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Information 2016, 7(2), 24; doi:10.3390/info7020024

Super-Activation as a Unique Feature of Secure Communication in Malicious Environments

Information Theory and Applications Chair, Technische Universität Berlin, 10587 Berlin, Germany
Institute of Theoretical Information Technology, Technische Universität München, 80333 Munich, Germany
Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editor: Willy Susilo
Received: 28 January 2016 / Revised: 25 April 2016 / Accepted: 27 April 2016 / Published: 12 May 2016
(This article belongs to the Special Issue Physical Layer Security in Wireless Networks)
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The wiretap channel models secure communication between two users in the presence of an eavesdropper who must be kept ignorant of transmitted messages. This communication scenario is studied for arbitrarily varying channels (AVCs), in which the legitimate users know only that the true channel realization comes from a pre-specified uncertainty set and that it varies from channel use to channel use in an arbitrary and unknown manner. This concept not only captures the case of channel uncertainty, but also models scenarios in which malevolent adversaries influence or jam the transmission of the legitimate users. For secure communication over orthogonal arbitrarily varying wiretap channels (AVWCs) it has been shown that the phenomenon of super-activation occurs; that is, there are orthogonal AVWCs, each having zero secrecy capacity, which allow for transmission with positive rate if they are used together. It is shown that for such orthogonal AVWCs super-activation is generic in the sense that whenever super-activation is possible, it is possible for all AVWCs in a certain neighborhood as well. As a consequence, a super-activated AVWC is robust and continuous in the uncertainty set, although a single AVWC might not be. Moreover, it is shown that the question of super-activation and the continuity of the secrecy capacity solely depends on the legitimate link. Accordingly, the single-user AVC is subsequently studied and it is shown that in this case, super-activation for non-secure message transmission is not possible making it a unique feature of secure communication over AVWCs. However, the capacity for message transmission of the single-user AVC is shown to be super-additive including a complete characterization. Such knowledge is important for medium access control and in particular resource allocation as it determines the overall performance of a system. View Full-Text
Keywords: wiretap channel; arbitrarily varying channel (AVC); secrecy capacity; super-activation; super-additivity; active attacks; malicious behavior wiretap channel; arbitrarily varying channel (AVC); secrecy capacity; super-activation; super-additivity; active attacks; malicious behavior

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Schaefer, R.F.; Boche, H.; Poor, H.V. Super-Activation as a Unique Feature of Secure Communication in Malicious Environments. Information 2016, 7, 24.

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