A Course in Number Theory and Cryptography (Graduate Texts in Mathematics) (Hardcover)

~ (Author) "Most of the topics reviewed in this chapter are probably well known to most readers..." (more)
Key Phrases: affine enciphering transformations, ciphertext digraphs, least absolute residue, Hasse's Theorem, Information Theory, Prime Number Theorem (more...)

Editorial Reviews

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

• Hardcover: 235 pages
• Publisher: Springer; 2nd edition (September 2, 1994)
• Language: English
• ISBN-10: 0387942939
• ISBN-13: 978-0387942933
• Product Dimensions: 9.3 x 6.3 x 0.7 inches
• Shipping Weight: 12.8 ounces (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (14 customer reviews)
• Amazon.com Sales Rank: #456,514 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

56 of 56 people found the following review helpful:

4.0 out of 5 stars Cryptographer's toolbox, September 2, 1999

By A Customer

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.

7 of 8 people found the following review helpful:

5.0 out of 5 stars Get your concepts cleared!!, April 25, 2002

By	qubit (Los Angeles, CA) - See all my reviews

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.

3 of 3 people found the following review helpful:

5.0 out of 5 stars Excellent book for self study, January 6, 2004

By	PST "A Reader from Germany" (Eislingen Deutschland) - See all my reviews

This review is from: A course in number theory and cryptography (Graduate texts in mathematics) (Hardcover)

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.