Cryptographic Protocols Based on Nielsen Transformations

Benjamin Fine; Anja IS Moldenhauer; Gerhard Rosenberger

doi:10.4236/jcc.2016.412004

Cryptographic Protocols Based on Nielsen Transformations

Benjamin Fine, Anja IS Moldenhauer, Gerhard Rosenberger

Fairfield University

Research output: Contribution to journal › Article › peer-review

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 bases of F defines an automorphism of F.

Original language	American English
Journal	Journal of Computer and Communications
Volume	4
DOIs	https://doi.org/10.4236/jcc.2016.412004
State	Published - Jan 1 2016

Disciplines

Mathematics
Physical Sciences and Mathematics

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10.4236/jcc.2016.412004License: CC BY

Cryptographic Protocols Based on Nielsen TransformationsFinal published version, 808 KBLicense: CC BY

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title = "Cryptographic Protocols Based on Nielsen Transformations",

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 bases of F defines an automorphism of F.",

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N2 - 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.

AB - 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.

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M3 - Article

VL - 4

JO - Journal of Computer and Communications

JF - Journal of Computer and Communications

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Cryptographic Protocols Based on Nielsen Transformations

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