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Applications of Group Theory in Cryptography: Post-quantum Group-based Cryptography
 
Delaram Kahrobaei Queens College, The City University of New York, Flushing, NY and University of York, York, United Kingdom
Ramón Flores University of Seville, Seville, Spain
Marialaura Noce University of Salerno, Salerno, Italy
Maggie E. Habeeb Pennsylvania Western University, California, PA
Christopher Battarbee University of York, York, United Kingdom
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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Applications of Group Theory in Cryptography: Post-quantum Group-based Cryptography
Delaram Kahrobaei Queens College, The City University of New York, Flushing, NY and University of York, York, United Kingdom
Ramón Flores University of Seville, Seville, Spain
Marialaura Noce University of Salerno, Salerno, Italy
Maggie E. Habeeb Pennsylvania Western University, California, PA
Christopher Battarbee University of York, York, United Kingdom
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
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2782024; 141 pp
    MSC: 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.

    Readership

    Graduate students and researchers interested in algebraic methods of cryptography.

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2782024; 141 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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