Algebraic properties of the Richard Thompson’s groupfand its applications in cryptography

Download

12626187.pdf

Date

2021-3-05

Author

Yeter, Hakan

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

447
views

443
downloads

Thompson’s groupsF,TandV, especiallyF, are widely studied groups in grouptheory. With their unique properties, they appear and become counterexamples formany general problems in different areas of mathematics. Developments in scienceand technology raise the importance of security for transmission and storage of pri-vate information, which can be provided by secure cryptosystems. In this thesis, weinvestigate algebraic properties of the Thompson’s groupFand its applications tocryptography.

Subject Keywords

Piecewise linear homeomorphisms, Finitely presented groups, SimpleGroups, Public key cryptography, Group based cryptography

URI

https://hdl.handle.net/11511/89839

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Generalized chillingworth classes on subsurface torelli groups Ünlü Eroğlu, Hatice; Korkmaz, Mustafa; Department of Mathematics (2018) The Torelli group is the subgroup of the mapping class group that acts trivially on homology. Putman's subsurface Torelli groups are an important construction for working with the Torelli group, as they restore the functoriality essential for the inductive arguments on which mapping class group arguments are invariably based. The other important structure on the Torelli group is the Johnson homomorphism. The contraction of the image of the Johnson homomorphism is the Chillingworth class. In this thesis, a c...
Limit monomial groups Bostan, Sezen; Kuzucuoğlu, Mahmut; Department of Mathematics (2021-3-03) In this thesis, monomial groups, which are obtained by using strictly diagonal embeddings of complete monomial groups over a group of finite degree, are studied. The direct limit of complete monomial groups of finite degree with strictly diagonal embeddings is called limit monomial group . Normal subgroup structure of limit monomial groups over abelian groups is studied. We classified all subgroups of rational numbers, containing integers, by using base subgroup of limit monomial groups. We also studied the...
The mapping class group is generated by two commutators Baykur, R. Inanc; Korkmaz, Mustafa (2021-05-01) We show that the mapping class group of any closed connected orientable surface of genus at least five is generated by only two commutators, and if the genus is three or four, by three commutators. (C) 2021 Elsevier Inc. All rights reserved.
Algebraic And Combinatorial Methods İn Finite Fields, Coding Theory And Cryptography Özbudak, Ferruh; Tutdere, Seher; Çalık, Çağdaş; Yayla, Oğuz; Muş, Köksal(2013-12-31) Bu projede, kombinatorik, cebirsel fonksiyonel cisimler ve sonlu cebirsel geometri teknikleri kullanarak kodlama teorisi, sonlu cisimler ve kriptografi üzerine çalışmalar yapılması amaçlanmaktadır. Bunların arasında BAP-07-05- 2011-002 nolu projemizde başlayan bazı çalışmalar da devam ettirileceği planlanmaktadır. Bu çalışmalarla ilgili olarak bazı techizat alımı ve bilgi/deneyim arttırılması, makale sunumu gibi gerekçelerle uluslararası konferanslarda katılınması bu projenin amaçlarıdır. Konferans veya de...
Lineer Grupların direkt limiti şeklindeki Lokal sonlu gruplarda merkezleyenler Kuzucuoğlu, Mahmut; Bostan, Sezen(2017-12-31) Lineer grupların birbirleri içine köşegen olarak gömülmesiyle elde edilen lokal sonlu gruplar, limit grupları olarak elde edilen gruplar içinde özel bir önem taşımaktadır. Bu yöntemle sayılamaz sonsuzlukta birbirleri ile eş yapılı olmayan basit grup üretilmektedir. Projede bu grupların Steinetz sayıları kullanılarak sınıflandırılması problemi ve sonlu altgruplarının merkezleyenlerinin yapıları incelenecektir.

Citation Formats

H. Yeter, “Algebraic properties of the Richard Thompson’s groupfand its applications in cryptography,” M.S. - Master of Science, Middle East Technical University, 2021.