Introduction to cryptography : principles and applications

Includes index

Includes bibliography (p. 297-304) and references

1. Introduction 1.1 Encryption and Secrecy 1.2 The Objectives of Cryptography 1.3 Attacks 1.4 Cryptographic Protocols 1.5 Provable Security 2. Symmetric-Key Encryption 2.1 Stream Ciphers 2.2 Block Ciphers 3. Public-Key Cryptography 3.1 The Concept of Public-Key Cryptography 3.2 Modular Arithmetic 3.3 RSA 3.4 Hash Functions 3.5 The Discrete Logarithm 3.6 Modular Squaring 4. Cryptographic Protocols 4.1 Key Exchange and Entity Authentication 4.2 Identification Schemes 4.3 Commitment Schemes 4.4 Electronic Elections 4.5 Digital Cash 5. Probabilistic Algorithms 5.1 Coin-Tossing Algorithms 5.2 Monte Carlo and Las Vegas Algorithms 6. One-Way Functions and the Basic Assumptions 6.1 A Notation for Probabilities 6.2 Discrete Exponential Function 6.3 Uniform Sampling Algorithms 6.4 Modular Powers 6.5 Modular Squaring 6.6 Quadratic Residuosity Property 6.7 Formal Definition of One-Way Functions 6.8 Hard-Core Predicates 7. Bit Security of One-Way Functions 7.1 Bit Security of the Exp Family 7.2 Bit Security of the RSA Family 7.3 Bit Security of the Square Family 8. One-Way Functions and Pseudorandomness 8.1 Computationally Perfect Pseudorandom Bit Generators 8.2 Yao’s Theorem 9. Provably Secure Encryption 9.1 Classical Information-Theoretic Security 9.2 Perfect Secrecy and Probabilistic Attacks 9.3 Public-Key One-Time Pads 9.4 Computationally Secret Encryption Schemes 9.5 Unconditional Security of Cryptosystems 10. Provably Secure Digital Signatures 10.1 Attacks and Levels of Security 10.2 Claw-Free Pairs and Collision-Resistant Hash Functions 10.3 Authentication-Tree-Based Signatures 10.4 A State-Free Signature Scheme A. Algebra and Number Theory A.1 The Integers A.2 Residues A.3 The Chinese Remainder Theorem A.4 Primitive Roots and the Discrete Logarithm A.5 Quadratic Residues A.6 Modular Square Roots A.7 Primes and Primality Tests B. Probabilities and Information Theory B.1 Finite Probability Spaces and Random Variables B.2 The Weak Law of Large Numbers B.3 Distance Measures B.4 Basic Concepts of Information Theory References.

In the first part, this book covers the key concepts of cryptography on an undergraduate level, from encryption and digital signatures to cryptographic protocols. Essential techniques are demonstrated in protocols for key exchange, user identification, electronic elections and digital cash. In the second part, more advanced topics are addressed, such as the bit security of one-way functions and computationally perfect pseudorandom bit generators. The security of cryptographic schemes is a central topic. Typical examples of provably secure encryption and signature schemes and their security proofs are given. Though particular attention is given to the mathematical foundations, no special background in mathematics is presumed. The necessary algebra, number theory and probability theory are included in the appendix. Each chapter closes with a collection of exercises.