Cryptography: An Introduction (3rd edition)
| Date: 15 April 2011, 02:53
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Nigel Smart’s Cryptography provides the rigorous detail required for advanced cryptographic studies, yet approaches the subject matter in an accessible style in order to gently guide new students through difficult mathematical topics. Covering the latest developments in computer cryptography, including the Rijndael algorithm chosen for the new Advanced Encryption Standard, the OAEP padding system for RSA and modern stream ciphers, this book is a complete introduction to cryptography.
Cryptography incorporates practical examples and real-world case studies to examine strategies for security in various contexts. The author gives specific focus to implementation issues such as exponentiation in DSA and RSA, and to provably secure algorithms with and without random oracles.
The book is divided into five parts. Part 1 gives the mathematical background needed and could be skipped at first reading and referred back to when needed. Part 2 discusses symmetric key encryption algorithms and the key distribution problem that results from their use. Part 3 discusses public key algorithms for encryption and signatures. Part 4 discusses security issues including provable security. Part 5 discusses advanced protocols including commitments, oblivious transfer and secure multi-party computation.
Contents:
Part 1. Mathematical Background
Chapter 1. Modular Arithmetic, Groups, Finite Fields and Probability
1. Modular Arithmetic
2. Finite Fields
3. Basic Algorithms
4. Probability
Chapter 2. Elliptic Curves
1. Introduction
2. The Group Law
3. Elliptic Curves over Finite Fields
4. Projective Coordinates
5. Point Compression
Part 2. Symmetric Encryption
Chapter 3. Historical Ciphers
1. Introduction
2. Shift Cipher
3. Substitution Cipher
4. Vigenere Cipher
5. A Permutation Cipher
Chapter 4. The Enigma Machine
1. Introduction
2. An Equation For The Enigma
3. Determining The Plugboard Given The Rotor Settings
4. Double Encryption Of Message Keys
5. Determining The Internal Rotor Wirings
6. Determining The Day Settings
7. The Germans Make It Harder
8. Known Plaintext Attack And The Bombe's
9. Ciphertext Only Attack
Chapter 5. Information Theoretic Security
1. Introduction
2. Probability and Ciphers
3. Entropy
4. Spurious Keys and Unicity Distance
Chapter 6. Historical Stream Ciphers
1. Introduction To Symmetric Ciphers
2. Stream Cipher Basics
3. The Lorenz Cipher
Chapter 7. Modern Stream Ciphers
1. Linear Feedback Shift Registers
2. Combining LFSRs
3. RC4
Chapter 8. Block Ciphers
1. Introduction To Block Ciphers
2. Feistel Ciphers and DES
3. Rijndael
4. Modes of Operation
Chapter 9. Symmetric Key Distribution
1. Key Management
2. Secret Key Distribution
3. Formal Approaches to Protocol Checking
Chapter 10. Hash Functions and Message Authentication Codes
1. Introduction
2. Hash Functions
3. Designing Hash Functions
4. Message Authentication Codes
Part 3. Public Key Encryption and Signatures
Chapter 11. Basic Public Key Encryption Algorithms
1. Public Key Cryptography
2. Candidate One-way Functions
3. RSA
4. ElGamal Encryption
5. Rabin Encryption
Chapter 12. Primality Testing and Factoring
1. Prime Numbers
2. Factoring Algorithms
3. Modern Factoring Methods
4. Number Field Sieve
Chapter 13. Discrete Logarithms
1. Introduction
2. Pohlig-Hellman
3. Baby-Step/Giant-Step Method
4. Pollard Type Methods
5. Sub-exponential Methods for Finite Fields
6. Special Methods for Elliptic Curves
Chapter 14. Key Exchange and Signature Schemes
1. Diffie-Hellman Key Exchange
2. Digital Signature Schemes
3. The Use of Hash Functions In Signature Schemes
4. The Digital Signature Algorithm
5. Schnorr Signatures
6. Nyberg-Rueppel Signatures
7. Authenticated Key Agreement
Chapter 15. Implementation Issues
1. Introduction
2. Exponentiation Algorithms
3. Exponentiation in RSA
4. Exponentiation in DSA
5. Multi-precision Arithmetic
6. Finite Field Arithmetic
Chapter 16. Obtaining Authentic Public Keys
1. Generalities on Digital Signatures
2. Digital Certificates and PKI
3. Example Applications of PKI
4. Other Applications of Trusted Third Parties
5. Implicit Certificates
6. Identity Based Cryptography
Part 4. Security Issues
Chapter 17. Attacks on Public Key Schemes
1. Introduction
2. Wiener's Attack on RSA
3. Lattices and Lattice Reduction
4. Lattice Based Attacks on RSA
5. Partial Key Exposure Attacks
6. Fault Analysis
Chapter 18. Definitions of Security
1. Security of Encryption
2. Security of Actual Encryption Algorithms
3. A Semantically Secure System
4. Security of Signatures
Chapter 19. Complexity Theoretic Approaches
1. Polynomial Complexity Classes
2. Knapsack-Based Cryptosystems
3. Bit Security
4. Random Self-reductions
5. Randomized Algorithms
Chapter 20. Provable Security: With Random Oracles
1. Introduction
2. Security of Signature Algorithms
3. Security of Encryption Algorithms
Chapter 21. Hybrid Encryption
1. Introduction
2. Security of Symmetric Ciphers
3. Hybrid Ciphers
4. Constructing KEMs
Chapter 22. Provable Security: Without Random Oracles
1. Introduction
2. The Strong RSA Assumption
3. Signature Schemes
4. Encryption Algorithms
Part 5. Advanced Protocols
Chapter 23. Secret Sharing Schemes
1. Introduction
2. Access Structures
3. General Secret Sharing
4. Reed-Solomon Codes
5. Shamir Secret Sharing
6. Application: Shared RSA Signature Generation
Chapter 24. Commitments and Oblivious Transfer
1. Introduction
2. Commitment Schemes
3. Oblivious Transfer
Chapter 25. Zero-Knowledge Proofs
1. Showing a Graph Isomorphism in Zero-Knowledge
2. Zero-Knowledge and NP
3. Sigma Protocols
4. An Electronic Voting System
Chapter 26. Secure Multi-Party Computation
1. Introduction
2. The Two-Party Case
3. The Multi-Party Case: Honest-but-Curious Adversaries
4. The Multi-Party Case: Malicious Adversaries
Appendix A. Basic Mathematical Terminology
1. Sets
2. Relations
3. Functions
4. Permutations
5. Operations
6. Groups
7. Rings
8. Fields
9. Vector Spaces
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