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© 2004

Introduction to Cryptography

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Johannes A. Buchmann
    Pages 1-27
  3. Johannes A. Buchmann
    Pages 29-70
  4. Johannes A. Buchmann
    Pages 71-114
  5. Johannes A. Buchmann
    Pages 115-126
  6. DES
    Johannes A. Buchmann
    Pages 127-137
  7. AES
    Johannes A. Buchmann
    Pages 139-149
  8. Johannes A. Buchmann
    Pages 151-161
  9. Johannes A. Buchmann
    Pages 163-198
  10. Johannes A. Buchmann
    Pages 199-211
  11. Johannes A. Buchmann
    Pages 213-233
  12. Johannes A. Buchmann
    Pages 235-248
  13. Johannes A. Buchmann
    Pages 249-275
  14. Johannes A. Buchmann
    Pages 277-283
  15. Johannes A. Buchmann
    Pages 285-292
  16. Johannes A. Buchmann
    Pages 293-297
  17. Johannes A. Buchmann
    Pages 299-306
  18. Back Matter
    Pages 307-338

About this book

Introduction

Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control, etc. Therefore, users should not only know how its techniques work, but they must also be able to estimate their efficiency and security. For this new edition, the author has updated the discussion of the security of encryption and signature schemes and recent advances in factoring and computing discrete logarithms. He has also added descriptions of time-memory trade of attacks and algebraic attacks on block ciphers, the Advanced Encryption Standard, the Secure Hash Algorithm, secret sharing schemes, and undeniable and blind signatures.

Johannes A. Buchmann is a Professor of Computer Science and Mathematics at the Technical University of Darmstadt, and the Associate Editor of the Journal of Cryptology. In 1985, he received the Feodor Lynen Fellowship of the Alexander von Humboldt Foundation. Furthermore, he has received the most prestigious award in science in Germany, the Leibniz Award of the German Science Foundation.

About the first edition:

It is amazing how much Buchmann is able to do in under 300 pages: self-contained explanations of the relevant mathematics (with proofs); a systematic introduction to symmetric cryptosystems, including a detailed description and discussion of DES; a good treatment of primality testing, integer factorization, and algorithms for discrete logarithms; clearly written sections describing most of the major types of cryptosystems....This book is an excellent reference, and I believe it would also be a good textbook for a course for mathematics or computer science majors..."

-Neal Koblitz, The American Mathematical Monthly

Keywords

access control AES computer science cryptography cryptology DES digital signature encryption hash function prime number secret sharing

Authors and affiliations

  1. 1.Department of Computer ScienceTechnical UniversityDarmstadtGermany

About the authors

Johannes A. Buchmann is Professor of Computer Science and Mathematics at the Technical University of Darmstadt, and an Associate Editor of the Journal of Cryptology. In 1985, he received a Feodor Lynen Fellowship of the Alexander von Humboldt Foundation. He has also received the most prestigious award in science in Germany, the Leibniz Award of the German Science Foundation (Deutsche Forschungsgemeinschaft).

Bibliographic information

  • Book Title Introduction to Cryptography
  • Authors Johannes Buchmann
  • Series Title Undergraduate Texts in Mathematics
  • DOI https://doi.org/10.1007/978-1-4419-9003-7
  • Copyright Information Springer-Verlag New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-21156-5
  • Softcover ISBN 978-0-387-20756-8
  • eBook ISBN 978-1-4419-9003-7
  • Series ISSN 0172-6056
  • Edition Number 2
  • Number of Pages XVI, 338
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
    Data Structures and Information Theory
  • Buy this book on publisher's site
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Reviews

From the reviews:

Zentralblatt Math

"[......] Of the three books under review, Buchmann's is by far the most sophisticated, complete and up-to-date. It was written for computer-science majors -  German ones at that - and might be rough going for all but the best American undergraduates. It is amazing how much Buchmann is able to do in under 300 pages: self-contained explanations of the relevant mathematics (with proofs); a systematic introduction to symmetric cryptosystems, including a detailed description and discussion of DES; a good treatment of primality testing, integer factorization, and algorithms for discrete logarithms, clearly written sections describing most of the major types of cryptosystems, and explanations of basic concepts of practical cryptography such as hash functions, message authentication codes, signatures, passwords, certification authorities, and certificate chains. This book is an excellent reference, and I believe that it would also be a good textbook for a course for mathematics or computer science majors, provided that the instructor is prepared to supplement it with more leisurely treatments of some of the topics."

N. Koblitz  (Seattle, WA)   - American Math. Society Monthly.

J.A. Buchmann

Introduction to Cryptography

"It gives a clear and systematic introduction into the subject whose popularity is ever increasing, and can be recommended to all who would like to learn about cryptography. The book contains many exercises and examples. It can be used as a textbook and is likely to become popular among students. The necessary definitions and concepts from algebra, number theory and probability theory are formulated, illustrated by examples and applied to cryptography." —ZENTRALBLATT MATH

"For those of use who wish to learn more about cryptography and/or to teach it, Johannes Buchmann has written this book. … The book is mathematically complete and a satisfying read. There are plenty of homework exercises … . This is a good book for upperclassmen, graduate students, and faculty. … This book makes a superior reference and a fine textbook." (Robert W. Vallin, MathDL, January, 2001)

"Buchmann’s book is a text on cryptography intended to be used at the undergraduate level. … the intended audiences of this book are ‘readers who want to learn about modern cryptographic algorithms and their mathematical foundations … . I enjoy reading this book. … Readers will find a good exposition of the techniques used in developing and analyzing these algorithms. … These make Buchmann’s text an excellent choice for self study or as a text for students … in elementary number theory and algebra." (Andrew C. Lee, SIGACT News, Vol. 34 (4), 2003)

From the reviews of the second edition:

"This is the english translation of the second edition of the author’s prominent german textbook ‘Einführung in die Kryptographie’. The original text grew out of several courses on cryptography given by the author at the Technical University Darmstadt; it is aimed at readers who want to learn about modern cryptographic techniques and its mathematical foundations … . As compared with the first edition the number of exercises has almost been doubled and some material … has been added." (R. Steinbauer, Monatshefte für Mathematik, Vol. 150 (4), 2007)