Introduction to Modern Cryptography: Principles and Protocols

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Features

  • Includes formal definitions, precise assumptions, and rigorous proofs
  • Discusses many widely used cryptographic algorithms and standards
  • Covers topics, such as pseudorandom generators/functions, Paillier encryption, and the random oracle model, often not found in other texts
  • Contains suggestions for further reading as well as numerous exercises at the end of each chapter
  • Assumes minimal prerequisites-all necessary mathematical background is included in the text
  • Summary

    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.

    Table of Contents

    PREFACE

    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

    INDEX

    Each chapter contains References, Additional Reading, and Exercises.

    Editorial Reviews

    This book is a comprehensive, rigorous introduction to what the authors name ‘modern’ cryptography … a novel approach to how cryptography is taught, replacing the older, construction-based approach. … The concepts are clearly stated, both in an intuitive fashion and formally. … I would heartily recommend this book to anyone who is interested in cryptography. … the exercises are challenging and interesting, and can benefit readers of all academic levels. …
    —IACR book reviews, January 2010

    Over the past 30 years, cryptography has been transformed from a mysterious art into a mathematically rigorous science. The textbook by Jonathan Katz and Yehuda Lindell finally makes this modern approach to cryptography accessible to a broad audience. Readers of this text will learn how to think precisely about the security of protocols against arbitrary attacks, a skill that will remain relevant and useful regardless of how technology and cryptography standards change. The book uses just enough formalism to maintain precision and rigor without obscuring the development of ideas. It manages to convey both the theory's conceptual beauty and its relevance to practice. I plan to use it every time I teach an undergraduate course in cryptography.
    —Salil Vadhan, Harvard University, Cambridge, Massachusetts, USA

    … the greatest attribute is the fact that the material is presented in such a unified way. These are not just a collection of topics from cryptography, thrown together at random. One topic leads effortlessly to the next. As such, this is a virtually indispensible resource for modern cryptography.
    —Donald L. Vestal, South Dakota State University, MAA Online, July 2008

    … gives an excellent introduction to the theoretical background of cryptography. It would be a fine textbook for an advanced undergraduate (or graduate) course in theoretical computer science for students who have already seen the rudiments of cryptography. It will be a valuable reference for researchers in the field …
    —Steven D. Galbraith, Mathematical Reviews, 2009b

    The book is highly recommended as a textbook in cryptography courses at graduate or advanced undergraduate levels … covers in a splendid way the main notions of current cryptography from the point of view of information-theoretical security. This corresponds indeed to a modern cryptography approach.
    —Guillermo Morales-Luna, Zentralblatt MATH, Vol. 1143