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.
Journal of Computer and Communications
Fine, Benjamin; Moldenhauer, Anja IS; and Rosenberger, Gerhard, "Cryptographic Protocols Based on Nielsen Transformations" (2016). Math & Computer Science Faculty Publications. 49.
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