Strong secrecy and reliable byzantine detection in the presence of an untrusted relay

Xiang He, Aylin Yener

    Research output: Contribution to journalArticle

    38 Scopus citations

    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 proposed scheme are the nested lattice code, the privacy amplification scheme, 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.

    Original languageEnglish (US)
    Article number6293896
    Pages (from-to)177-192
    Number of pages16
    JournalIEEE Transactions on Information Theory
    Volume59
    Issue number1
    DOIs
    StatePublished - Jan 7 2013

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    All Science Journal Classification (ASJC) codes

    • Information Systems
    • Computer Science Applications
    • Library and Information Sciences

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