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IEEE Transactions on Information Theory

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

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

Published Feb 16, 2023• 5 citations
Publisher

Abstract

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).

DOI
10.1109/tit.2023.3245722

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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).
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.
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.
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.
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.