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Publisher:

Springer-Verlag

Publication Date:

2004

Number of Pages:

335

Format:

Hardcover

Edition:

2

Series:

Undergraduate Texts in Mathematics

Price:

42.95

ISBN:

0-387-21156-X

Category:

Textbook

[Reviewed by , on ]

Robert W. Vallin

01/20/2001

We’ve all heard about the links between mathematics and secret codes. These connections have been there from the Caesar cipher up to the RSA public encryption scheme. For those of us who wish to learn more about cryptography and/or to teach it, Johannes Buchmann has written this book. In a little over 300 pages, he conveys the mathematics needed to understand cryptography along with the methods one uses to attack a cryptographic system.

The sixteen chapters are short, composed of sections that are a few pages each. However, the writing is not terse and there are plenty of examples for most every topic. The book is mathematically complete and a satisfying read. There are plenty of homework exercises at the end of each chapter with some of the answers in the back.

This is a good book for upperclassmen, graduate students, and faculty. While all the necessary background is included, this book requires a lot of mathematical maturity. For example, induction is covered in one paragraph on page 2 with no examples and no homework problems. Of course, if this is not enough induction, more examples can be found elsewhere. As long as we’re on the subject of other sources, there is a very nice list of books and web sites for reference (73, to be precise). This book makes a superior reference and a fine textbook.

Robert W. Vallin (robert.vallin@sru.edu) is Associate Professor of Mathematics at Slippery Rock University of Pennsylvania.

Integers.- Congruences and Residue Class Rings.- Encryption.- Probability and Perfect Secrecy.- DES.- AES.- Prime Number Generation.- Public-Key Encryption.- Factoring.- Discrete Logarithms.- Cryptographic Hash Functions.- Digital Signatures.- Other Systems.- Identification.- Public-Key Infrastructures.- Solutions of the Odd Exercises.- Subject Index.- Bibliography.

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