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arXiv:1410.8078 · IEEE Transactions on Information Theory

A Channel Under Simultaneous Jamming and Eavesdropping Attack—Correlated Random Coding Capacities Under Strong Secrecy Criteria

Moritz Wiese, Janis Nötzel, Holger Boche

Published May 10, 2016• 70 citations
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Abstract

We give a complete characterization of the correlated random coding secrecy capacity of arbitrarily varying wiretap channels (AVWCs). We apply two alternative strong secrecy criteria, which both lead to the same multi-letter formula. The difference of these criteria lies in the treatment of correlated randomness; they coincide in the case of uncorrelated 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, in contrast to the discontinuous uncorrelated coding secrecy capacity. 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 arbitrarily varying from the sender to the eavesdropper.

DOI
10.1109/tit.2016.2565482

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We give a complete characterization of the correlated random coding secrecy capacity of arbitrarily varying wiretap channels (AVWCs). We apply two alternative strong secrecy criteria, which both lead to the same multi-letter formula. The difference of these criteria lies in the treatment of correlated randomness; they coincide in the case of uncorrelated 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, in contrast to the discontinuous uncorrelated coding secrecy capacity. 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 arbitrarily varying from the sender to the eavesdropper.
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.
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 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.
We investigate secure communication over a channel under two different classes of attacks at the same time: a passive eavesdropper and an active jammer. This scenario is perfectly modeled by the concept of arbitrarily varying wiretap channels (AVWCs). It has been shown that uncorrelated codes are not always capable of overcoming the various jamming attacks. On the other hand, correlated random codes that can always neutralize the role of the jammer require the existence of a shared common randomness between the legitimate nodes. These constraints lead to the instability of the secrecy capacity of AVWCs. In this paper, we provide a new coding scheme that combines the principle of list decoding and the techniques of correlated random codes. Our coding scheme does not only stabilize the secrecy capacity of the AVWC, but it can also be used to provide some additional features required for practical scenarios such as transceiver synchronization and channel estimation.
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 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.