Providing Secrecy with Lattice Codes

TL;DR

This paper develops a method to analyze secrecy rates using lattice codes in Gaussian channels, demonstrating their effectiveness in secure communication scenarios like wiretap channels and multi-hop networks.

Contribution

It introduces a new technique to compute secrecy rates with lattice codes, bridging the gap between lattice coding and secrecy analysis in Gaussian channels.

Findings

Secrecy rates can be effectively computed with lattice codes.

Lattice codes enable positive secrecy rates in multi-hop networks regardless of hop count.

The approach is demonstrated in wiretap and multi-hop network examples.

Abstract

Recent results have shown that lattice codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. On the other hand, for Gaussian channels with secrecy constraints, efforts to date rely on random codes. In this work, we provide a tool to bridge these two areas so that the secrecy rate can be computed when lattice codes are used. In particular, we address the problem of bounding equivocation rates under nonlinear modulus operation that is present in lattice encoders/decoders. The technique is then demonstrated in two Gaussian channel examples: (1) a Gaussian wiretap channel with a cooperative jammer, and (2) a multi-hop line network from a source to a destination with untrusted intermediate relay nodes from whom the information needs to be kept secret. In both cases, lattice codes are used to facilitate cooperative jamming. In the second case, interestingly, we demonstrate that a non-vanishing positive secrecy rate is achievable regardless of the number of hops.