- Series: Graduate Texts in Mathematics (Book 114)
- Hardcover: 235 pages
- Publisher: Springer; 2nd edition (September 2, 1994)
- Language: English
- ISBN-10: 0387942939
- ISBN-13: 978-0387942933
- Product Dimensions: 6.1 x 0.6 x 9.2 inches
- Shipping Weight: 12.8 ounces (View shipping rates and policies)
- Customer Reviews: 15 customer reviews
- Amazon Best Sellers Rank: #426,864 in Books (See Top 100 in Books)
A Course in Number Theory and Cryptography (Graduate Texts in Mathematics) 2nd Edition
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From the Back Cover
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.
15 customer reviews
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This is one of the first books I ever read on mathematical foundations of cryptography. It says graduate on the cover but don't listen to that. It's really an undergraduate level book. All you need to know is a bit of algebra. Book starts with a review of several key number theory topics, moves to finite fields, then to the public key cryptography, RSA, zero-knowledge proofs, then primality testing, factoring and finally elliptic curves.
This book follows definition-theorem-proof-example style that I like and it has many exercises with answers. If you like math but don't have experience with fundamentals of cryptography then this is the book to get to quickly get yourself up to speed. Fundamentals don't change and once you master what's in this book (shouldn't take more than a week or two if you're smart and dedicated), you'll be able to read any crypto text.
I've placed this book #17 in my Top 100 Programming, Computer and Science books list:
(If this link gets removed, google for >>catonmat top 100 programming computer science books<< to find my article.)
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.
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.