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Publisher:

Chapman & Hall/CRC

Publication Date:

2008

Number of Pages:

534

Format:

Hardcover

Series:

Chapman & Hall/CRC Cryptography and Network Security

Price:

79.95

ISBN:

9781584885511

Category:

Textbook

[Reviewed by , on ]

Donald L. Vestal

06/13/2008

In the information age, one of the most common applications of mathematics is cryptography. Throughout the twentieth century, mathematicians tried to develop a cogent theory to explain the various encryption schemes and try to measure their security. This book gives a nice overview of this theory. It mentions some of the history and presents the mathematical ideas in a precise manner.

The topics covered include: the key principles that an encryption scheme should satisfy as well as attack scenarios that they should survive, Shannon’s Theorem on perfect secrecy, Computationally-Secure Encryption, the use of pseudorandom functions to create CPA-Secure Encryption Schemes, creating Secure Message Authentication Codes and collision resistant hash functions (including the Markle-Damgård transform), combining encryption and authentication, design principles for constructing (modern) block ciphers, the theory behind the constructing pseudorandom objects, primality testing and implications for the RSA system, discrete logarithms and Diffie-Hellman problems, elliptic curve groups, algorithms for factoring (Pollard’s p–1 method, Pollard’s rho method, and the Quadratic Sieve, algorithms for computing discrete logarithms (the baby-step/giant-step method and the Pohlig-Hellman algorithm) , management and distribution of private keys, the Diffie-Hellman key exchange, Public-Key Encryption (including the issue of security), combinations of public- and private-key schemes, the RSA and El Gamal Encryption schemes, the use of trapdoor permutations, other Public-Key Encryption schemes (the Goldwasser-Micali scheme, the Rabin scheme, and the Paillier scheme), digital signatures , digital certificates, message integrity, and the Random Oracle Model in validating cryptographic schemes.

The book contains enough information to serve as a textbook for an undergraduate course as well as a graduate course. Also, since the authors intend for the material to be mathematically rigorous, appendices with appropriate mathematical background are included. Each chapter ends with a collection of exercises and a list of 149 references is included. If I could change one thing, it would be this; the authors use many acronyms (such as CPA for “chosen plaintext attack”), and while there is a list of common notation just before the appendices, not all terms are included. I think a more complete list might have been handy .

However, 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 is an Assistant Professor of Mathematics at South Dakota State University. His interests include number theory, combinatorics, spending time with his family, and working on his hot sauce collection. He can be reached at Donald.Vestal(AT)sdstate.edu.

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

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