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Backing off from rayleigh and rice: Achieving perfect secrecy in wireless fading channels

Pablo Ramirez‐Espinosa, F. Javier López‐Martínez

Published Sep 1, 2020• 0 citations
OpenAlex

Abstract

We show that for a legitimate communication under multipath quasi-static fading with a reduced number of scatter- ers, it is possible to achieve perfect secrecy even in the presence of a passive eavesdropper for which no channel state information is available. Specifically, we show that the outage probability of secrecy capacity (OPSC) is zero for a given range of average signal-to-noise ratios (SNRs) at the legitimate and eavesdropper’s receivers. As an application example, we analyze the OPSC for the case of two scatterers, explicitly deriving the relationship between the average SNRs, the secrecy rate RS and the fading model parameters required for achieving perfect secrecy.

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We show that for a legitimate communication under multipath quasi-static fading with a reduced number of scatter- ers, it is possible to achieve perfect secrecy even in the presence of a passive eavesdropper for which no channel state information is available. Specifically, we show that the outage probability of secrecy capacity (OPSC) is zero for a given range of average signal-to-noise ratios (SNRs) at the legitimate and eavesdropper’s receivers. As an application example, we analyze the OPSC for the case of two scatterers, explicitly deriving the relationship between the average SNRs, the secrecy rate RS and the fading model parameters required for achieving perfect secrecy.
We show that for a legitimate communication under multipath quasi-static fading with a reduced number of scatterers, it is possible to achieve perfect secrecy even in the presence of a passive eavesdropper for which no channel state information (CSI) is available. Specifically, we show that the outage probability of secrecy capacity (OPSC) is zero for a given range of average signal-to-noise ratios (SNRs) at the legitimate and eavesdropper's receivers. As an application example, we analyze the OPSC for the case of two scatterers, explicitly deriving the relationship between the average SNRs, the secrecy rate R S and the fading model parameters required for achieving perfect secrecy. The impact of increasing the number of scatterers is also analyzed, showing that it is always possible to achieve perfect secrecy in this scenario, provided that (i) the dominant specular component for the legitimate channel is sufficiently large compared to the remaining scattered waves, and (ii) a exclusion area on which no eavesdroppers can be placed is considered.
We show that for a legitimate communication under multipath quasi-static fading with a reduced number of scatterers, it is possible to achieve perfect secrecy even in the presence of a passive eavesdropper for which no channel state information (CSI) is available. Specifically, we show that the outage probability of secrecy capacity (OPSC) is zero for a given range of average signal-to-noise ratios (SNRs) at the legitimate and eavesdropper's receivers. As an application example, we analyze the OPSC for the case of two scatterers, explicitly deriving the relationship between the average SNRs, the secrecy rate RSand the fading model parameters required for achieving perfect secrecy. The impact of increasing the number of scatterers is also analyzed, showing that it is always possible to achieve perfect secrecy in this scenario, provided that (i) the dominant specular component for the legitimate channel is sufficiently large compared to the remaining scattered waves, and (ii) a exclusion area on which no eavesdroppers can be placed is considered.
We consider the transmission of confidential data over wireless channels with multiple communicating parties. Based on an information-theoretic problem formulation in which two legitimate partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through another independent quasi-static fading channel, we define the secrecy capacity in terms of outage probability and provide a complete characterization of the maximum transmission rate at which the eavesdropper is unable to decode any information. In sharp contrast with known results for Gaussian wiretap channels (without feedback), our contribution shows that in the presence of fading information-theoretic security is achievable even when the eavesdropper has a better average signal-to-noise ratio (SNR) than the legitimate receiver - fading thus turns out to be a friend and not a foe.
In this two-part paper, we consider the transmission of confidential data over wireless wiretap channels. The first part presents an information-theoretic problem formulation in which two legitimate partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through another independent quasi-static fading channel. We define the secrecy capacity in terms of outage probability and provide a complete characterization of the maximum transmission rate at which the eavesdropper is unable to decode any information. In sharp contrast with known results for Gaussian wiretap channels (without feedback), our contribution shows that in the presence of fading information-theoretic security is achievable even when the eavesdropper has a better average signal-to-noise ratio (SNR) than the legitimate receiver - fading thus turns out to be a friend and not a foe. The issue of imperfect channel state information is also addressed. Practical schemes for wireless information-theoretic security are presented in Part II, which in some cases comes close to the secrecy capacity limits given in this paper.
In this paper, a wireless multicast scenario is considered in which the transmitter sends a common message to multiple client receivers in the presence of an eavesdropper. We are interested in protecting this common message against eavesdropping. Based on an information-theoretic formulation of the problem, in which the transmitter and the mutually independent multiple client receivers communicate over quasi-static Rayleigh fading channels and an eavesdropper observes their transmissions through another quasi-static Rayleigh fading channel, we define the secrecy-sum capacity in terms of secure outage probability. Moreover, we also present a formulation of ergodic perfect secrecy multicast capacity at which the eavesdropper is unable to decode any information.
The resilience of block fading wireless orthogonal frequency division multiple access (OFDMA) networks to passive eavesdroppers is investigated. The network secrecy capacity is evaluated in scenarios involving a base station and several terminals, some of which constitute passive eavesdroppers. Assuming a block fading Rayleigh channel, the probability of a secrecy outage during a transmission frame is evaluated with respect to a target secrecy rate τ in the following cases: (i) in the absence of any cooperation between the network nodes, and, (ii) when the full multi-user diversity is exploited both by the legitimate users as well as by the eavesdroppers. Remarkably, it is demonstrated that in a network of as few as 12 legitimate users and a single eavesdropper it is possible to transmit 1 bit/sec/Hz with a probability of secrecy outage less than 1%. Furthermore, the delay constrained secrecy capacity of this network is evaluated when the full channel state information (CSI) is available both at the base station and at all receiving nodes. A secure waterfilling scheme is discussed, satisfying a short-term power constraint.