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Article
Cryptographic Protocols Based on Nielsen Transformations
Journal of Computer and Communications
  • Benjamin Fine, Fairfield University
  • Anja IS Moldenhauer
  • Gerhard Rosenberger
Document Type
Article
Article Version
Publisher's PDF
Publication Date
1-1-2016
Abstract

We introduce in this paper cryptographic protocols which use combinatorial group theory. Based on a combinatorial distribution of shares we present secret sharing schemes and cryptosystems using Nielsen transformations. Nielsen transformations are a linear technique to study free groups and general infinite groups. In addition the group of all automorphisms of a free group F, denoted by ( )Aut F, is generated by a regular Nielsen transformation between two basis of F, and each regular Nielsen transformation between two bases of F defines an automorphism of F.

Comments

Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/

Published Citation
Fine, Benjamin, Anja IS Moldenhauer, and Gerhard Rosenberger. "Cryptographic Protocols Based on Nielsen Transformations." Journal of Computer and Communications 4, no. 12 (2016): 63-107. 10.4236/jcc.2016.412004
DOI
10.4236/jcc.2016.412004
None
Peer Reviewed
Citation Information
Benjamin Fine, Anja IS Moldenhauer and Gerhard Rosenberger. "Cryptographic Protocols Based on Nielsen Transformations" Journal of Computer and Communications Vol. 4 Iss. 12 (2016)
Available at: http://works.bepress.com/benjamin_fine/9/