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IEEE Global Conference on Signal and Information Processing

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

Ahmed S. Mansour, Holger Boche

Published Dec 1, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.1109/globalsip.2016.7905992

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•Oct 29, 2014•14 citations
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.
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.
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 modelled by the concept of arbitrarily varying wiretap channels (AVWCs). In this paper, we derive a full characterization of the list secrecy capacity of the AVWC, showing that the list secrecy capacity is equivalent to the correlated random secrecy capacity if the list size L is greater than the order of symmetrizability of the AVC between the transmitter and the legitimate receiver. Otherwise, it is zero. Our result indicates that for a sufficiently large list size L, list codes can overcome the drawbacks of correlated and uncorrelated codes and provide a stable secrecy capacity for AVWCs. Furthermore, we investigate the effect of relaxing the reliability and secrecy constraints by allowing a non-vanishing error probability and information leakage on the list size L. We found that we can construct a list code whose rate is close to the correlated secrecy capacity using a finite list size L that only depends on the average error probability requested. Finally, we point out that our capacity characterization is an important step in investigating the analytical properties of the capacity function such as: the continuity behavior, Turing computability and super-activation of parallel AVWCs.
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.
We give a complete characterization of the secrecy capacity of arbitrarily varying wiretap channels (AVWCs) with correlated random coding under a strong secrecy criterion where the eavesdropper may also know the correlated randomness. We obtain that the correlated random coding secrecy capacity is continuous as a function of the AVWC. We show that the deterministic coding secrecy capacity of the AVWC either equals 0 or the correlated random coding secrecy capacity. For the case that only a weak secrecy criterion is applied, a complete characterization of the corresponding secrecy capacity for deterministic codes is possible. In the proof of the secrecy capacity formula for correlated random codes, we apply an auxiliary channel which is compound from the sender to the intended receiver and varies arbitrarily from the sender to the eavesdropper. We discuss the relation between the usual mutual information secrecy criterion and a criterion formulated in terms of total variation distance, and investigate the robustness of the AVWC model.
We investigate secure communication over a channel that undergoes two different classes of attacks at the same time: passive eavesdropping and active jamming. This scenario is perfectly modeled by the concept of arbitrarily varying wiretap channels (AVWCs). We derive a full characterization of the secrecy capacity of AVWCs under list decoding. We show that the list secrecy capacity is either equivalent to the correlated random secrecy capacity or zero depending on the order of symmetrizability of the legitimate AVC. Differently from correlated random codes, our coding scheme does not assume any restrictions on the communication between the eavesdropper and the jammer.
We give a complete characterization of the secrecy capacity of arbitrarily varying wiretap channels (AVWCs) with correlated random coding. We apply two alternative strong secrecy criteria, which both lead to the same formula and which coincide in the case of deterministic codes. On the basis of the derived formula, we show that the correlated random coding secrecy capacity is continuous as a function of the AVWC. We show that the deterministic coding secrecy capacity of the AVWC either equals 0 or the correlated random coding secrecy capacity. For the case that only a weak secrecy criterion is applied, we derive a complete characterization of the corresponding secrecy capacity for deterministic codes. In the proof of the secrecy capacity formula for correlated random codes, we apply an auxiliary channel which is compound from the sender to the intended receiver and varies arbitrarily from the sender to the eavesdropper.