LEADER 04910nam 2200721 450 001 9910797015603321 005 20180731043641.0 010 $a1-4704-2263-8 035 $a(CKB)3710000000393353 035 $a(EBL)3114280 035 $a(SSID)ssj0001451537 035 $a(PQKBManifestationID)11843280 035 $a(PQKBTitleCode)TC0001451537 035 $a(PQKBWorkID)11477873 035 $a(PQKB)11163909 035 $a(MiAaPQ)EBC3114280 035 $a(RPAM)18245062 035 $a(PPN)19710276X 035 $a(EXLCZ)993710000000393353 100 $a20150416h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aAlgorithmic problems of group theory, their complexity, and applications to cryptography /$fDelaram Kahrobaei, Vladimir Shpilrain, editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2015. 210 4$dİ2015 215 $a1 online resource (123 p.) 225 1 $aContemporary Mathematics,$x1098-3627 ;$v633 300 $a"AMS Special Session on Algorithmic Problems of Group Theory and Applications to Information Security, April 6-7, 2013, Boston College, Chestnut Hill, MA."--Cover. 300 $a"AMS Special Session on Algorithmic Problems of Group Theory and Their Complexity, January 9-10, 2013, San Diego, CA."--Cover. 311 $a0-8218-9859-0 320 $aIncludes bibliographical references at the end of each chapters. 327 $a""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Secret sharing using non-commutative groups and the shortlex order""; ""1. Introduction""; ""2. Formal Definition""; ""3. Shamira???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"" 327 $a""2. The graph I??( )""""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 Magnusa??? Theorem""; ""4. Cyclic Centralizers and Commuting Elements""; ""5. Hyperbolicity and Stable Hyperbolicity""; ""6. The Retract Theorem and Turner Groups"" 327 $a""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 Stallingsa??? pregroups""; ""1. Introduction""; ""2. Adds, Prees and Pregroups""; ""3. Kushnera???s Generalization of a Pregroup. T2-prees""; ""4. Axiom [GLS2]""; ""5. Generalizations""; ""References""; ""A CCA secure cryptosystem using matrices over group rings"" 327 $a""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 a??²-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"" 327 $a""4. Open problems"" 410 0$aContemporary mathematics (American Mathematical Society) ;$v633. 606 $aGroup theory$vCongresses 606 $aNoncommutative algebras$vCongresses 606 $aAlgorithms$vCongresses 606 $aData encryption (Computer science)$vCongresses 606 $aCryptography$vCongresses 606 $aAlgebra$vCongresses 615 0$aGroup theory 615 0$aNoncommutative algebras 615 0$aAlgorithms 615 0$aData encryption (Computer science) 615 0$aCryptography 615 0$aAlgebra 676 $a652/.8015122 686 $a20-XX$a68-XX$2msc 702 $aKahrobaei$b Delaram$f1975- 702 $aShpilrain$b Vladimir$f1960- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910797015603321 996 $aAlgorithmic problems of group theory, their complexity, and applications to cryptography$93717501 997 $aUNINA