Algorithmic problems of group theory, their complexity, and applications to cryptography /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Kahrobaei, Delaram, 1975- (Editor ), Shpilrain, Vladimir, 1960- (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, 2015.
Colección:Contemporary mathematics (American Mathematical Society) ; 633.
Temas:
Group theory > Congresses.
Noncommutative algebras > Congresses.
Algorithms > Congresses.
Data encryption (Computer science) > Congresses.
Cryptography > Congresses.
Algebra > Congresses.
Théorie des groupes > Congrès.
Algèbres non commutatives > Congrès.
Algorithmes > Congrès.
Chiffrement (Informatique) > Congrès.
Cryptographie > Congrès.
Algèbre > Congrès.
BUSINESS & ECONOMICS > Business Writing.
Algebra
Algorithms
Cryptography
Data encryption (Computer science)
Group theory
Noncommutative algebras
Group theory and generalizations.
Computer science.
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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

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