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Group Theoretic Cryptography
— —
Maria Isabel Gonzalez Vasco Spyros Magliveras
Group Theoretic Cryptography by Maria Isabel Gonzalez Vasco at Abbey's Bookshop,

Group Theoretic Cryptography

Maria Isabel Gonzalez Vasco Spyros Magliveras Rainer Steinwandt Douglas R. Stinson


Chapman & Hall/CRC

Data encryption


244 pages

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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.

By:   Maria Isabel Gonzalez Vasco, Spyros Magliveras, Rainer Steinwandt
Series edited by:   Douglas R. Stinson
Imprint:   Chapman & Hall/CRC
Country of Publication:   United States
Volume:   9
Dimensions:   Height: 235mm,  Width: 156mm,  Spine: 18mm
Weight:   499g
ISBN:   9781584888369
ISBN 10:   1584888369
Series:   Chapman & Hall/CRC Cryptography and Network Security Series
Pages:   244
Publication Date:   April 2015
Audience:   Professional and scholarly ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active

Universidad Rey Juan Carlos, Madrid, Spain Florida Atlantic University, Boca Raton, FL University of Waterloo, Ontario, Canada

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

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