Group-based Cryptography by Alexei Myasnikov
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.-
Harmonic and Geometric Analysis
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Integral Geometry and Valuations
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Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension
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Mean Curvature Flow and Isoperimetric Inequalities
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Elliptic Curves, Hilbert Modular Forms and Galois Deformations
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Contemporary Cryptology
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The Geometry of the Word Problem for Finitely Generated Groups
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Simplicial Methods for Operads and Algebraic Geometry
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Combinatorial Number Theory and Additive Group Theory
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Compactifying Moduli Spaces
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Ramsey Methods in Analysis
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Hyperbolic Cross Approximation
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Central Configurations, Periodic Orbits, and Hamiltonian Systems
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Crossed Products of C*-Algebras, Topological Dynamics, and Classification
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Numerical Solutions of Partial Differential Equations
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Proper Group Actions and the Baum-Connes Conjecture
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Homotopy Theoretic Methods in Group Cohomology
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An Introduction to Piecewise Smooth Dynamics
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Geometry and Dynamics of Integrable Systems
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Building Bridges Between Algebra and Topology
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Combinatorial Matrix Theory
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Lectures on Algebraic Quantum Groups
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Polynomial Identity Rings
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Kolmogorov Equations for Stochastic PDEs
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String Topology and Cyclic Homology
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Symplectic Geometry of Integrable Hamiltonian Systems
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Algorithmic and Geometric Topics Around Free Groups and Automorphisms
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Geometry and Quantization of Moduli Spaces
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From Levy-Type Processes to Parabolic SPDEs
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Variable Lebesgue Spaces and Hyperbolic Systems
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Higher Structures and Operadic Calculus
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Advances in Poisson Geometry
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Analysis on h-Harmonics and Dunkl Transforms
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An Introduction to C*-Algebras and the Classification Program
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Global Riemannian Geometry: Curvature and Topology
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)
| SKU | Unavailable |
| ISBN 13 | 9783764388263 |
| ISBN 10 | 3764388269 |
| Title | Group-based Cryptography |
| Author | Alexei Myasnikov |
| Series | Advanced Courses In Mathematics - Crm Barcelona |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Birkhauser Verlag AG |
| Year published | 2008-07-17 |
| Number of pages | 183 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |