Overview
- 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 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)
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Table of contents (11 chapters)
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Front Matter
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Background on Groups, Complexity, and Cryptography
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Front Matter
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Non-commutative Cryptography
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Front Matter
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Generic Complexity and Cryptanalysis
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Front Matter
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Asymptotically Dominant Properties and Cryptanalysis
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Front Matter
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Back Matter
Keywords
About this book
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)
Authors and Affiliations
Bibliographic Information
Book Title: Group-based Cryptography
Authors: Alexei Myasnikov, Alexander Ushakov, Vladimir Shpilrain
Series Title: Advanced Courses in Mathematics - CRM Barcelona
DOI: https://doi.org/10.1007/978-3-7643-8827-0
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2008
Softcover ISBN: 978-3-7643-8826-3Published: 17 July 2008
eBook ISBN: 978-3-7643-8827-0Published: 04 November 2008
Series ISSN: 2297-0304
Series E-ISSN: 2297-0312
Edition Number: 1
Number of Pages: XV, 183
Topics: Group Theory and Generalizations, Combinatorics, Computational Mathematics and Numerical Analysis