Author(s)

Benjamin Fine¹, Anja I. S. Moldenhauer², Gerhard Rosenberger²

¹Department of Mathematics, Fairfield University, Fairfield, CT, USA.
²Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany.

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.

Nielsen Transformation, Matrix Group SL(2, Q) , Secret Sharing Protocol, Private Key Cryptosystem, Public Key Cryptosystem

Fine, B. , Moldenhauer, A. and Rosenberger, G. (2016) Cryptographic Protocols Based on Nielsen Transformations. Journal of Computer and Communications, 4, 63-107. doi: 10.4236/jcc.2016.412004.