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Publisher:

Chapman & Hall/CRC

Publication Date:

2005

Number of Pages:

679

Format:

Hardcover

Series:

Discrete Mathematics and Its Applications

Price:

79.95

ISBN:

1-58488-470-3

Category:

Textbook

[Reviewed by , on ]

Tom Shulte

12/28/2005

Mollin's thick tome (679 pages) tells the story of codes and code breaking from antiquity to the future. It is full of engaging detail on the many personalities that have been drawn to this branch of applied mathematics. Did you know Elizabeth Friedman, wife of founding NSA cryptologist William Friedman, got her own start in cryptanalysis breaking the codes of Depression-era rum runners? There are enough such historical tangents that one can get a good feel for the human story of cryptology from Caesar's classic cipher to the promise of quantum cryptology without skipping over much mathematics. Further reaches are probed with the rather judicious use of footnotes, which sometimes seem a bit unnecessary, such as footnotes to explain "scam" and "to boot" a computer.

Obviously, Mollin means to be complete and accessible, and there is nothing wrong with that. Over 30% of the book is supporting material, including appendices to support all mathematics covered and exercises not only for the chapters, but for the appendixes as well. Thus, this book is a self-contained guide to the subject covering material from basic arithmetic to the foundations of group theory and probability. I would say it aims at the university level but is accessible to serious high school math students. Among books at this level, this one stands out for some of its vivid examples. Particularly enlightening is the discussion of quantum computing: rather than merely touching on the subject, Mollin provides a particularly illustrative and detailed example.

There is plenty here to satisfy the detail-oriented. Such encrypting processes as Advanced Encryption Standard (AES), the Secure Electronic Transaction, and more get a thorough analysis as to methodology, strengths and weaknesses. Mollin also places the application of cryptology in context. Of course, in this day and age, that largely means the Internet and its many opportunities for information to be compromised. So after antique techniques, he discusses symmetric- and public-key cryptography and how the Internet was made more secure, examining protocols from SSL to electronic voting. He also covers message authentication, e-mail security, wireless security, and securing networks. Straying from ways to strive for secrecy but largely exploring applications of the same mathematics, Mollin also devotes two chapters on such topics as information theory and coding, viruses and their ilk, and legal issues. About a dozen pages are dedicated to discussing exactly what a "hacker" is and who were the first wave, second wave and so on.

Tom Schulte is in graduate studies in mathematics at Oakland University (Rochester, MI). He just survived Abstract Algebra and is looking forward to Coding Theory in the spring. When finding the wonder in numbers, he broadcasts on Oakland University's college radio station at wxou.org.

Preface

FROM THE RIDDLES OF ANCIENT EGYPT TO CRYPTOGRAPHY IN THE RENAISSANCE-3,500 YEARS IN THE MAKING

Antiquity-From Phaistos

Cryptography in Classical Literature

The Middle Ages

Cryptology and the Arabs

Rise of the West

FROM SIXTEENTH-CENTURY CRYPTOGRAPHY TO THE NEW MILLENNIUM-THE LAST 500 YEARS

Three Post-Renaissance Centuries

The American Colonies

Nineteenth-Century Cryptography

Two World Wars

The Post War Era and the Future

SYMMETRIC-KEY CRYPTOGRAPHY

Block Ciphers and DES

S-DES and DES

Modes of Operation

Blowfish

The Advanced Encryption Standard

Stream Ciphers

RC4

PUBLIC-KEY CRYPTOGRAPHY

The Ideas Behind PKC

RSA

Digital Signatures

ElGamal

CRYPTOGRAPHIC PROTOCOLS

Introduction

Keys

Identification

Commitment

Secret Sharing

Electronic Voting

Protocol Layers and SSL

Digital Cash Schemes

KEY MANAGEMENT

Authentication, Exchange, and Distribution

Public-Key Infrastructure (PKI)

Secure Electronic Transaction (SET)

MESSAGE AUTHENTICATION

Authentication Functions

Message Authentication Codes

Encryption Functions

Authentication Applications

ELECTRONIC MAIL AND INTERNET SECURITY

Pretty Good Privacy (PGP)

S/MIME and PGP

IPSec

Internetworking and Security-Firewalls

Client-Server Model and Cookies

History of the Internet and the WWW

APPLICATIONS AND THE FUTURE

Login and Network Security

Wireless Security

Smart Cards

Biometrics

Quantum Cryptography

Nuclear Test Ban Treaty Compliance

NON-CRYPTOGRAPHIC SECURITY ISSUES

Cybercrime

Hackers

Viruses and Other Infections

Legal Matters and Controversy

INFORMATION THEORY AND CODING

Shannon

Entropy

Huffman Codes

Information Theory of Cryptosystems

Error-Correcting Codes

APPENDIX A: MATHEMATICAL FACTS

Sets, Relations, and Functions

Basic Arithmetic

Modular Arithmetic

Groups, Fields, Modules, and Rings

Vector Spaces

Basic Matrix Theory

Continued Fractions

Elliptic Curves

Complexity

APPENDIX B: PSEUDO-RANDOM NUMBER GENERATION

ANSI X9.17

The Blum-Blum-Shub-(BBS) PRNG

APPENDIX C: FACTORING LARGE INTEGERS

Classical Factorization Methods

The Continued Fraction Algorithm

Pollard's p-1 Algorithm

Pollard's Rho-Method

The Quadratic Sieve (QS)

Multipolynomial Quadratic Sieve (MPQS)

The Elliptic Curve Method (ECM)

The General Number Field Sieve

APPENDIX D: TECHNICAL AND ADVANCED DETAILS

AES

Silver-Pohlig-Hellman

Baby-Step Giant-Step Algorithm

Index-Calculus Algorithm

Brands' Digital Cash Scheme

Radix-64 Encoding

APPENDIX E: PROBABILITY THEORY

Basic Probability

Randomness, Expectation, and Variance

Binomial Distribution

The Law of Large Numbers

Probability and Error Detection

APPENDIX F: RECOGNIZING PRIMES

Primality and Compositeness Tests

Miller-Selfridge-Rabin

Primes is in P

Generation of Random Primes

Decision Problem or Primality Test?

APPENDIX G: EXERCISES

BIBLIOGRAPHY

LIST OF SYMBOLS

INDEX

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