Introduction to Modern Cryptography

摘要: Preface I. Introduction and Classical Cryptography Modern The Setting of Private-Key Encryption Historical Ciphers Their Cryptanalysis Principles Principle 1 - Formal Definitions 2 Precise Assumptions 3 Proofs Security Provable Real-World References Additional Reading Exercises Perfectly Secret One-Time Pad Limitations Perfect Secrecy Shannon's Theorem II. (Symmetric) Computational Concrete Approach Asymptotic Defining Computationally Secure Basic Definition Semantic Constructing Schemes Pseudorandom Generators Stream by Reduction A Fixed-Length Scheme Stronger Notions for Multiple Encryptions Chosen-Plaintext Attacks CPA-Security CPA-Secure Functions Block from Modes Operation Stream-Cipher Block-Cipher Chosen-Ciphertext CCA-Security Padding-Oracle Message Authentication Codes Integrity vs. MAC Domain Extension MACs CBC-MAC Construction Proof Authenticated Generic Constructions Communication Sessions CCA-Secure Information-Theoretic on Hash Applications Collision Resistance Weaker Extension: Merkle-Damgard Transform Using Hash-and-MAC HMAC Birthday Finding Collisions Small-Space Time/Space Tradeoffs Inverting Random-Oracle Model in Detail Is the Methodology Sound? Fingerprinting Deduplication Merkle Trees Password Hashing Key Derivation Commitment Practical Symmetric-Key Primitives Linear-Feedback Shift Registers Adding Nonlinearity Trivium RC4 Substitution-Permutation Networks Feistel DES Data Standard 3DES: Increasing Length a Cipher AES Advanced Differential Linear MD5 SHA-0, SHA-1, SHA-2 SHA-3 (Keccak) Theoretical One-Way Candidate Hard-Core Predicates From to Pseudorandomness Simple Case More Involved Full with Minimal Expansion Factor (Strong) Permutations Indistinguishability III. Public-Key (Asymmetric) Number Theory Cryptographic Hardness Preliminaries Group Primes Divisibility Modular Arithmetic Groups ZN Isomorphisms Chinese Remainder Primes, Factoring, RSA Generating Random Primality Testing Factoring Assumption Relating Cyclic Discrete-Logarithm/Diffie-Hellman Working (Subgroups of) Zp Elliptic Curves Collision-Resistant Algorithms Computing Discrete Logarithms Pollard's p Algorithm Rho Quadratic Sieve Pohlig-Hellman Baby-Step/Giant-Step Index Calculus Recommended Lengths Management Revolution Distribution Partial Solution: Key-Distribution Centers Exchange Diffie-Hellman Protocol An Overview against Hybrid KEM/DEM Paradigm CDH/DDH-Based El Gamal DDH-Based Encapsulation CDH-Based KEM DHIES/ECIES Plain Padded PKCS #1 v1.5 without Oracles OAEP v Implementation Issues Pitfalls Digital Signature Signatures Hash-and-Sign RSA-FDH Discrete-Logarithm Problem Schnorr DSA ECDSA Lamport's Chain-Based Tree-Based Certificates Infrastructures Putting It All Together SSL/TLS Signcryption Topics Trapdoor Paillier Structure ZN2 Homomorphic Sharing Threshold Verifiable Electronic Voting Goldwasser-Micali Residues Modulo Prime Composite Residuosity Rabin Square Roots Permutation Based Common Notation Appendix A: Mathematical Background Identities Inequalities Probability "Birthday" Finite Fields B: Algorithmic Integer Operations Euclidean Extended Inverses Exponentiation Montgomery Multiplication Choosing Uniform Element Generator Group-Theoretic Efficient