Cryptography plays a key role in ensuring the privacy and integrity of data and the security of computer networks. Introduction to Modern Cryptography provides a rigorous yet accessible treatment of modern cryptography, with a focus on formal definitions, precise assumptions, and rigorous proofs.
The authors introduce the core principles of modern cryptography, including the modern, computational approach to security that overcomes the limitations of perfect secrecy. An extensive treatment of private-key encryption and message authentication follows. The authors also illustrate design principles for block ciphers, such as the Data Encryption Standard (DES) and the Advanced Encryption Standard (AES), and present provably secure constructions of block ciphers from lower-level primitives. The second half of the book focuses on public-key cryptography, beginning with a self-contained introduction to the number theory needed to understand the RSA, Diffie-Hellman, El Gamal, and other cryptosystems. After exploring public-key encryption and digital signatures, the book concludes with a discussion of the random oracle model and its applications.
Serving as a textbook, a reference, or for self-study, Introduction to Modern Cryptography presents the necessary tools to fully understand this fascinating subject.
INTRODUCTION AND CLASSICAL CRYPTOGRAPHY INTRODUCTION Cryptography and Modern Cryptography The Setting of Private-Key Encryption Historical Ciphers and Their Cryptanalysis The Basic Principles of Modern Cryptography
PERFECTLY SECRET ENCRYPTION Definitions and Basic Properties The One-Time Pad (Vernam's Cipher)
Limitations of Perfect Secrecy Shannon's Theorem Summary
PRIVATE-KEY (SYMMETRIC) CRYPTOGRAPHY PRIVATE-KEY ENCRYPTION AND PSEUDORANDOMNESS A Computational Approach to Cryptography A Definition of Computationally Secure Encryption Pseudorandomness Constructing Secure Encryption Schemes Security against Chosen-Plaintext Attacks (CPA)
Constructing CPA-Secure Encryption Schemes Security against Chosen-Ciphertext Attacks (CCA)
MESSAGE AUTHENTICATION CODES AND COLLISION-RESISTANT HASH FUNCTIONS Secure Communication and Message Integrity Encryption vs. Message Authentication Message Authentication Codes-Definitions Constructing Secure Message Authentication Codes CBC-MAC Collision-Resistant Hash Functions NMAC and HMAC Constructing CCA-Secure Encryption Schemes Obtaining Privacy and Message Authentication
PRACTICAL CONSTRUCTIONS OF PSEUDORANDOM PERMUTATIONS (BLOCK CIPHERS)
Substitution-Permutation Networks Feistel Networks The Data Encryption Standard (DES)
Increasing the Key Size of a Block Cipher The Advanced Encryption Standard (AES)
Differential and Linear Cryptanalysis-A Brief Look
THEORETICAL CONSTRUCTIONS OF PSEUDORANDOM OBJECTS One-Way Functions Overview: From One-Way Functions to Pseudorandomness A Hard-Core Predicate for Any One-Way Function Constructing Pseudorandom Generators Constructing Pseudorandom Functions Constructing (Strong) Pseudorandom Permutations Necessary Assumptions for Private-Key Cryptography A Digression-Computational Indistinguishability
PUBLIC-KEY (ASYMMETRIC) CRYPTOGRAPHY NUMBER THEORY AND CRYPTOGRAPHIC HARDNESS ASSUMPTIONS Preliminaries and Basic Group Theory Primes, Factoring, and RSA Assumptions in Cyclic Groups Cryptographic Applications of Number-Theoretic Assumptions
FACTORING AND COMPUTING DISCRETE LOGARITHMS Algorithms for Factoring Algorithms for Computing Discrete Logarithms
PRIVATE-KEY MANAGEMENT AND THE PUBLIC-KEY REVOLUTION Limitations of Private-Key Cryptography A Partial Solution-Key Distribution Centers The Public-Key Revolution Diffie-Hellman Key Exchange
PUBLIC-KEY ENCRYPTION Public-Key Encryption-An Overview Definitions Hybrid Encryption RSA Encryption The El Gamal Encryption Scheme Security against CCA Trapdoor Permutations
ADDITIONAL PUBLIC-KEY ENCRYPTION SCHEMES The Goldwasser-Micali Encryption Scheme The Rabin Encryption Scheme The Paillier Encryption Scheme
DIGITAL SIGNATURE SCHEMES Digital Signatures-An Overview Definitions RSA Signatures The Hash-and-Sign Paradigm Lamport's One-Time Signature Scheme Signatures from Collision-Resistant Hashing The Digital Signature Standard Certificates and Public-Key Infrastructures
PUBLIC-KEY CRYPTOSYSTEMS IN THE RANDOM ORACLE MODEL The Random Oracle Methodology Public-Key Encryption in the Random Oracle Model Signatures in the Random Oracle Model
APPENDIX A: MATHEMATICAL BACKGROUND Identities and Inequalities Asymptotic Notation Basic Probability The Birthday Problem
APPENDIX B: SUPPLEMENTARY ALGORITHMIC NUMBER THEORY Integer Arithmetic Modular Arithmetic Finding a Generator of a Cyclic Group
Each chapter contains References, Additional Reading, and Exercises.