Group-based Cryptography

Alexei Myasnikov

ISBN 10: 3764388269 / ISBN 13: 9783764388263

Published by Springer, Basel, Birkhäuser Basel, Birkhäuser Jul 2008, 2008

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 183 pp. Englisch.

Seller Inventory # 9783764388263

Bibliographic Details

• Title: Group-based Cryptography
• Publisher: Springer, Basel, Birkhäuser Basel, Birkhäuser Jul 2008
• Publication Date: 2008
• Language: English
• ISBN 10: 3764388269
• ISBN 13: 9783764388263
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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.