04879nam 2200709 450 991048024830332120180731043641.01-4704-2263-8(CKB)3710000000393353(EBL)3114280(SSID)ssj0001451537(PQKBManifestationID)11843280(PQKBTitleCode)TC0001451537(PQKBWorkID)11477873(PQKB)11163909(MiAaPQ)EBC3114280(PPN)19710276X(EXLCZ)99371000000039335320150416h20152015 uy 0engur|n|---|||||txtccrAlgorithmic problems of group theory, their complexity, and applications to cryptography /Delaram Kahrobaei, Vladimir Shpilrain, editorsProvidence, Rhode Island :American Mathematical Society,2015.©20151 online resource (123 p.)Contemporary Mathematics,1098-3627 ;633"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.0-8218-9859-0 Includes bibliographical references at the end of each chapters.""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 Groups""""8. 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 cryptosystem""""2. 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""""4. Open problems""Contemporary mathematics (American Mathematical Society) ;633.Group theoryCongressesNoncommutative algebrasCongressesAlgorithmsCongressesData encryption (Computer science)CongressesCryptographyCongressesAlgebraCongressesElectronic books.Group theoryNoncommutative algebrasAlgorithmsData encryption (Computer science)CryptographyAlgebra652/.8015122Kahrobaei Delaram1975-Shpilrain Vladimir1960-MiAaPQMiAaPQMiAaPQBOOK9910480248303321Algorithmic problems of group theory, their complexity, and applications to cryptography2188964UNINA