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Capacity Results for Classes of Wiretap Channels

Jochen Sommerfeld

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

In this thesis we study wireless communication systems in terms of information-theoretic secure data transmission. We consider two models of a wiretap channel in the absence of channel state information, in particular the compound wiretap channel and the arbitrarily varying wiretap channel (AVWC). For both systems we derive results for the secrecy capacity, which is defined in terms of the maximum respective average error probability and the strong secrecy criterion.

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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.

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Cryptographic and Information-theoretic Security Capacities for General Arbitrarily Varying Wiretap Channels

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We compare the strong secrecy capacities of Arbitrarily Varying Wiretap Channels (AVWCs) and General Arbitrarily Varying Wiretap Channels (GAVWCs) with their capacities under semantic secrecy constraint and other equivalent cryptographic secrecy constraints. It turns out that the average error and strong secrecy capacity of an AVWC is always equal to its maximal error and semantic secrecy capacity. However, this equivalence does not hold for all general communication systems, and we prove this by a counterexample. We also show that, for the GAVWC, semantic security and the other cryptographic security measures considered achieve the same capacity values. Finally, we bound the gap between the strong secrecy capacity and the semantic secrecy capacity for the GAVWC. The gap vanishes if the choice of the jammer is sub-double-exponential with respect to the block length n, which gives a sufficient condition for the strong and semantic secrecy capacities to be equal for GAVWCs.

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

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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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Ebrahim MolavianJazi

In this thesis, we consider a class of information protection problems requiring confidentiality (secrecy) from eavesdropping and integrity (reliability) from jamming in an information-theoretic context. For this purpose, we introduce the arbitrarily varying wire-tap channel (AVWTC) model consisting of a family of wiretap channels indexed by some state that is selected by the jammer in an arbitrary and time-varying manner. We study this model for traditional wiretap codes and randomized wiretap codes, and develop insights about the corresponding secrecy capacity and randomized-code secrecy capacity, respectively. We characterize a lower bound on the randomized-code secrecy capacity of the AVWTC that suggests the secrecy is mainly dictated by a worst-case scenario. Additionally, we establish two upper bounds on the randomized-code secrecy capacity that suggest a single bad ``averaged' state can preclude secure communication, while certain superiorities of the legitimate receiver over the eavesdropper in all ``averaged' states result in a positive secrecy capacity. Finally, we prove that the secrecy capacity of the AVWTC is either zero or equal to its randomized-code secrecy capacity. We show that a ``two-layer' wiretap code is appropriate for combatting the two non-colluding jamming and eavesdropping adversaries.

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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.

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On arbitrarily varying wiretap channels for different classes of secrecy measures

Holger Boche, Rafael F. Schaefer, H. Vincent Poor

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.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2014•12 citations
In this thesis we study wireless communication systems in terms of information-theoretic secure data transmission. We consider two models of a wiretap channel in the absence of channel state information, in particular the compound wiretap channel and the arbitrarily varying wiretap channel (AVWC). For both systems we derive results for the secrecy capacity, which is defined in terms of the maximum respective average error probability and the strong secrecy criterion.
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 compare the strong secrecy capacities of Arbitrarily Varying Wiretap Channels (AVWCs) and General Arbitrarily Varying Wiretap Channels (GAVWCs) with their capacities under semantic secrecy constraint and other equivalent cryptographic secrecy constraints. It turns out that the average error and strong secrecy capacity of an AVWC is always equal to its maximal error and semantic secrecy capacity. However, this equivalence does not hold for all general communication systems, and we prove this by a counterexample. We also show that, for the GAVWC, semantic security and the other cryptographic security measures considered achieve the same capacity values. Finally, we bound the gap between the strong secrecy capacity and the semantic secrecy capacity for the GAVWC. The gap vanishes if the choice of the jammer is sub-double-exponential with respect to the block length n, which gives a sufficient condition for the strong and semantic secrecy capacities to be equal for GAVWCs.
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.
In this thesis, we consider a class of information protection problems requiring confidentiality (secrecy) from eavesdropping and integrity (reliability) from jamming in an information-theoretic context. For this purpose, we introduce the arbitrarily varying wire-tap channel (AVWTC) model consisting of a family of wiretap channels indexed by some state that is selected by the jammer in an arbitrary and time-varying manner. We study this model for traditional wiretap codes and randomized wiretap codes, and develop insights about the corresponding secrecy capacity and randomized-code secrecy capacity, respectively. We characterize a lower bound on the randomized-code secrecy capacity of the AVWTC that suggests the secrecy is mainly dictated by a worst-case scenario. Additionally, we establish two upper bounds on the randomized-code secrecy capacity that suggest a single bad ``averaged' state can preclude secure communication, while certain superiorities of the legitimate receiver over the eavesdropper in all ``averaged' states result in a positive secrecy capacity. Finally, we prove that the secrecy capacity of the AVWTC is either zero or equal to its randomized-code secrecy capacity. We show that a ``two-layer' wiretap code is appropriate for combatting the two non-colluding jamming and eavesdropping adversaries.
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.
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.