Well-Rounded Lattices and Applications to Physical Layer Security

Thumbnail Image

Files

isbn9789526400426.pdf (1.46 MB)
isbn9789526400426_errata.pdf (175.44 KB)

URL

Journal Title

Journal ISSN

Volume Title

School of Science | Doctoral thesis (article-based) | Defence date: 2020-11-06
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.

Authors

Date

2020

Department

Matematiikan ja systeemianalyysin laitos
Department of Mathematics and Systems Analysis

Major/Subject

Mcode

Degree programme

Language

en

Pages

86 + app. 130

Series

Aalto University publication series DOCTORAL DISSERTATIONS, 160/2020

Abstract

 This thesis is devoted to the analysis and construction of well-rounded lattices. The main motivation for studying these objects comes from problems in wireless communications.  In particular, we study lattice codes for wiretap channels in the context of physical layer security. The set of well-rounded lattices has been investigated from topological, geometric and arithmetic point of views.  We contribute to this study by first answering various questions about well-rounded lattices arising from real quadratic fields. Then, motivated by number theoretic constructions, we derive a more general generic construction of lattices generated by their minimal vectors in every dimension.  The last part of the thesis is dedicated to analysing the performance of lattice codes carved from well-rounded lattices. We then motivate the use of such codes over fading channels to achieve both reliable and secure communication. We show that these codes provide nearly optimal solutions in terms of reliability for both additive white Gaussian noisy channels and Rayleigh fading channels. For the security part, we led an experimental and analytical study of well-rounded lattice codes on the wiretap channel.  We conclude that, similarly as well-rounded lattices provide maximisers of lattice sphere packings, they also provide excellent candidates for minimising the eavesdroppers' chances of intercepting a transmitted message.

Description

Supervising professor

Hollanti Camilla, Prof., Aalto University, Department of Mathematics and Systems Analysis, Finland

Thesis advisor

Hollanti Camilla, Prof., Aalto University, Department of Mathematics and Systems Analysis, Finland

Keywords

well-rounded lattices, number theory, communication, security

Other note

Parts

  • [Publication 1]: Mohamed Taoufiq Damir, David Karpuk. Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields. Journal of Number Theory, 196, pp. 168–196, 2019.
    DOI: 10.1016/j.jnt.2018.09.017 View at publisher
  • [Publication 2]: Mohamed Taoufiq Damir, Lenny Fukshansky. Canonical Basis Twists of Ideal Lattices from Real Quadratic Number Fields. Houston Journal of Mathematics, 45, pp. 103–107, 2019
  • [Publication 3]: Mohamed Taoufiq Damir, Laia Amorós, Oliver Gnilke, Camilla Hollanti. Analysis of Some Well-Rounded Lattices in Wiretap Channels. 2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), June, 2018.
    Full text in Acris/Aaltodoc: http://urn.fi/URN:NBN:fi:aalto-201812106348
    DOI: 10.1109/SPAWC.2018.8445937 View at publisher
  • [Publication 4]: Mohamed Taoufiq Damir, Alex Karrila, Laia Amorós, Oliver Gnilke, David Karpuk, Camilla Hollanti. Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels. Submitted, 29 pages, December 2019
  • [Publication 5]: Mohamed Taoufiq Damir, Guillermo Mantilla-Soler. Bases of Minimal Vectors in Lagrangian Lattices. Submitted, 24 pages, June 2020

Citation

Permanent link to this item

https://urn.fi/URN:ISBN:978-952-64-0042-6

Collections

[diss] Perustieteiden korkeakoulu / SCI