Strong Secrecy and Reliable Byzantine Detection in the Presence of an Untrusted Relay

TL;DR

This paper introduces a novel coding scheme combining lattice codes, privacy amplification, and AMD codes to ensure strong secrecy and reliable Byzantine attack detection in a Gaussian two-hop network with an untrusted relay.

Contribution

It presents the first application of lattice coding with AMD codes in a noisy channel to achieve both secrecy and attack detection.

Findings

The probability of undetected Byzantine attack decreases exponentially with channel uses.

Secrecy rate loss can be made arbitrarily small compared to honest relay scenarios.

The scheme achieves strong secrecy in Gaussian channels, unlike prior work.

Abstract

We consider a Gaussian two-hop network where the source and the destination can communicate only via a relay node who is both an eavesdropper and a Byzantine adversary. Both the source and the destination nodes are allowed to transmit, and the relay receives a superposition of their transmitted signals. We propose a new coding scheme that satisfies two requirements simultaneously: the transmitted message must be kept secret from the relay node, and the destination must be able to detect any Byzantine attack that the relay node might launch reliably and fast. The three main components of the scheme are the nested lattice code, the privacy amplification and the algebraic manipulation detection (AMD)code. Specifically, for the Gaussian two-hop network, we show that lattice coding can successfully pair with AMD codes enabling its first application to a noisy channel model. We prove, using this new coding scheme, that the probability that the Byzantine attack goes undetected decreases exponentially fast with respect to the number of channel uses, while the loss in the secrecy rate, compared to the rate achievable when the relay is honest, can be made arbitrarily small. In addition, in contrast with prior work in Gaussian channels, the notion of secrecy provided here is strong secrecy.