Analysis of Some Well-Rounded Lattices in Wiretap Channels

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.