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Semantic Security for the Fast Fading Wiretap Channel.

Parker Pavlicek

Published Jan 1, 2018• 1 citation
OpenAlex

Abstract

We provide a set of semantically secure achievable rates for the fast fading wiretap channel. In particular, we do so for the cases where there is channel state information at the transmitter (CSIT) for both the main and eavesdropper channels (full CSIT), for only the main channel (partial CSIT), and for neither channel (statistical CSIT). In the case of partial CSIT and statistical CSIT fast-fading channels, we show that this coding scheme can achieve the best known achievable rates. In the case of full CSIT fast-fading wiretap channels, we show that this coding scheme can actually achieve the secrecy capacity. In particular, this implies that the semantic secrecy capacity for these channels is equivalent to the weak and strong secrecy capacities. Moreover, we achieve these rates in a way that is non-invasive to existing systems and also happens to be explicitly given as well as efficient in implementation.

Related papers

Achieving Shannon Capacity in a Fading Wiretap Channel.

Shahid Mehraj Shah, Vinod Sharma

Reliable communication imposes an upper limit on the achievable rate, namely the Shannon capacity. Wyner's wiretap coding, which ensures a security constraint also in addition to reliability, results in decrease of the achievable rate. To mitigate the loss in the secrecy rate, we propose a coding scheme paper where we use sufficiently old messages as key and for this scheme prove that multiple messages are secure with respect to (w.r.t.) all the information possessed by the eavesdropper. We also show that we can achieve security in the strong sense. Next we consider a fading wiretap channel with full channel state information of the eavesdropper's channel and use our coding/decoding scheme to achieve secrecy capacity close to the Shannon capacity of the main channel (in the ergodic sense). Finally we also consider the case where the transmitter does not have the instantaneous information of the channel state of the eavesdropper, but only its distribution.

arXiv:1505.01374•May 6, 2015•1 citation

On the secrecy capacity of fading Gaussian wiretap channel

Md. K. Hossan, Sanjay Karmakar, Anirban Ghosh

We consider the fast-fading Gaussian wiretap channel with single antenna nodes and without channel state information at the transmitter (CSIT), where the fading processes of the two links are arbitrary and independent of each other. We derive an upper bound to the secrecy capacity for this channel and an achievable rate as well. Subsequently, we identify a class of channel statistics for which the outer bound and the achievable rates are identical thereby characterizes the exact secrecy capacity of the channel. The class of channels with such channel statistics are called stochastically degraded in this paper. Many practical wireless settings including the Rayleigh fading environment fall under this stochastically degraded class. We illustrate our results by computing explicit expression for the secrecy capacity for Rayleigh distributed wiretap channels.

Canadian Workshop on Information Theory (CWIT)•Jul 1, 2015•5 citations

Enhancing secrecy in fading wiretap channels with only transmitter-side channel state information

Pang-Chang Lan, Y.-W. Peter Hong, C.‐C. Jay Kuo

This work examines the advantages of having only channel state information at the transmitter (CSIT), and not at the receiver and the eavesdropper, when achieving secrecy in fading wiretap channels. The key idea is that, with only CSIT, the transmitter can pre-compensate for the amplitude and phase distortions on the main channel. This allows the receiver to decode coherently even without knowledge of the CSI, while leaving the eavesdropper confused by the unknown variations of its own channel. When the channel is reciprocal, this CSI assumption can be achieved in practice through reverse training, i.e., by having the receiver emit the training signal so that the transmitter can estimate the channel by itself. Two secrecy-enhancing transmission schemes are proposed to exploit the CSIT. The truncated channel inversion scheme is used when the receiver and the eavesdropper have no CSI available, and the truncated phase compensation scheme is adopted when they can practically measure the SNR. The achievable secrecy rates of these schemes are derived for both single-antenna and multi-antenna wireless fading scenarios. Numerical results show significant improvements in secrecy rate compared to the case with full CSI at all terminals.

IEEE Globecom Workshops (GC Wkshps)•Dec 1, 2014•6 citations

On secure beamforming for wiretap channels with partial channel state information at the transmitter

Pin-Hsun Lin, Shih‐Chun Lin, Szu-Hsiang Lai +1 more

In this paper, we consider the secure transmission in ergodic fast fading multiple-input single-output single-antenna-eavesdropper (MISOSE) wiretap channels with only the statistics of eavesdropper's channel state information at the transmitter (CSIT). Two kinds of the legitimate CSIT are assumed, that is, full and statistical legitimate CSIT. With full legitimate CSIT, we generalize and optimize the previously proposed artificial noise (AN) aided secure beamforming to improve its secrecy rate performance. The AN covariance matrix in our scheme is more flexible than previous scheme and the region of non-zero secrecy rate is enlarged significantly according to our simulations. For the case with statistical legitimate CSIT, we further prove that the secure beamforming is secrecy capacity achieving for the Rayleigh faded channels. In this case, the AN is not necessary. Extensions to cases where legitimate receiver and eavesdropper have multiple antennas will also be discussed.

Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC)•Dec 1, 2012•4 citations

Stochastic Orders, Alignments, and Ergodic Secrecy Capacity

Pin-Hsun Lin, Eduard Axel Jorswieck

We investigate the relation between different stochastic orders and the degradedness of a fast fading wiretap channel with statistical channel state information at the transmitter (CSIT). In particular, we derive sufficient conditions to identify the ergodic secrecy capacities for both single and multiple antenna cases even though there is only statistical CSIT. Introduction To design a wiretap code with higher secrecy rate, channel state information at the transmitter of the legitimate and eavesdropper's channels1 should be known to a certain degree. When there is perfect CSIT of both channels, the secrecy capacity of a Gaussian wiretap channel can be achieved by a Gaussian input. However, due to several practical issues such as (1) being a malicious user, Eve is by no means intending to feed back the correct CSI to Alice; (2) limited feedback bandwidth; (3) the delay caused by channel estimation; (4) the speed of channel variation, etc., it is more reasonable to consider cases where perfect CSIT is unavailable. In this chapter we consider the cases when only statistical CSIT of both channels from Alice to Bob and Alice to Eve, respectively, are available. One possible way to get such information from Eve virtually is as follows. For some bounded space like indoor parking lots or malls, it is possible to collect the channel statistics offline of most of the positions within that space, where the channel variation may be due to the movement of people or cars, etc. When Alice wants to transmit, she can use the known statistics measured offline of the channel between her and the unknown user closest to her as Eve's channel information to design her wiretap code for the worst-case scenario. Although the secrecy capacity formula for discrete memoryless non-degraded wiretap channels was proved in [1], the optimal selection of the auxiliary random variable and channel prefixing are still unknown for additive white Gaussian noise (AWGN) channels with partial CSIT in general. Only a few capacity results under the considered scenario are known, and are summarized as follows.

Cambridge University Press eBooks•Jun 16, 2017•1 citation

1 On Secrecy Capacity of Fast Fading MIMOME Wiretap Channels With Statistical CSIT

Shih‐Chun Lin, Cheng-Liang Lin

In this paper, we consider secure transmissions in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When the antennas at the legitimate receiver are more than (or equal to) those at the eavesdropper, we prove the first MIMOME secrecy capacity with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is to form an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of the submatrices to be the same as the eavesdropper's channel matrix. Next, under the total power constraint over all transmit antennas, we analytically solve the channel-input covariance matrix optimization problem to fully characterize the MIMOME secrecy capacity. Typically, the MIMOME optimization problems are non-concave. However, thanks to the proposed degraded channel, we can transform the stochastic MIMOME optimization problem to be a Schur-concave one and then find its solution. Besides total power constraint, we also investigate the secrecy capacity when the transmitter is subject to the practical per-antenna power constraint. The corresponding optimization problem is even more difficult since it is not Schur-concave. Under the two power constraints considered, the corresponding MIMOME secrecy capacities can both scale with the signal-to-noise ratios (SNR) when the difference between numbers of antennas at legitimate receiver and eavesdropper are large enough. However, when the legitimate receiver and eavesdropper have a single antenna each, such SNR scalings do not exist for both cases.

•Aug 16, 2016•44 citations
We provide a set of semantically secure achievable rates for the fast fading wiretap channel. In particular, we do so for the cases where there is channel state information at the transmitter (CSIT) for both the main and eavesdropper channels (full CSIT), for only the main channel (partial CSIT), and for neither channel (statistical CSIT). In the case of partial CSIT and statistical CSIT fast-fading channels, we show that this coding scheme can achieve the best known achievable rates. In the case of full CSIT fast-fading wiretap channels, we show that this coding scheme can actually achieve the secrecy capacity. In particular, this implies that the semantic secrecy capacity for these channels is equivalent to the weak and strong secrecy capacities. Moreover, we achieve these rates in a way that is non-invasive to existing systems and also happens to be explicitly given as well as efficient in implementation.
Reliable communication imposes an upper limit on the achievable rate, namely the Shannon capacity. Wyner's wiretap coding, which ensures a security constraint also in addition to reliability, results in decrease of the achievable rate. To mitigate the loss in the secrecy rate, we propose a coding scheme paper where we use sufficiently old messages as key and for this scheme prove that multiple messages are secure with respect to (w.r.t.) all the information possessed by the eavesdropper. We also show that we can achieve security in the strong sense. Next we consider a fading wiretap channel with full channel state information of the eavesdropper's channel and use our coding/decoding scheme to achieve secrecy capacity close to the Shannon capacity of the main channel (in the ergodic sense). Finally we also consider the case where the transmitter does not have the instantaneous information of the channel state of the eavesdropper, but only its distribution.
We consider the fast-fading Gaussian wiretap channel with single antenna nodes and without channel state information at the transmitter (CSIT), where the fading processes of the two links are arbitrary and independent of each other. We derive an upper bound to the secrecy capacity for this channel and an achievable rate as well. Subsequently, we identify a class of channel statistics for which the outer bound and the achievable rates are identical thereby characterizes the exact secrecy capacity of the channel. The class of channels with such channel statistics are called stochastically degraded in this paper. Many practical wireless settings including the Rayleigh fading environment fall under this stochastically degraded class. We illustrate our results by computing explicit expression for the secrecy capacity for Rayleigh distributed wiretap channels.
This work examines the advantages of having only channel state information at the transmitter (CSIT), and not at the receiver and the eavesdropper, when achieving secrecy in fading wiretap channels. The key idea is that, with only CSIT, the transmitter can pre-compensate for the amplitude and phase distortions on the main channel. This allows the receiver to decode coherently even without knowledge of the CSI, while leaving the eavesdropper confused by the unknown variations of its own channel. When the channel is reciprocal, this CSI assumption can be achieved in practice through reverse training, i.e., by having the receiver emit the training signal so that the transmitter can estimate the channel by itself. Two secrecy-enhancing transmission schemes are proposed to exploit the CSIT. The truncated channel inversion scheme is used when the receiver and the eavesdropper have no CSI available, and the truncated phase compensation scheme is adopted when they can practically measure the SNR. The achievable secrecy rates of these schemes are derived for both single-antenna and multi-antenna wireless fading scenarios. Numerical results show significant improvements in secrecy rate compared to the case with full CSI at all terminals.
In this paper, we consider the secure transmission in ergodic fast fading multiple-input single-output single-antenna-eavesdropper (MISOSE) wiretap channels with only the statistics of eavesdropper's channel state information at the transmitter (CSIT). Two kinds of the legitimate CSIT are assumed, that is, full and statistical legitimate CSIT. With full legitimate CSIT, we generalize and optimize the previously proposed artificial noise (AN) aided secure beamforming to improve its secrecy rate performance. The AN covariance matrix in our scheme is more flexible than previous scheme and the region of non-zero secrecy rate is enlarged significantly according to our simulations. For the case with statistical legitimate CSIT, we further prove that the secure beamforming is secrecy capacity achieving for the Rayleigh faded channels. In this case, the AN is not necessary. Extensions to cases where legitimate receiver and eavesdropper have multiple antennas will also be discussed.
We investigate the relation between different stochastic orders and the degradedness of a fast fading wiretap channel with statistical channel state information at the transmitter (CSIT). In particular, we derive sufficient conditions to identify the ergodic secrecy capacities for both single and multiple antenna cases even though there is only statistical CSIT. Introduction To design a wiretap code with higher secrecy rate, channel state information at the transmitter of the legitimate and eavesdropper's channels1 should be known to a certain degree. When there is perfect CSIT of both channels, the secrecy capacity of a Gaussian wiretap channel can be achieved by a Gaussian input. However, due to several practical issues such as (1) being a malicious user, Eve is by no means intending to feed back the correct CSI to Alice; (2) limited feedback bandwidth; (3) the delay caused by channel estimation; (4) the speed of channel variation, etc., it is more reasonable to consider cases where perfect CSIT is unavailable. In this chapter we consider the cases when only statistical CSIT of both channels from Alice to Bob and Alice to Eve, respectively, are available. One possible way to get such information from Eve virtually is as follows. For some bounded space like indoor parking lots or malls, it is possible to collect the channel statistics offline of most of the positions within that space, where the channel variation may be due to the movement of people or cars, etc. When Alice wants to transmit, she can use the known statistics measured offline of the channel between her and the unknown user closest to her as Eve's channel information to design her wiretap code for the worst-case scenario. Although the secrecy capacity formula for discrete memoryless non-degraded wiretap channels was proved in [1], the optimal selection of the auxiliary random variable and channel prefixing are still unknown for additive white Gaussian noise (AWGN) channels with partial CSIT in general. Only a few capacity results under the considered scenario are known, and are summarized as follows.
In this paper, we consider secure transmissions in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When the antennas at the legitimate receiver are more than (or equal to) those at the eavesdropper, we prove the first MIMOME secrecy capacity with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is to form an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of the submatrices to be the same as the eavesdropper's channel matrix. Next, under the total power constraint over all transmit antennas, we analytically solve the channel-input covariance matrix optimization problem to fully characterize the MIMOME secrecy capacity. Typically, the MIMOME optimization problems are non-concave. However, thanks to the proposed degraded channel, we can transform the stochastic MIMOME optimization problem to be a Schur-concave one and then find its solution. Besides total power constraint, we also investigate the secrecy capacity when the transmitter is subject to the practical per-antenna power constraint. The corresponding optimization problem is even more difficult since it is not Schur-concave. Under the two power constraints considered, the corresponding MIMOME secrecy capacities can both scale with the signal-to-noise ratios (SNR) when the difference between numbers of antennas at legitimate receiver and eavesdropper are large enough. However, when the legitimate receiver and eavesdropper have a single antenna each, such SNR scalings do not exist for both cases.