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Group-based Cryptography (Advanced Courses in Mathematics - CRM Barcelona)

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en Limba Engleză Carte Paperback – 17 Jul 2008
Covering relations between three different areas of mathematics and theoretical computer science, this book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography.
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Specificații

ISBN-13: 9783764388263
ISBN-10: 3764388269
Pagini: 204
Dimensiuni: 170 x 240 x 11 mm
Greutate: 0.50 kg
Ediția: 2008
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seria Advanced Courses in Mathematics - CRM Barcelona

Locul publicării: Basel, Switzerland

Public țintă

Graduate

Cuprins

Background on Groups, Complexity, and Cryptography.- Background on Public Key Cryptography.- Background on Combinatorial Group Theory.- Background on Computational Complexity.- Non-commutative Cryptography.- Canonical Non-commutative Cryptography.- Platform Groups.- Using Decision Problems in Public Key Cryptography.- Generic Complexity and Cryptanalysis.- Distributional Problems and the Average-Case Complexity.- Generic Case Complexity.- Generic Complexity of NP-complete Problems.- Asymptotically Dominant Properties and Cryptanalysis.- Asymptotically Dominant Properties.- Length-Based and Quotient Attacks.

Recenzii

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)

Textul de pe ultima copertă

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.

Caracteristici

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