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arXiv:2001.03035

Arbitrarily Varying Wiretap Channels with Non-Causal Side Information at the Jammer

Carsten Rudolf Janda, Moritz Wiese, Eduard Axel Jorswieck, Holger Boche

Published Jan 9, 2020• 0 citations
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Abstract

Secure communication in a potentially malicious environment becomes more and more important. The arbitrarily varying wiretap channel (AVWC) provides information theoretical bounds on how much information can be exchanged even in the presence of an active attacker. If the active attacker has non-causal side information, situations in which a legitimate communication system has been hacked, can be modeled. We investigate the AVWC with non-causal side information at the jammer for the case that there exists a best channel to the eavesdropper. Non-causal side information means that the transmitted codeword is known to an active adversary before it is transmitted. By considering the maximum error criterion, we allow also messages to be known at the jammer before the corresponding codeword is transmitted. A single letter formula for the common randomness secrecy capacity is derived. Additionally, we provide a single letter formula for the common randomness secrecy capacity, for the cases that the channel to the eavesdropper is strongly degraded, strongly noisier, or strongly less capable with respect to the main channel. Furthermore, we compare our results to the random code secrecy capacity for the cases of maximum error criterion but without non-causal side information at the jammer, maximum error criterion with non-causal side information of the messages at the jammer, and the case of average error criterion without non-causal side information at the jammer.

DOI
10.48550/arxiv.2001.03035

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Secure communication in a potentially malicious environment becomes more and more important. The arbitrarily varying wiretap channel (AVWC) provides information theoretical bounds on how much information can be exchanged even in the presence of an active attacker. If the active attacker has non-causal side information, situations in which a legitimate communication system has been hacked, can be modeled. We investigate the AVWC with non-causal side information at the jammer for the case that there exists a best channel to the eavesdropper. Non-causal side information means that the transmitted codeword is known to an active adversary before it is transmitted. By considering the maximum error criterion, we allow also messages to be known at the jammer before the corresponding codeword is transmitted. A single letter formula for the common randomness secrecy capacity is derived. Additionally, we provide a single letter formula for the common randomness secrecy capacity, for the cases that the channel to the eavesdropper is strongly degraded, strongly noisier, or strongly less capable with respect to the main channel. Furthermore, we compare our results to the random code secrecy capacity for the cases of maximum error criterion but without non-causal side information at the jammer, maximum error criterion with non-causal side information of the messages at the jammer, and the case of average error criterion without non-causal side information at the jammer.
We investigate the Arbitrarily Varying Wiretap Channel (AVWC) with non-causal side information at the jammer for the case that there exists a best channel to the eavesdropper. Non-causal side information means that codewords are known at an active adversary before they are transmitted. By considering the maximum error criterion, we allow also messages to be known at the jammer before the corresponding codeword is transmitted. A multi letter formula for the common randomness secrecy capacity is derived. Furthermore, we compare our results to the random code secrecy capacity for the cases of maximum error criterion but without non-causal side information at the jammer, maximum error criterion with non-causal side information of the messages at the jammer, and the case of average error criterion without non-causal side information at the jammer.
Secure communication in a potentially hostile environment is becoming more and more critical. TheArbitrarilyVaryingWiretapChannel (AVWC) provides information-theoretical bounds on how much information can be exchanged even in the presence of an active attacker. If the active attacker has non-causal side information, situations in which a legitimate communication system has been hacked can be modeled. We investigate the AVWC with non-causal side information at the jammer for the case that there exists a best channel to the eavesdropper. Non-causal side information means that the transmitted codeword is known to an active adversary before it is transmitted. By considering the maximum error criterion, we also allow messages to be known at the jammer before the corresponding codeword is transmitted. A single-letter formula for theCommonRandomness (CR)-assisted secrecy capacity is derived. Additionally, we provide a formula for the CR-assisted secrecy capacity for the cases where the channel to the eavesdropper is strongly degraded, strongly noisier, or strongly less capable with respect to the main channel. Furthermore, we compare our results to the CR-assisted secrecy capacity for the cases of maximum error criterion but without non-causal side information at the jammer (blind adversary), maximum error criterion with non-causal side information of the messages at the jammer (semi-blind adversary), and the case of average error criterion without non-causal side information at the jammer (blind adversary).
We investigate the Arbitrarily Varying Wiretap Channel (AVWC) with non-causal side information at the jammer for the case that there exists a best channel to the eavesdropper and under the condition that strong degradedness holds. Non-causal side information means that codewords are known at an active adversary before they are transmitted. By considering the maximum error criterion, we allow also messages to be known at the jammer before the corresponding codeword is transmitted. A single letter formula for the common randomness secrecy capacity is derived.
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.
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.
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.