Article citationsMore>>

Camps, T., Groβe Rebel, V. and Rosenberger, G. (2008) Einführung in die kombinatorische und die geometrische Gruppentheorie. Berliner Studienreihe zur Mathematik Band 19. Heldermann Verlag, Berlin.

has been cited by the following article:

• 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.