IEEE International Conference on Communications workshops

Arbitrarily varying wiretap channels with finite coordination resources

Holger Boche, Rafael F. Schaefer

Published Jun 1, 2014• 9 citations

Abstract

The wiretap channel models secure communication in the presence of a non-legitimate eavesdropper who has to be kept ignorant. In this paper, the arbitrarily varying wiretap channel (AVWC) is studied, in which the channel to both legitimate receiver and eavesdropper may vary in an unknown and arbitrary manner from channel use to channel use. It has been shown that for AVCs coordination between the transmitter and legitimate receiver based on common randomness (CR) is indispensable for reliable communication. Approaches taken so far yield CR-assisted strategies where the needed amount of CR increases unbounded with the block length. In this paper, it is shown that if we allow for a small but non-vanishing average probability of error and information leakage (in terms of weak secrecy), the amount of CR is always finite and independent of the block length. The corresponding secrecy capacity equals the one with asymptotically vanishing performance requirements. Furthermore, it is shown that the average decoding error at the eavesdropper can be made arbitrarily close to 1 regardless of the applied decoding strategy.

DOI: 10.1109/iccw.2014.6881289

Related papers

On arbitrarily varying wiretap channels for different classes of secrecy measures

Holger Boche, Rafael F. Schaefer, H. Vincent Poor

The wiretap channel models secure communication in the presence of an eavesdropper who must be kept ignorant of transmitted messages. In this paper, the arbitrarily varying wiretap channel (AVWC), in which the channel may vary in an unknown and arbitrary manner from channel use to channel use, is considered. For arbitrarily varying channels (AVCs) the capacity might differ depending on whether deterministic or common randomness (CR) assisted codes are used. The AVWC has been studied for both coding strategies and the relation between the corresponding secrecy capacities has been established. However, a characterization of the CR-assisted secrecy capacity itself or even a general CR-assisted achievable secrecy rate remain open in general for weak and strong secrecy. Here, the secrecy measure of high decoding error at the eavesdropper is considered, where the eavesdropper is further assumed to know channel states and to adapt its decoding strategy accordingly. For this secrecy measure a general CR-assisted achievable secrecy rate is established. The relation between secrecy capacities for different secrecy measures is discussed: The weak and strong secrecy capacities are smaller than or equal to the one for high decoding error. It is conjectured that this relation can be strict for certain channels.

IEEE International Symposium on Information Theory (ISIT)Jun 1, 201412 citations

Strong secrecy capacity of arbitrarily varying wiretap channels with finite coordination resources

Ahmed S. Mansour, Holger Boche

We study a secure communication scenario in which the channel is under two classes of attacks at the same time: a passive eavesdropper and an active jammer. This scenario is modelled using the arbitrarily varying wiretap channel (AVWC), in which the channel varies from one channel use to the other. It has been shown that in general reliable communication over AVWCs requires some sort of coordination between the transmitter and the legitimate receiver. However, most of the established coding techniques use an amount of coordination resources that grows with the code block length. Recently, it was shown that if we allow for a small but non vanishing average error probability and weak secrecy information leakage, we can construct a correlated random code that only requires finite coordination resources. In this paper, we extend this result to the strong secrecy criterion. In particular, we show that we can construct a correlated random code with finite correlated randomness, such that the information leakage in terms of the strong secrecy criterion decays exponentially fast.

IEEE Global Conference on Signal and Information ProcessingDec 1, 20160 citations

List decoding for arbitrarily varying wiretap channels

Ahmed S. Mansour, Holger Boche, Rafael F. Schaefer

We consider a communication scenario in which the channel undergoes two different classes of attacks at the same time: a passive eavesdropper and an active jammer. This scenario is modeled by the concept of arbitrarily varying wiretap channels (AVWCs), in which the channel varies from one channel use to the other in an unknown and arbitrary manner. It has been shown that uncorrelated codes fail to establish reliable communication over the class of symmetrizable AVWCs. For this class more sophisticated coding techniques such as correlated random codes are needed. Correlated random codes are not easy to realize in practice because they require a sort of coordination between the transmitter and the receiver, which is not always possible. In this paper, we aim to resolve the ambiguity of symmetrizable AVWCs in the absence of coordination resources using list decoding. In particular, we show that for an AVWC where we allow for a non-vanishing decoding error probability, we can construct a list code whose rate is close to the correlated secrecy capacity. The list size needed by such code is shown to be finite and independent of the block length. Moreover, the constructed list code assures that the information leakage of the confidential message with respect to the strong secrecy criterion decays exponentially fast.

IEEE Conference on Communications and Network SecurityOct 1, 20164 citations

Comparison of different attack classes in arbitrarily varying wiretap channels

Holger Boche, Rafael F. Wyrembelski

For communication over arbitrarily varying channels (AVC), common randomness is an important resource to establish reliable communication, especially if the AVC is symmetrizable. In this paper the arbitrarily varying wiretap channel (AVWC) with active wiretapper is studied. Here the wiretapper is active in the sense that it can exploit the knowledge about the common randomness to control the channel conditions of the legitimate users. The common randomness assisted secrecy capacity of the AVWC with active wiretapper is analyzed and is related to the corresponding secrecy capacity of the AVWC with passive wiretapper. If the active secrecy capacity is positive, it equals the corresponding passive secrecy capacity. The case of zero active capacity is also studied.

IEEE International Workshop on Information Forensics and SecurityDec 1, 20127 citations

Capacity results, coordination resources, and super-activation in wiretap channels

Holger Boche, Rafael F. Schaefer

Availability of channel state information, especially to non-legitimate users, is one major challenge for secure communication in wireless systems. For arbitrarily varying channels (AVC), coordination resources such as common randomness have been shown to be important for reliable communication; especially for symmetrizable AVCs. In this paper, the arbitrarily varying wiretap channel (AVWC) with active wiretapper is studied. Such an wiretapper may or may not exploit his knowledge about the coordination resources to control the channel conditions. Secrecy capacity results are derived for different forms of coordination resources including common randomness and correlated sources. Finally, it is demonstrated how two orthogonal AVWCs, each with zero secrecy capacity, i.e., useless for secure transmission, can be super-activated to a useful channel allowing for secure communication at non-zero secrecy rates.

IEEE International Symposium on Information Theory (ISIT)Jul 1, 20138 citations

Strong secrecy in arbitrarily varying wiretap channels

Igor Bjelaković, Holger Boche, Jochen Sommerfeld

In this work the arbitrarily varying wiretap channel AVWC under the average error criterion and the strong secrecy criterion is studied. We show that in the case of a non-symmetrisable channel to the legitimate receiver the deterministic code secrecy capacity equals the random code secrecy capacity and thus we establish a result for the AVWC similar to that of Ahlswede's dichotomy for ordinary AVCs. We derive a lower bound on the random code secrecy capacity in the case of a best channel to the eavesdropper. We further prove upper bounds on the deterministic code secrecy capacity, which in special cases results in explicit expressions of the secrecy capacity.

IEEE Information Theory Workshop (ITW)Sep 1, 201213 citations