Analysis of Some Well-Rounded Lattices in Wiretap Channels

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Abstract

Recently, various criteria for constructing wiretap lattice coset codes have been proposed, most prominently the minimization of the so-called flatness factor. However, these criteria are not constructive per se. As explicit constructions, well-rounded lattices have been proposed as possible minimizers of the flatness factor, but no rigorous proof has been given. In this paper, we study various well-rounded lattices, including the best sphere packings, and analyze their shortest vector lengths, minimum product distances, and flatness factors, with the goal of acquiring a better understanding of the role of these invarients regarding secure communications. Simulations are carried out in dimensions four and eight, yielding the conclusion that the best sphere packing does not necessarily yield the best performance, not even when compared to other well-rounded lattices having the same superlattice. This motivates further study and construction of well-rounded lattices for physical laver security.

Original languageEnglish
Title of host publication2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2018
PublisherIEEE
Pages496-500
Number of pages5
Volume2018-June
ISBN (Print)9781538635124
DOIs
Publication statusPublished - 24 Aug 2018
MoE publication typeA4 Article in a conference publication
EventIEEE International Workshop on Signal Processing Advances in Wireless Communications - Kalamata, Greece
Duration: 25 Jun 201828 Jun 2018
Conference number: 19

Publication series

NameIEEE International Workshop on Signal Processing Advances in Wireless Communications
PublisherIEEE
ISSN (Print)2325-3789

Workshop

WorkshopIEEE International Workshop on Signal Processing Advances in Wireless Communications
Abbreviated titleSPAWC
CountryGreece
CityKalamata
Period25/06/201828/06/2018

Keywords

  • Algebraic number fields
  • coset coding
  • ideals
  • single-input single-output (SISO) channels
  • sphere packings
  • well-rounded lattices
  • wiretap channels

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