Introduction to cryptography : principles and applications / Hans Delfs, Helmut Knebl.

Includes bibliographical references (pages 483-499) and index.

Chapter 1. Introduction. 1.1. Encryption and secrecy ; 1.2. The objectives of cryptography ; 1.3. Attacks ; 1.4. Cryptographic protocols ; 1.5. Provable security -- Chapter 2. Symmetric-key cryptography. 2.1. Symmetric-key encryption. 2.1.1. Stream ciphers ; 2.1.2. Block ciphers ; 2.1.3. DES ; 2.1.4. AES ; 2.1.5. Modes of operation ; 2.2. Cryptographic hash functions. 2.2.1. Security requirements for hash functions ; 2.2.2. Construction of hash functions ; 2.2.3. Data integrity and message authentication ; 2.2.4. Hash functions as random functions -- Chapter 3. Public-key cryptography. 3.1. The concept of public-key cryptography ; 3.2. Modular arithmetic. 3.2.1. The integers ; 3.2.2. The integers modulo n ; 3.3. RSA. 3.3.1. Key generation and encryption ; 3.3.2. Attacks against RSA encryption ; 3.3.3. Probabilistic RSA encryption ; 3.3.4. Digital signatures - the basic scheme ; 3.3.5. Signatures with has functions ; 3.4. The discrete logarithm. 3.4.1. ElGamal encryption ; 3.4.2. ElGamal signatures ; 3.4.3. Digital signature algorithm, ; 3.4.4. ElGamal encryption in a prime-order subgroup ; 3.5. Modular squaring. 3.5.1. Rabin's encryption ; 3.5.2. Rabin's signature scheme ; 3.6. Homomorphic encryption algorithms. 3.6.1. ElGamal encryption ; 3.6.2. Paillier encryption ; 3.6.3. Re-encryption of ciphertexts ; 3.7. Elliptic curve cryptography. 3.7.1. Selecting the curve and the base point ; 3.7.2. Diffie-Hellman key exchange ; 3.7.3. ElGamal encryption ; 3.7.4. Elliptic curve digital signature algorithm -- Chapter 4. Cryptographic protocols. 4.1. Key exchange and entity authentication. 4.1.1. Kerberos ; 4.1.2. Diffie-Hellman key agreement ; 4.1.3. Key exchange and mutual authentication ; 4.1.4. Station-to-station protocol ; 4.1.5. Public-key management techniques ; 4.2. Identification schemes. 4.2.1. Interactive proof systems ; 4.2.2. Simplified Fiat-Shamir identification scheme ; 4.2.3. Zero-knowledge ; 4.2.4. Fiat-Shamir identification scheme ; 4.2.5. Fiat-Shamir signature scheme ; 4.4. Secret sharing ; 4.5. Verifiable electronic elections. 4.5.1. A multi-authority election scheme ; 4.5.2. Proofs of knowledge ; 4.5.3. Non-interactive proofs of knowledge ; 4.5.4. Extension to multi-way elections ; 4.5.5. Eliminating the trusted center ; 4.6. Mix net and shuffles. 4.6.1. Decryption mix nets ; 4.6.2. Re-encryption mix nets ; 4.6.3. Proving knowledge of the plaintext ; 4.6.4. Zero-knowledge proofs of shuffles ; 4.7. Receipt-free and coercion-resistant elections. 4.7.1. Receipt-freeness by randomized re-encryption ; 4.7.2. A coercion-resistant protocol ; 4.8. Digital cash. 4.8.1. Blindly issues proofs ; 4.8.2. A fair electronic cash system ; 4.8.3. Underlying problems -- Chapter 5. Probabilistic algorithms. 5.1. Coin-tossing algorithms ; 5.2. Monte Carlo and Las Vegas algorithms -- Chapter 6. One-way functions and the basic assumptions. 6.1. A notation for probabilities ; 6.2. Discrete exponential functions ; 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 -- Chapter 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 -- Chapter 8. One-way functions and pseudorandomness. 8.1. Computationally perfect pseudorandom bit generators ; 8.2. Yao's theorem -- Chapter 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. Passive eavesdroppers ; 9.5. Chosen-ciphertext attacks. 9.5.1. A security proof in the random oracle model ; 9.5.2. Security under standard assumptions -- Chapter 10. Unconditional security of cryptosystems. 10.1. The bounded storage model ; 10.2. The noisy channel model ; 10.3. Unconditionally secure message authentication. 10.3.1. Almost universal classes of hash functions ; 10.3.2. Message authentication with universal hash families ; 10.3.3. Authenticating multiple messages ; 10.4. Collision entropy and privacy amplification. 10.4.1. Rényi entropy ; 10.4.2. Privacy amplification ; 10.4.3. Extraction of a secret key ; 10.5. Quantum key distribution. 10.5.1. Quantum bits and quantum measurements ; 10.5.2. The BB84 protocol ; 10.5.3. Estimation of the error rate ; 10.5.4. Intercept-and-resend attacks ; 10.5.5. Information reconciliation ; 10.5.6. Exchanging a secure key - an example ; 10.5.7. General attacks and security proofs -- Chapter 11. Provably secure digital signatures. 11.1. Attacks and levels of security ; 11.2. Claw-free pairs and collision-resistant hash functions ; 11.3. Authentication-tree-based signatures ; 11.4. A state-free signature scheme -- Appendix 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. Polynomials and finite fields. A.5.1. The ring of polynomials ; A.5.2. Residue class rings ; A.6. Solving quadratic equations in binary fields ; A.7. Quadratic residues ; A.8. Modular square roots ; A.9. The group Zn2 ; A.10. Primes and primality tests ; A.11. Elliptic curves. A.11.1. Plane curves ; A.11.2. Normal forms of elliptic curves ; A.11.3. Point addition on elliptic curves ; A.11.4. Group order and group structure of elliptic curves -- Appendix B. Probabilities and information theory. B.1. Finite probability spaces and random variables ; B.2. Some useful and important inequalities ; B.3. The weak law of large numbers ; B.4. Distance measures ; B.5. Basic concepts of information theory.

The first part of 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. In the second edition the authors added a complete description of the AES, an extended section on cryptographic hash functions, and new sections on random oracle proofs and public-key encryption schemes that are provably secure against adaptively-chosen-ciphertext attacks. The third edition is a further substantive extension, with new topics added, including: elliptic curve cryptography; Paillier encryption; quantum cryptography; the new SHA-3 standard for cryptographic hash functions; a considerably extended section on electronic elections and Internet voting; mix nets; and zero-knowledge proofs of shuffles. The book is appropriate for undergraduate and graduate students in computer science, mathematics, and engineering.