Product Description

The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, that have been at the center of interest in applications of number theory, particularly in cryptography. No background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasizing estimates of the efficiency of the techniques that arise from the theory. A special feature is the inclusion of recent application of the theory of elliptic curves. Extensive exercises and careful answers have been included in all of the chapters. Because number theory and cryptography are fast-moving fields, this new edition contains substantial revisions and updated references.

Product Details

• Amazon Sales Rank: #298230 in Books
• Published on: 1994-09-02
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 235 pages

Customer Reviews

Cryptographer's toolbox
Two areas of this book deserve special mention. The first chapter develops a careful treatment of the _exact_ bit complexity of operations on numbers, such as +,-,*,/, modular powering, and gcd. While other books give crude estimates, or leave out such details entirely, Koblitz invests a good deal of time not only in giving the number of operations, but in teaching the reader how to make his own estimates. *Highly* useful.

Second, the book contains a concise introduction to modern factoring algorithms. After a discussion of primality testing, it goes on to develop the notion of a "B-smooth" number and then show how this leads to algorithms which use factor bases. Examples are given in the text, and the reasons behind that funny-looking time estimate O(e^(c*sqrt(log n log log n)) are provided. Seriously good stuff.

The exercises are also first rate - fun, intriguing, and serve to teach new ideas (not just test knowledge of the chapter).

In parts it shows its age (1994); for example, the Chor-Rivest knapsack described on p.115 has been broken by Serge Vaudenay. Much more discussion of randomized cryptography would also have been nice (though perhaps much in an intro book?). The most glaring deficiency is the lack of any real discussion of chosen ciphertext attacks, signature forgery, or padding schemes. You can't use this by itself to develop a new real-world project.

Instead, it's more like a "cryptographer's toolbox," which gives you a thorough introduction to the primitives involved, giving you the understanding necessary to start thinking intelligently about how they are used.

Get your concepts cleared!!
This is a truly lovely book written by Koblitz. I agree with some of the comments made by earlier reviewers that the content might be outdated, however, it is important to realize that this book is there for building one's foundation in number theory and cryptography. After one is done doing that, one can go and read the current literature in cryptography. I have used this book for a graduate crypto course at USC, and I think it really helped me a lot. This book is a great reference and a great buy.

Excellent book for self study
This is an excellent book fot those, who are interested in the theoretical background of cryptography. It was also my first book in number theory, and I had no trouble following most of the text ( except the chapter on Elliptic curves, which -as I realize now- IS difficult)

Highly recommendable! A pleasant surprise is, that there are virtually no typos.