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Moldenhauer, A.I.S. (2016) Cryptographic Protocols Based on Inner Product Spaces and Group Theory with a Special Focus on the Use of Nielsen Transformations. Ph.D. Thesis, University of Hamburg, Hamburg.

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.