Customer Reviews

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

5 star:		(8)
4 star:		(6)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

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.

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 I agree with some of the comments made by earlier reviewers that the content might be outdated, however, it is important to realize that this book is there for building one's foundation in number theory and cryptography.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.

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.

I was a little leery of this book as I'm certainly no William Friedman or Alan Turing. But I was surprised to find the topic not as daunting as I thought although people who lock up when they see formulas may be intimidated at first glance. This book deals with number theory, dealing with some fundamental properties of numbers with application to cryptographic uses. Each section takes you slowly through the theory and provides exercises at the end of each chapter you can work through. (The answers are in the back of the book.) This is a particularly useful book if you are conversant in programming and want to play with certain aspects of number theory and cryptography to 'see how it really works.' It's like a course in tumblers and pins for someone who is fascinated by locks.

I'm using this book for my math undergraduate thesis in integer factorization. The book goes in-depth into some more arcane factorization methods (e.g., Fermat factorization has been deemed too slow by other books on cryptography), but still catches the wave of the newer methods (e.g., elliptic curve). Overall, this book is a good tool which should be used in conjunction with other books on the topic of interest, but certainly should not be used solo.

Neal Koblitz. The name says all. He is the cocreator of the elliptic curve cryptosystems. If you have studied 1 year of college algebra (Herstein or Fraleigh) and you want to learn cryptography mathematically, this is THE reference. If you are an engineer and/or just want to know the practical (and as always, superficial) issues of the subject, skip it.

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.

This book is a real gem - very clearly written and covering the subject matter concisely but comprehensively. Particularly welcome are the exercises which are ingenious and extend the subject matter rather than just test knowledge of the chapter. It is extremely helpful too (and rare in a graduate text book) that solutions to all of the problems are provided at the back of the book. Exceptionally, and again very helpfully, there seem to be zero errors/typos in the text.

Strongly recommended as the best introduction to this fascinating and important field

How Neal Koblitz manages to squeeze the amount of material he presents into this slim volume is a miracle of nature. It even includes what most authors of graduate works leave out as a matter of course: answers to exercises. More amazing still is that far from being terse and unreadable the text is a delight.

My advice to anyone interested in this field is to have this book by their side at all times. Then if the need arises to find out what makes an algorithm tick or to refresh one's mind about a well known concept it's just the flick of a page away.

I have really enjoyed this book, but reading it has required an entirely new type of discipline. I can't expect to get through more than a couple pages without being overwhelmed. However, every page is terrific. Some more verbage, I think, might make the more subtle points clearer, but I also value the conciseness and preciseness of the text.