TITLE:
Cryptographic Protocols Based on Nielsen Transformations
AUTHORS:
Benjamin Fine, Anja I. S. Moldenhauer, Gerhard Rosenberger
KEYWORDS:
Nielsen Transformation, Matrix Group SL(2, Q), Secret Sharing Protocol, Private Key Cryptosystem, Public Key Cryptosystem
JOURNAL NAME:
Journal of Computer and Communications,
Vol.4 No.12,
October
31,
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 basis of F defines an automorphism of F.