<p>From the reviews:</p><p>“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)</p>

This book is about relations between three di?erent areas of mathematics and theoreticalcomputer science: combinatorialgroup theory, cryptography,and c- plexity theory. We explorehownon-commutative(in?nite) groups,which arety- callystudiedincombinatorialgrouptheory,canbeusedinpublickeycryptography. We also show that there is a remarkable feedback from cryptography to com- natorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research - enues within group theory. Then, we employ complexity theory, notably generic case complexity of algorithms,for cryptanalysisof various cryptographicprotocols based on in?nite groups. We also use the ideas and machinery from the theory of generic case complexity to study asymptotically dominant properties of some in?nite groups that have been used in public key cryptography so far. It turns out that for a relevant cryptographic scheme to be secure, it is essential that keys are selected from a "very small" (relative to the whole group, say) subset rather than from the whole group. Detecting these subsets ("black holes") for a part- ular cryptographic scheme is usually a very challenging problem, but it holds the keyto creatingsecurecryptographicprimitives basedonin?nite non-commutative groups. The book isbased onlecture notesfor the Advanced Courseon Group-Based CryptographyheldattheCRM,BarcelonainMay2007. Itisagreatpleasureforus to thank Manuel Castellet, the HonoraryDirector of the CRM, for supporting the idea of this Advanced Course. We are also grateful to the current CRM Director, JoaquimBruna,and to the friendly CRM sta?,especially Mrs. N. PortetandMrs. N. Hern' andez, for their help in running the Advanced Course and in preparing the lecture notes.
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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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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.
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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.
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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 Includes supplementary material: sn.pub/extras
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GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
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Produktdetaljer

ISBN
9783764388263
Publisert
2008-07-17
Utgiver
Vendor
Birkhauser Verlag AG
Høyde
240 mm
Bredde
170 mm
Aldersnivå
Graduate, UU, UP, P, 05, 06
Språk
Product language
Engelsk
Format
Product format
Heftet