

Softcover ISBN: | 978-1-4704-7469-0 |
Product Code: | SURV/278 |
List Price: | $135.00 |
MAA Member Price: | $121.50 |
AMS Member Price: | $108.00 |
eBook ISBN: | 978-1-4704-7621-2 |
Product Code: | SURV/278.E |
List Price: | $125.00 |
MAA Member Price: | $112.50 |
AMS Member Price: | $100.00 |
Softcover ISBN: | 978-1-4704-7469-0 |
eBook: ISBN: | 978-1-4704-7621-2 |
Product Code: | SURV/278.B |
List Price: | $260.00 $197.50 |
MAA Member Price: | $234.00 $177.75 |
AMS Member Price: | $208.00 $158.00 |


Softcover ISBN: | 978-1-4704-7469-0 |
Product Code: | SURV/278 |
List Price: | $135.00 |
MAA Member Price: | $121.50 |
AMS Member Price: | $108.00 |
eBook ISBN: | 978-1-4704-7621-2 |
Product Code: | SURV/278.E |
List Price: | $125.00 |
MAA Member Price: | $112.50 |
AMS Member Price: | $100.00 |
Softcover ISBN: | 978-1-4704-7469-0 |
eBook ISBN: | 978-1-4704-7621-2 |
Product Code: | SURV/278.B |
List Price: | $260.00 $197.50 |
MAA Member Price: | $234.00 $177.75 |
AMS Member Price: | $208.00 $158.00 |
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Book DetailsMathematical Surveys and MonographsVolume: 278; 2024; 141 ppMSC: Primary 94; 81; 20
This book is intended as a comprehensive treatment of group-based cryptography accessible to both mathematicians and computer scientists, with emphasis on the most recent developments in the area. To make it accessible to a broad range of readers, the authors started with a treatment of elementary topics in group theory, combinatorics, and complexity theory, as well as providing an overview of classical public-key cryptography. Then some algorithmic problems arising in group theory are presented, and cryptosystems based on these problems and their respective cryptanalyses are described. The book also provides an introduction to ideas in quantum cryptanalysis, especially with respect to the goal of post-quantum group-based cryptography as a candidate for quantum-resistant cryptography.
The final part of the book provides a description of various classes of groups and their suitability as platforms for group-based cryptography.
The book is a monograph addressed to graduate students and researchers in both mathematics and computer science.
ReadershipGraduate students and researchers interested in algebraic methods of cryptography.
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Table of Contents
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Background information
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Group theory
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Algorithmic problems in group theory
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Classical cryptography
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Post-quantum cryptography and cryptanalysis
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Noncommutative cryptographic protocols
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Attacks
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Quantum cryptanalysis
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Cryptographic platforms
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Braid groups
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Hyperbolic groups
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Small cancellation groups
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Polycyclic groups
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Graph groups
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Arithmetic groups
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Engel groups
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Self-similar groups
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Additional Material
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
This book is intended as a comprehensive treatment of group-based cryptography accessible to both mathematicians and computer scientists, with emphasis on the most recent developments in the area. To make it accessible to a broad range of readers, the authors started with a treatment of elementary topics in group theory, combinatorics, and complexity theory, as well as providing an overview of classical public-key cryptography. Then some algorithmic problems arising in group theory are presented, and cryptosystems based on these problems and their respective cryptanalyses are described. The book also provides an introduction to ideas in quantum cryptanalysis, especially with respect to the goal of post-quantum group-based cryptography as a candidate for quantum-resistant cryptography.
The final part of the book provides a description of various classes of groups and their suitability as platforms for group-based cryptography.
The book is a monograph addressed to graduate students and researchers in both mathematics and computer science.
Graduate students and researchers interested in algebraic methods of cryptography.
-
Background information
-
Group theory
-
Algorithmic problems in group theory
-
Classical cryptography
-
Post-quantum cryptography and cryptanalysis
-
Noncommutative cryptographic protocols
-
Attacks
-
Quantum cryptanalysis
-
Cryptographic platforms
-
Braid groups
-
Hyperbolic groups
-
Small cancellation groups
-
Polycyclic groups
-
Graph groups
-
Arithmetic groups
-
Engel groups
-
Self-similar groups