Title Algorithmic problems of group theory, their complexity, and applications to cryptography / Delaram Kahrobaei, Vladimir Shpilrain, editors

Published Providence, Rhode Island : American Mathematical Society, 2015 ©2015

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Description 1 online resource (136 pages) Series Contemporary Mathematics, 1098-3627 ; 633 Contemporary mathematics (American Mathematical Society) ; 633. Contents Cover -- Title page -- Contents -- Preface -- Secret sharing using non-commutative groups and the shortlex order -- 1. Introduction -- 2. Formal Definition -- 3. Shamirâ€?s Secret Sharing Scheme -- 4. Secret Sharing Using Non-commutative Groups -- 5. Updating Relators -- 6. Conclusion -- References -- An algorithm that decides conjugacy in a certain generalized free product -- 1. Introduction -- 2. Preliminaries -- 3. The Algorithm -- References -- Classification of automorphic conjugacy classes in the free group on two generators -- 1. Introduction 2. The graph Î?()3. Non-root classes -- 4. Root classes -- 5. Enumeration -- Appendix A. Table of automorphic conjugacy classes -- Appendix B. Number of automorphic conjugacy classes of each type -- Appendix C. Number of paths of each size -- Acknowledgement -- References -- On elementary free groups -- 1. Introduction -- 2. The Tarski Problems and Elementary Free Groups -- 3. Surface Groups and Magnusâ€? Theorem -- 4. Cyclic Centralizers and Commuting Elements -- 5. Hyperbolicity and Stable Hyperbolicity -- 6. The Retract Theorem and Turner Groups 7. Conjugacy Separability of Elementary Free Groups8. Tame Automorphisms of Elementary Free Groups -- 9. Faithful Representations in (2,\C) -- References -- An application of a localized version of an axiom of Ian Chiswell -- 1. Introduction -- 2. Questions -- References -- A note on Stallingsâ€? pregroups -- 1. Introduction -- 2. Adds, Prees and Pregroups -- 3. Kushnerâ€?s Generalization of a Pregroup. T2-prees -- 4. Axiom [GLS2] -- 5. Generalizations -- References -- A CCA secure cryptosystem using matrices over group rings 1. Cramer-Shoup cryptosystem2. A CCA-2 secure cryptosystem using matrices over group rings -- 3. Adaptive CCA security for matrices over group rings -- References -- The MOR cryptosystem and finite -groups -- 1. Introduction -- 2. Definitions and notations -- 3. The MOR cryptosystem -- 4. MOR cryptosystems on finite -groups using ′-automorphisms -- 5. The MOR cryptosystem and elementary abelian -group -- 6. The extra-special -groups and its automorphism group -- 7. MOR cryptosystems on finite -groups using -automorphisms -- 8. Conclusion Notes "AMS Special Session on Algorithmic Problems of Group Theory and Applications to Information Security, April 6-7, 2013, Boston College, Chestnut Hill, MA."--Cover "AMS Special Session on Algorithmic Problems of Group Theory and Their Complexity, January 9-10, 2013, San Diego, CA."--Cover Bibliography Includes bibliographical references Notes Print version record Subject Group theory -- Congresses Noncommutative algebras -- Congresses Algorithms -- Congresses Data encryption (Computer science) -- Congresses Cryptography -- Congresses Algebra -- Congresses BUSINESS & ECONOMICS -- Business Writing. Algebra Algorithms Cryptography Data encryption (Computer science) Group theory Noncommutative algebras Group theory and generalizations. Computer science. Genre/Form Conference papers and proceedings Form Electronic book Author Kahrobaei, Delaram, 1975- editor. Shpilrain, Vladimir, 1960- editor. ISBN 9781470422639 1470422638

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