Rating: 
Summary: Outstanding presentations
Review: This book is an outstanding introduction to cryptographic techniques and algorithms Although it's labelled as a "graduate text in mathematics", most of it should be accessible to anyone who knows a little linear algebra. For readers just interested in the how-to of the algorithms, not even that is needed. Koblitz does a thorough job of leading up to each algorithm and proving its formal properties. He also presents the algorithms themselves, unencumbered by denser material of interest to mathematicians.The book covers a variety of topics - public-key encryption, primality testing, factoring, and cryptographic protocols. It introduces zero-knowledge proofs and blind transfer, techniques that offer real hope of personal privacy in a world where data transfer is mandatory. I was a little disappointed by the chapters on elliptic cryptography, however. I hoped that Koblitz would bring is explanatory powers to bear on the algorithms. Somehow, I never quite connected with his descriptions of elliptic curves - perhaps I'm just thick, or perhaps a bit more introductory material would have helped. The rest of the book is a very fine example of clear, readable math writing. Its clarity its range of topics earn it a place with anyone interested in cryptography, factoring, and prime numbers.
Rating:
Summary: Get your concepts cleared!!
Review: 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 I agree with some of the comments made by earlier reviewers that the content might be outdated, however, it is important to realize that this book is there for building one's foundation in number theory and cryptography.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.
Rating:
Summary: Get your concepts cleared!!
Review: 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 I agree with some of the comments made by earlier reviewers that the content might be outdated, however, it is important to realize that this book is there for building one's foundation in number theory and cryptography.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.
Rating:
Summary: Excellent book for self study
Review: 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.
Rating: 
Summary: Cryptographer's toolbox
Review: 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.
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