Title

Cryptographic Protocols Based on Nielsen Transformations

Authors

Benjamin Fine, Fairfield UniversityFollow
Anja IS Moldenhauer
Gerhard Rosenberger

Document Type

Article

Article Version

Publisher's PDF

Publication Date

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/

Publication Title

Journal of Computer and Communications

Repository Citation

Fine, Benjamin; Moldenhauer, Anja IS; and Rosenberger, Gerhard, "Cryptographic Protocols Based on Nielsen Transformations" (2016). Mathematics Faculty Publications. 49.
https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/49

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

Peer Reviewed