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: #373508 in Books
• Published on: 1994-09-22
• 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.

Practical Tools
At a time when POP, as in POP-Maths, POP-Science etc, floods book-seller's shelves; it is clear that everyone wants quick results: Ah, yes: The new superman, Corporate, Tan and with a conversational knowledge of the generalised number sieve. Even the professional is drawn into this, producing books which give results: This is why Godel is important...this is what Diffie and Hellman did. The problem with propogating this tendency is that it suppresses an ability to engage with the METHODS used by the authors of these giant leaps: These methods are what will make up a readers toolbox for applying these theories more broadly. Cryptography, even at a professional maths level, is full of similar tendencies, books either give pseudo-political histories in a neurotic attempt at justifying their existence or they reflect the authors mathematical proclivities with respect to particular applications of number theory. Too much method and the wrong context. Neal Koblitz's book gives the methods AND results: Just enough to allow you to engage actively with the developments in the field. I was inspired and have great respect for his dedication of the royalties of this book to victims of US agression in America and South-East Asia. This is the kind of context we want. read this book. Sincerely Justin Arbuckle

Absolutely astounding!
Perfect. It gives the reader far more than what they expect in a wonderful manner. Highly recommended to anyone who has seen some Abstract Algebra.