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Introduction to Modern Cryptography
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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.

About the Author

University of Maryland, College Park, USA Bar-Ilan University, Ramat Gan, Israel

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

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