Introduction to cryptography: principles and applications

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.