Advanced Courses in Mathematics - CRM Barcelona

Group-based Cryptography

Authors: Myasnikov, Alexei, Shpilrain, Vladimir, Ushakov, Alexander

  • Increased interest in applications of combinatorial group theory to cryptography
  • First monograph exploring the area of "non-commutative cryptography"
  • Employing decision problems (as opposed to search problems) in public key cryptography allows us to construct cryptographic protocols with new properties
  • First presentation of a rigorous mathematical justification of security for protocols based on infinite groups, as an alternative to the security model known as semantic security
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eBook $34.99
price for USA (gross)
  • ISBN 978-3-7643-8827-0
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-7643-8826-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory.

Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant properties of some infinite groups that have been applied in public key cryptography so far.

Its elementary exposition makes the book accessible to graduate as well as undergraduate students in mathematics or computer science.

Reviews

From the reviews:

“The book at hand has the aim to introduce the reader into the rich world of group-based asymmetric encryption. … The basics necessary for the understanding are given in introducing chapters. Many hints for further reading are given. So, the book might be useful for the beginner, who wants to get a clear introduction, as well as for the expert, who gets an elaborate survey as well as much stimulation for proceeding research.” (Michael Wüstner, Zentralblatt MATH, Vol. 1248, 2012)


Table of contents (11 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-7643-8827-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-7643-8826-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Group-based Cryptography
Authors
Series Title
Advanced Courses in Mathematics - CRM Barcelona
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-8827-0
DOI
10.1007/978-3-7643-8827-0
Softcover ISBN
978-3-7643-8826-3
Series ISSN
2297-0304
Edition Number
1
Number of Pages
XV, 183
Topics