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). Mathematics 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