Semantically Secure Lattice Codes for the Gaussian Wiretap Channel

TL;DR

This paper introduces a new lattice coding scheme for the Gaussian wiretap channel that guarantees semantic security and strong secrecy, utilizing the flatness factor as a key design criterion.

Contribution

It proposes the concept of secrecy-good lattices and a novel secrecy coding scheme based on discrete Gaussian distributions, achieving near secrecy capacity without requiring message distribution assumptions.

Findings

Achieves semantic security and strong secrecy over Gaussian wiretap channels.

Introduces the flatness factor as a new lattice design criterion.

Attains secrecy capacity within half a nat under mild conditions.

Abstract

We propose a new scheme of wiretap lattice coding that achieves semantic security and strong secrecy over the Gaussian wiretap channel. The key tool in our security proof is the flatness factor which characterizes the convergence of the conditional output distributions corresponding to different messages and leads to an upper bound on the information leakage. We not only introduce the notion of secrecy-good lattices, but also propose the {flatness factor} as a design criterion of such lattices. Both the modulo-lattice Gaussian channel and the genuine Gaussian channel are considered. In the latter case, we propose a novel secrecy coding scheme based on the discrete Gaussian distribution over a lattice, which achieves the secrecy capacity to within a half nat under mild conditions. No \textit{a priori} distribution of the message is assumed, and no dither is used in our proposed schemes.