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The Arbitrarily Varying Wiretap Channel - deterministic and correlated random coding capacities under the strong secrecy criterion.

Moritz Wiese, Janis Nötzel, Holger Boche

Published Oct 29, 2014• 14 citations
OpenAlex

Abstract

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.

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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.

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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.

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The secrecy capacity of the arbitrarily varying wiretap channel under list decoding

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 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.

Advances in Mathematics of Communications•Dec 19, 2018•2 citations
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 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.
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.
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.
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 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.