Subgroups of zz _{𝑝}* 10.5. Discrete Logarithm 10.6. Key Encapsulation 10.7. Hybrid Encryption 10.8. Summary Exercises Chapter 11. Digital Signatures 11.1. Definitions and Security Requirements 11.2. Plain RSA Signature 11.3. Probabilistic Signature Scheme 11.4. Summary Exercises Chapter 12. Elliptic Curve Cryptography 12.1. Weierstrass Equations and Elliptic Curves 12.2. Elliptic Curve Diffie-Hellman 12.3. Efficiency and Security of Elliptic Curve Cryptography 12.4. Elliptic Curve Factoring Method 12.5. Summary Exercises Chapter 13. Quantum Computing 13.1. Quantum Bits 13.2. Multiple Qubit Systems 13.3. Quantum Algorithms 13.4. Quantum Fourier Transform 13.5. Shor’s Factoring Algorithm 13.6. Quantum Key Distribution 13.7. Summary Exercises Chapter 14. Lattice-based Cryptography 14.1. Lattices 14.2. Lattice Algorithms 14.3. GGH Cryptosystem 14.4. NTRU 14.5. Learning with Errors 14.6. Summary Exercises Chapter 15. Code-based Cryptography 15.1. Linear Codes 15.2. Bounds on Codes 15.3. Goppa Codes 15.4. McEliece Cryptosystem 15.5. Summary Exercises Bibliography Index Back cover