
Group Theoretic Cryptography
Chapman & Hall/CRC (Publisher)
1st Edition
Published on 14. October 2024
Book
Paperback/Softback
248 pages
978-1-032-92550-9 (ISBN)
Description
Group theoretic problems have propelled scientific achievements across a wide range of fields, including mathematics, physics, chemistry, and the life sciences. Many cryptographic constructions exploit the computational hardness of group theoretical problems, and the area is viewed as a potential source of quantum-resilient cryptographic primitives for the future.
Group Theoretic Cryptography supplies an ideal introduction to cryptography for those who are interested in group theory and want to learn about the possible interplays between the two fields. Assuming an undergraduate-level understanding of linear algebra and discrete mathematics, it details the specifics of using non-Abelian groups in the field of cryptography.
Moreover, the book evidences how group theoretic techniques help us gain new insight into well known, seemingly unrelated, cryptographic constructions, such as DES.
The book starts with brief overviews of the fundamentals of group theory, complexity theory, and cryptography. Part two is devoted to public-key encryption, including provable security guarantees, public-key encryption in the standard model, and public-key encryption using infinite groups.
The third part of the book covers secret-key encryption. It examines block ciphers, like the Advanced Encryption Standard, and cryptographic hash functions and message authentication codes. The last part delves into a number of cryptographic applications which are nowadays as relevant as encryption-identification protocols, key establishment, and signature schemes are covered.
The book supplies formal security analyses and highlights potential vulnerabilities for cryptographic constructions involving group theory. Summaries and references for further reading, as well as exercises, are included at the end of each chapter. Selected solutions for exercises are provided in the back of the book.
Group Theoretic Cryptography supplies an ideal introduction to cryptography for those who are interested in group theory and want to learn about the possible interplays between the two fields. Assuming an undergraduate-level understanding of linear algebra and discrete mathematics, it details the specifics of using non-Abelian groups in the field of cryptography.
Moreover, the book evidences how group theoretic techniques help us gain new insight into well known, seemingly unrelated, cryptographic constructions, such as DES.
The book starts with brief overviews of the fundamentals of group theory, complexity theory, and cryptography. Part two is devoted to public-key encryption, including provable security guarantees, public-key encryption in the standard model, and public-key encryption using infinite groups.
The third part of the book covers secret-key encryption. It examines block ciphers, like the Advanced Encryption Standard, and cryptographic hash functions and message authentication codes. The last part delves into a number of cryptographic applications which are nowadays as relevant as encryption-identification protocols, key establishment, and signature schemes are covered.
The book supplies formal security analyses and highlights potential vulnerabilities for cryptographic constructions involving group theory. Summaries and references for further reading, as well as exercises, are included at the end of each chapter. Selected solutions for exercises are provided in the back of the book.
Reviews / Votes
"Group Theoretic Cryptography is highly welcome. It provides an excellent introduction in group-based cryptography where algebraic properties of the platform groups, mainly from combinatorial group theory, are used prominently in both devising cryptosystems and in cryptanalysis. In particular the difficulty, in a complexity sense, of certain algorithmic problems in finitely presented groups has been crucial in encryption and decryption. ... I highly recommend the book under review. It is of great value for researchers in the area as well as for advanced students which start to work in cryptology. The excellent figures and algorithmic descriptions are clear and good to understand. They help the readers to see the important points.-Gerhard Rosenberger (Hamburg), writing in Zentralblatt MATH 1321 - 1
More details
Series
Language
English
Place of publication
Boca Raton
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
Professional and scholarly
Academic
Illustrations
53 s/w Abbildungen
53 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
Weight
453 gr
ISBN-13
978-1-032-92550-9 (9781032925509)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Maria Isabel Gonzalez Vasco | Rainer Steinwandt
Group Theoretic Cryptography
E-Book
04/2015
1st Edition
Chapman & Hall/CRC
€96.49
Available for download

Maria Isabel Gonzalez Vasco | Rainer Steinwandt
Group Theoretic Cryptography
Book
04/2015
1st Edition
Chapman & Hall/CRC
€165.90
Shipment within 15-20 days

Maria Isabel Gonzalez Vasco | Rainer Steinwandt
Group Theoretic Cryptography
E-Book
04/2015
1st Edition
Chapman and Hall
€96.49
Available for download
Persons
Maria Isabel Gonzalez Vasco, Rainer Steinwandt
Author
Universidad Rey Juan Carlos, Madrid, Spain
Florida Atlantic University, Boca Raton, FL
Content
Preliminaries. Public-Key Encryption. Secret-Key Encryption. Other Cryptographic Constructions. Appendix.