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Publisher:

Chapman & Hall/CRC

Publication Date:

2006

Number of Pages:

593

Format:

Hardcover

Edition:

3

Series:

Discrete Mathematics and Its Applications 36

Price:

69.95

ISBN:

1-58488-508-4

Category:

Textbook

The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by , on ]

Darren Glass

05/2/2006

Cryptography is a large and ever growing subject, which at times feels like a branch of mathematics, at times feels like a branch of computer science, and often involves bringing in questions of politics, marketing, business, and (since we are on the verge, or at least on the verge of being on the verge, of quantum cryptography) physics. Books in this area are therefore required to choose their target audience very carefully, trying to decide exactly which aspects to cover and what background they may assume, and they need to walk a fine line in order to be both useful and readable. Douglas Stinson's book *Cryptography: Theory and Practice* has walked that line well for more than a decade. It might not be as practical as some programmers would like or as rigorously theoretical as some mathematicians would like, but for most people who are between those two extremes this book does an excellent job.

The first edition of Stinson's book came out in 1995 and quickly became a mainstay on the syllabi of the cryptography courses that were starting to pop up in math and computer science departments around the globe (including, I should add for reasons of full disclosure, the course that I took at the University of Pennsylvania in 1998). The second edition, released in 2002, scaled back the scope of the book quite significantly, as the author intended to write a second volume to supplement the main book.

The third edition, released last year, once again expands the scope of the book and includes far more topics than one could include in a single course. Those topics include full chapters on Block Ciphers, Hash Functions, RSA Cryptosystems, ElGamal Cryptosystems, Signature Schemes, Pseudo-random Number Generators, Entity Authentication, Key Distribution, Secret Sharing Schemes, and Multicast Security as well as several other topics. (A full table of contents can be found above). Many of these are serious topics, and they are treated at a serious level. In order to discuss them well, Stinson spends a significant amount of time introducing ideas from mathematics that computer scientists may not know and ideas from computer science that mathematicians may not know, including some number theory, some probability theory, some information theory, and some of the theory of elliptic curves. In the process of doing so, he inevitably oversimplifies many of these topics, but he does as good a job as one could expect given the context, and the bibliography points the reader to many sources where they can get deeper information on these topics.

This book is extremely well written, and gets better with each passing edition. There are certainly easier introductions to cryptography available, and this would not be the first book I would recommend to an undergraduate student who was interested in the topic, but the clear exposition and large number of exercises would make the book a good choice for either a graduate level course or for a researcher who is interested in learning more about the field of cryptography to peruse. For a book that covers this quantity and depth of material I cannot imagine a better choice.

Darren Glass (dglass@gettysburg.edu) is an Assistant Professor at Gettysburg College.

CLASSICAL CRYPTOGRAPHY

Introduction: Some Simple Cryptosystems

Cryptanalysis

Notes

Exercises

SHANNON'S THEORY

Introduction

Elementary Probability Theory

Perfect Secrecy

Entropy

Properties of Entropy

Spurious Keys and Unicity Distance

Product Cryptosystems

Notes

Exercises

BLOCK CIPHERS AND THE ADVANCED ENCRYPTION STANDARD

Introduction

Substitution-Permutation Networks

Linear Cryptanalysis

Differential Cryptanalysis

The Data Encryption Standard

The Advanced Encryption Standard

Modes of Operation

Notes and References

Exercises

CRYPTOGRAPHIC HASH FUNCTIONS

Hash Functions and Data Integrity

Security of Hash Functions

Iterated Hash Functions

Message Authentication Codes

Unconditionally Secure MACs

Notes and References

Exercises

THE RSA CRYPTOSYSTEM AND FACTORING INTEGERS

Introduction to Public-key Cryptography

More Number Theory

The RSA Cryptosystem

Primality Testing

Square Roots Modulo n

Factoring Algorithms

Other Attacks on RSA

The Rabin Cryptosystem

Semantic Security of RSA

Notes and References

Exercises

PUBLIC-KEY CRYPTOGRAPHY AND DISCRETE LOGARITHMS

The ElGamal Cryptosystem

Algorithms for the Discrete Logarithm Problem

Lower Bounds on the Complexity of Generic Algorithms

Finite Fields

Elliptic Curves

Discrete Logarithm Algorithms in Practice

Security of ElGamal Systems

Notes and References

Exercises

SIGNATURE SCHEMES

Introduction

Security Requirements for Signature Schemes

The ElGamal Signature Scheme

Variants of the ElGamal Signature Scheme

Provably Secure Signature Schemes

Undeniable Signatures

Fail-stop Signatures

Notes and References

Exercises

PSEUDO-RANDOM NUMBER GENERATION

Introduction and Examples

Indistinguishability of Probability Distributions

The Blum-Blum-Shub Generator

Probabilistic Encryption

Notes and References

Exercises

IDENTIFICATION SCHEMES AND ENTITY AUTHENTICATION

Introduction

Challenge-and-Response in the Secret-Key Setting

Challenge-and-Response in the Public-Key Setting

The Schnorr Identification Scheme

The Okamoto Identification Scheme

The Guillou-Quisquater Identification Scheme

Notes and References

Exercises

KEY DISTRIBUTION

Introduction

Diffie-Hellman Key Predistribution

Unconditionally Secure Key Predistribution

Key Distribution Patterns

Session Key Distribution Schemes

Notes and References

Exercises

KEY AGREEMENT SCHEMES

Introduction

Diffie-Hellman Key Agreement

MTI Key Agreement Schemes

Key Agreement Using Self-Certifying Keys

Encrypted Key Exchange

Conference Key Agreement Schemes

Notes and References

Exercises

PUBLIC-KEY INFRASTRUCTURE

Introduction: What is a PKI?

Certificates

Trust Models

The Future of PKI?

Identity-Based Cryptography

Notes and References

Exercises

SECRET SHARING SCHEMES

Introduction: The Shamir Threshold Scheme

Access Structures and General Secret Sharing

Information Rate and Construction of Efficient Schemes

Notes and References

Exercises

MULTICAST SECURITY AND COPYRIGHT PROTECTION

Introduction to Multicast Security

Broadcast Encryption

Multicast Re-Keying

Copyright Protection

Tracing Illegally Redistributed Keys

Notes and References

Exercises

FURTHER READING

BIBLIOGRAPHY

INDEX

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