2- and 3-modular Lattice Wiretap Codes in Small Dimensions

TL;DR

This paper explores 2- and 3-modular lattice codes for Gaussian wiretap channels, demonstrating they generally outperform unimodular lattices in secrecy gain within small dimensions, with some odd 2-modular lattices excelling too.

Contribution

It investigates the secrecy gain of 2- and 3-modular lattices, showing they often surpass unimodular lattices in small dimensions for wiretap security.

Findings

Most even 2- and 3-modular lattices outperform unimodular lattices in secrecy gain.

Some odd 2-modular lattices outperform unimodular lattices.

Performance comparison in dimensions 2 to 23.

Abstract

A recent line of work on lattice codes for Gaussian wiretap channels introduced a new lattice invariant called secrecy gain as a code design criterion which captures the confusion that lattice coding produces at an eavesdropper. Following up the study of unimodular lattice wiretap codes [1], this paper investigates 2- and 3-modular lattices and compares them with unimodular lattices. Most even 2- and 3-modular lattices are found to have better performance, that is, a higher secrecy gain than the best unimodular lattices in dimension n, n is between 2 and 23. Odd 2-modular lattices are considered, too, and three lattices are found to outperform the best unimodular lattices.