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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Wiretap-channels with constrained active attacks

Carsten Rudolf Janda, Christian Scheunert, Eduard Axel Jorswieck

Published Nov 1, 2014• 5 citations
Publisher

Abstract

In this paper, we calculate an achievable secrecy rate for the Wiretap Channel (WTC) with an active eavesdropper, who is subject to a distortion constraint, in general. Furthermore, we consider the replacement attack and jamming attack explicitly, when imposing symbol, peak or an average constraint on the jamming sequence. We show, that in all cases the optimal strategy for the eavesdropper is to disturb each symbol equiprobable in the former case, or to jam each symbol with the same jamming power in the latter case. A consequence is, that the eavesdropper's replacement attack can be modeled as an additional Binary Symmetric Channel (BSC). Additionally, we demonstrate, that if the attacker is able to induce a channel corruption which corresponds to his own channel's degradedness or which is even worse, no positive secrecy rate is achievable.

DOI
10.1109/acssc.2014.7094818

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In this paper, we calculate an achievable secrecy rate for the Wiretap Channel (WTC) with an active eavesdropper, who is subject to a distortion constraint, in general. Furthermore, we consider the replacement attack and jamming attack explicitly, when imposing symbol, peak or an average constraint on the jamming sequence. We show, that in all cases the optimal strategy for the eavesdropper is to disturb each symbol equiprobable in the former case, or to jam each symbol with the same jamming power in the latter case. A consequence is, that the eavesdropper's replacement attack can be modeled as an additional Binary Symmetric Channel (BSC). Additionally, we demonstrate, that if the attacker is able to induce a channel corruption which corresponds to his own channel's degradedness or which is even worse, no positive secrecy rate is achievable.
We study the Gaussian multiple access channel in presence of an adversary, who is simultaneously able to eavesdrop and jam, i.e., an active wiretapper. We assume that the adversary has a power constraint, which she can utilize to have any arbitrary jamming strategy. The multiple access channel between the legitimate transmitters and the receiver thus becomes arbitrarily varying. We derive inner and outer bounds on the secrecy rate region of our model. In the case of a degraded channel, we characterize the optimal secrecy sum-rate, and within 0.5 bits per channel use the optimal individual rate constraints. As a special case, we obtain the secrecy capacity of the point-to-point Gaussian wiretap channel when the eavesdropper is able to arbitrarily jam.
We consider reliable and secure communication over intersymbol interference wiretap channels (ISI-WTCs). In particular, we first derive an achievable secure rate for ISI-WTCs without imposing any constraints on the input distribution. Afterwards, we focus on the setup where the input distribution of the ISI-WTC is constrained to be a time-invariant finite-order Markov chain. Optimizing the parameters of this Markov chain toward maximizing the achievable secure rates is a computationally intractable problem in general, and so, toward finding a local maximum, we propose an iterative algorithm that at every iteration replaces the secure rate function with a suitable surrogate function whose maximum can be found efficiently. Although the secure rates achieved in the unconstrained setup are potentially larger than the secure rates achieved in the constrained setup, the latter setup has the advantage of leading to efficient algorithms for estimating and optimizing the achievable secure rates, and also has the benefit of being the basis of efficient coding schemes.
This paper considers secure communication in the presence of an eavesdropper and a malicious jammer. The jammer is assumed to be oblivious of the communication signals emitted by the legitimate transmitter(s) but can employ any jamming strategy subject to a given power constraint and shares her jamming signal with the eavesdropper. Four such models are considered: (i) the Gaussian point-to-point wiretap channel; (ii) the Gaussian multiple-access wiretap channel; (iii) the Gaussian broadcast wiretap channel; and (iv) the Gaussian symmetric interference wiretap channel. The use of pre-shared randomness between the legitimate users is not allowed in our models. Inner and outer bounds are derived for these four models. For (i), the secrecy capacity is obtained. For (ii) and (iv) under a degraded setup, the optimal secrecy sum-rate is characterized. Finally, for (iii), ranges of model parameter values for which the inner and outer bounds coincide are identified.
Since a wireless transmission requires to access to a shared medium, the communication is susceptible to adversarial eavesdropping. This paper describes how eavesdropping can potentially be limited by resorting to waterfilling-like algorithms with additional constraints. A Gaussian wiretap channel (WTC) is considered in which a transmitter sends confidential messages to its reference receiver in the presence of a passive eavesdropper. We approach the problem from two different perspectives, focusing either on the rate of the main link or the secrecy level. Through numerical analysis, we show how the information-secrecy regions can be the means to evaluate the quality of the main link and the secrecy level, resulting from our algorithms application. Finally we analyze the case of interfering signals (induced by users sharing the same transmission resource) to show their effects on both information rate and secrecy, even in the case of an eavesdropper able to mitigate the interference.
The popular technique of secure signaling over Gaussian MIMO wiretap channels, which makes use of artificial noise (AN) to increase secrecy rates, is considered. First, we briefly review the current state of affairs in this area and then provide new analytical results and insights on the usefulness of AN (jamming) to boost secrecy rates. The settings considered here go beyond the total transmit power constraint and include a number of additional constraints, such as interference (cognitive radio) and energy-harvesting constraints, for which the feasible set is not isotropic anymore so that the standard tools of the analysis cannot be used. By closely examining optimal precoding for the information-bearing and AN signals, we identify a number of cases where it is optimal to transmit no artificial noise at all (so that all the transmit power goes to the information-bearing signal). These cases include a fixed (no fading) MIMO WTC with single eavesdropper (for which we give a direct matrix-theoretic proof using novel matrix inequalities), multi-eavesdropper (com-pound) degraded and reversely-degraded channels, and multi-eavesdropper channels where there exists a dominant eavesdropper (for which we give a precise definition) or when the eavesdroppers collude. To improve secrecy rates by using AN, one has to look elsewhere.
We consider the Gaussian wiretap channel with amplitude and variance constraints on the channel input. We first show that the entire rate-equivocation region of the Gaussian wiretap channel with an amplitude constraint is obtained by discrete input distributions with finite support. We prove this result by considering the existing single-letter description of the rate-equivocation region, and showing that discrete distributions with finite support exhaust this region. Our result highlights an important difference between the peak power (amplitude) constrained and the average power (variance) constrained cases. Although, in the average power constrained case, both the secrecy capacity and the capacity can be achieved simultaneously, our results show that in the peak power constrained case, in general, there is a tradeoff between the secrecy capacity and the capacity, in the sense that, both may not be achieved simultaneously. We also show that under sufficiently small amplitude constraints the possible tradeoff between the secrecy capacity and the capacity does not exist and they are both achieved by the symmetric binary distribution. Finally, we prove the optimality of discrete input distributions in the presence of an additional variance constraint.