Joy of Factoring

This book is about the theory and practice of integer factorisation presented in a historic perspective. It describes about twenty algorithms for factoring and a dozen other number theory algorithms that support the factoring algorithms. Most algorithms are described both in words and in pseudocode to satisfy both number theorists and computer scientists. Each of the ten chapters begins with a concise summary of its contents. The book starts with a general explanation of why factoring integers is important. The next two chapters present number theory results that are relevant to factoring. Further on there is a chapter discussing, in particular, mechanical and electronic devices for factoring, as well as factoring using quantum physics and DNA molecules. Another chapter applies factoring to breaking certain cryptographic algorithms. Yet another chapter is devoted to practical vs. theoretical aspects of factoring. The book contains more than 100 examples illustrating various algorithms and theorems. It also contains more than 100 interesting exercises to test the reader's understanding. Hints or answers are given for about a third of the exercises. The book concludes with a dozen suggestions of possible new methods for factoring integers. This book is written for readers who want to learn more about the best methods of factoring integers, many reasons for factoring, and some history of this fascinating subject. It can be read by anyone who has taken a first course in number theory.

It is, I think, a fairly safe bet that most students learning about factoring do not instinctively view the subject as having anything whatsoever to do with 'joy'. ... [B]y contrast, most people (even many math students) equate factoring with tedium. Consequently, anybody setting out to write a book entitled The Joy of Factoring is automatically faced with a double objective. The author must not only teach the reader something about factoring, but must also explain why anybody should care. The book under review succeeds on both counts. ... I think a second course in number theory, or senior seminar, based on this book would be quite interesting. ... The book could also be used as a text for an upper-level course in computer science for students with some background in number theory. It also certainly belongs in any good university library, if only because the material collected in it is not (to my knowledge at any rate) readily available in the textbook literature." - Mark Hunacek, MAA Reviews"This work is a pleasure to read; it is a must for anyone interested in numbers, programming, and codes. The extensive bibliography gives readers direction and the tools to quickly delve deeper into the field. ... Highly recommended." - CHOICE

Samuel S. Wagstaff, Jr., Purdue University, West Lafayette, IN, USA