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Codes: The Guide to Secrecy from Ancient to Modern Times

Richard A. Mollin
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
Tom Shulte
, on
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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