The Secrecy Gain of Formally Unimodular Lattices on the Gaussian Wiretap Channel

TL;DR

This paper investigates the secrecy properties of formally unimodular lattices in Gaussian wiretap channels, introducing a universal method to compute their secrecy gain and demonstrating their superior performance over existing lattices.

Contribution

It introduces formally unimodular lattices and a universal approach to determine their secrecy gain, showing they outperform known unimodular lattices in security.

Findings

Formally unimodular lattices share secrecy function behavior with unimodular lattices.

A universal method for calculating secrecy gain from self-dual codes is provided.

Formally unimodular lattices can achieve higher secrecy gains than existing lattices.

Abstract

We consider lattice coding for the Gaussian wiretap channel, where the challenge is to ensure reliable communication between two authorized parties while preventing an eavesdropper from learning the transmitted messages. Recently, a measure called the secrecy function of a lattice coding scheme was proposed as a design criterion to characterize the eavesdropper's probability of correct decision. In this paper, the family of formally unimodular lattices is presented and shown to possess the same secrecy function behavior as unimodular and isodual lattices. Based on Construction A, we provide a universal approach to determine the secrecy gain, i.e., the maximum value of the secrecy function, for formally unimodular lattices obtained from formally self-dual codes. Furthermore, we show that formally unimodular lattices can achieve higher secrecy gain than the best-known unimodular lattices from the literature.