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 transformation...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.展开更多
文摘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.
