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.