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IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

Improper Quantization Decision and Key Entropy Loss in Wireless Physical-Layer Security with False Channel Statistics Knowledge

Apirath Limmanee

Published Sep 12, 2022• 2 citations
Publisher

Abstract

Wireless physical-layer security is recently proposed for several types of cutting-edge networks, such as 5G and 6G. In wireless physical-layer security, it is usually suggested in literature that eavesdroppers need to locate themselves near legitimate transmitters or receivers if they want to steal some secret key information. By means of scenario analysis, this paper shows that if the eavesdropper knows the channel statistics better than the legitimate stations, e.g., know the K-factor estimates of Rician fading channel, they can exploit these knowledges to derive some secret key information. We define a concept called “improper quantization decision loss$k$” as the entropy loss in the generated key that can be obtained by the eavesdropper. We show step-by-step how the eavesdropper can obtain such information. We also propose mathematical expressions of$n$and derive some results based on empirical values of channel parameters available in literature. From our analytical result for an urban area case, the loss is as large as almost 4/5 of key information, thus requiring a privacy amplification process that yields about 1/5 of the original key length. With our new concept, the new upper and lower bounds of vulnerable key bits are derived.

DOI
10.1109/pimrc54779.2022.9977952

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In wireless physical-layer security, it is usually suggested in literature that eavesdroppers need to locate themselves near legitimate transmitters or receivers if they want to steal some secret key information. By means of scenario analysis, this paper shows that if the eavesdropper knows the channel statistics better than the legitimate stations, e.g., know the K-factor estimates of Rician fading channel, they can exploit these knowledges to derive some secret key information. We define a concept called “improper quantization decision loss $\left(I_{I D L}\right)$” as the entropy loss in the generated key that can be obtained by the eavesdropper. We show step-by-step how the eavesdropper can obtain such information. We also propose a mathematical expression and numerical value of $I_{I D L}$ based on empirical values of channel parameters available in literature. If the legitimate parties are aware of this approximated $I_{I D L}$, they will be able to design suitable privacy amplification scheme for preventing key information loss.

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Physical layer security (PLS) is a new paradigm aiming at securing communications between legitimate parties at the physical layer. Conventionally, achieving confidentiality in communication networks relies on cryptographic techniques such as public-key cryptography, secret-key distribution and symmetric encryption. Such techniques are deemed secure based on the assumption of limited computational abilities of a wiretapper. Given the relentless progress in computational capacities and the dynamic topology and proliferation of modern wireless networks, the relevance of the previous techniques in securing communications is more and more questionable and less and less reliable. In contrast to this paradigm, PLS does not assume a specific computational power at any eavesdropper, its premise to guarantee provable security via employing channel coding techniques at the physical layer exploiting the inherent randomness in most communication systems. In this dissertation, we investigate a particular aspect of PLS, which is secret-key agreement, also known as secret-sharing. In this setup, two legitimate parties try to distill a secret-key via the observation of correlated signals through a noisy wireless channel, in the presence of an eavesdropper who must be kept ignorant of the secret-key. Additionally, a noiseless public channel is made available to the legitimate parties to exchange public messages that are also accessible to the eavesdropper. Recall that key agreement is an important aspect toward realizing secure communications in the sense that the key can be used in a one-time pad scheme to send the confidential message. In the first part, our focus is on secret-sharing over Rayleigh fading quasi-static channels. We study the fundamental relationship relating the probability of error and a given target secret-key rate in the high power regime. This is characterized through the diversity multiplexing tradeoff (DMT) concept, that we define for our model and then characterize it. We show that the impact of the secrecy constraint is to reduce the effective number of transmit antennas by the number of antennas at the eavesdropper. Toward this characterization, we provide several schemes achieving the DMT and we highlight disparities between coding for the wiretap channel and coding for secret-key agreement. In the second part of the present work, we consider a fast-fading setting in which the wireless channels change during each channel use. We consider a correlated environment where transmit, legitimate receiver and eavesdropper antennas are correlated. We characterize the optimal strategy achieving the highest secret-key rate. We also identify the impact of correlation matrices and illustrate our analysis with various numerical results. Finally, we study the system from an energy-efficiency point of view and evaluate relevant metrics as the minimum energy required for sharing a secret-key bit and the wideband slope.

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Wireless physical-layer security is recently proposed for several types of cutting-edge networks, such as 5G and 6G. In wireless physical-layer security, it is usually suggested in literature that eavesdroppers need to locate themselves near legitimate transmitters or receivers if they want to steal some secret key information. By means of scenario analysis, this paper shows that if the eavesdropper knows the channel statistics better than the legitimate stations, e.g., know the K-factor estimates of Rician fading channel, they can exploit these knowledges to derive some secret key information. We define a concept called “improper quantization decision losskkk” as the entropy loss in the generated key that can be obtained by the eavesdropper. We show step-by-step how the eavesdropper can obtain such information. We also propose mathematical expressions ofnnnand derive some results based on empirical values of channel parameters available in literature. From our analytical result for an urban area case, the loss is as large as almost 4/5 of key information, thus requiring a privacy amplification process that yields about 1/5 of the original key length. With our new concept, the new upper and lower bounds of vulnerable key bits are derived.
In wireless physical-layer security, it is usually suggested in literature that eavesdroppers need to locate themselves near legitimate transmitters or receivers if they want to steal some secret key information. By means of scenario analysis, this paper shows that if the eavesdropper knows the channel statistics better than the legitimate stations, e.g., know the K-factor estimates of Rician fading channel, they can exploit these knowledges to derive some secret key information. We define a concept called “improper quantization decision loss (IIDL)\left(I_{I D L}\right)(IIDL​)” as the entropy loss in the generated key that can be obtained by the eavesdropper. We show step-by-step how the eavesdropper can obtain such information. We also propose a mathematical expression and numerical value of IIDLI_{I D L}IIDL​ based on empirical values of channel parameters available in literature. If the legitimate parties are aware of this approximated IIDLI_{I D L}IIDL​, they will be able to design suitable privacy amplification scheme for preventing key information loss.
Information security has been a very important issue in wireless networks. With the ever-increasing amount of data being exchanged over wireless networks, the confidentiality of information needs to be protected from unauthorized users called eavesdropper. Due to the broadcast nature of the wireless medium, the transmissions between legitimate users maybe overheard and intercepted by the unauthorized parties, which makes wireless transmission vulnerable to potential eavesdropping attacks. The security of wireless communications plays an increasingly important role in the cybercrime defense against unauthorized activities. We consider the wireless physical layer security which has been explored for the sake of enhancing the protection of wireless communications against eavesdroppers. We consider the problem of secret communication through Rayleigh fading channel in the presence of an eavesdropper in which the transmitter knows the channel state information of both the main and eavesdropper channel. Then, we analyze the average capacity of the main channel and eavesdropper channel from which an expression of secrecy capacity is derived based on the cumulative distribution function and probability density function of the signal to noise ratio. We also analyze an expression for the symbol error rate of the main channel, and the outage probability is obtained for the main transmission. Finally, we perform the numerical results in MATLAB.
We present a physical layer approach aimed at providing information-theoretic security in wireless communication systems. Our secret key agreement scheme, which uses state-of-the-art error correcting codes and borrows ideas from quantum key distribution such as Gaussian reconciliation and privacy amplification, is capable of exploiting the physical properties of wireless fading channels in order to generate secret encryption keys. Focusing on the case of imperfect channel knowledge, we provide a performance analysis of the proposed security sub-system - both In theory and in practice
There is growing interest in wireless security methods that provide strong or even perfect secrecy by taking advantage of features of the physical propagation channel. In advantage-based methods, high channel quality in an average or opportunistic sense is exploited between two legitimate nodes, such that nonzero secrecy capacity can be achieved. Since such methods require bounds on the quality of the eavesdropper channel, they are somewhat impractical. Secret key generation based on tracking channel evolution in time division duplex systems is a more attractive option, where two nodes generate secret key bits based on a mutually known random channel. Since the eavesdropper channel is typically independent of the legitimate channel, the key can only be broken by brute force attacks, which are difficult when new keys are continuously generated. In this paper, the information theoretic limits of key generation schemes are investigated, based on the level of estimation error, temporal correlation, and dependence of the eavesdropper and legitimate channels. Three practical candidate key generation schemes are also considered: channel quantization and channel quantization with guardband.
This work aims at addressing two critical security issues residing in the physical layer of wireless networks, namely intelligent jamming and eavesdropping. In the first two chapters we study the problem of jamming in a fixed-rate transmission system with fading, under the general assumption that the jammer has no knowledge about either the codebook used by the legitimate communication terminals, or the source’s output. Both transmitter and jammer are subject to power constraints which can be enforced over each codeword (peak) or over all codewords (average). All our jamming problems are formulated as zero-sum games, having the probability of outage as pay-off function and power control functions as strategies. We provide a comprehensive coverage of these problems, under fast and slow fading, peak and average power constraints, pure and mixed strategies, with and without channel state information (CSI) feedback. Contributions to the eavesdropping problem include a novel feedback scheme for transmitting secret messages between two legitimate parties, over an eavesdropped communication link, presented in Chapter 4. Relative to Wyner’s traditional encoding scheme, our feedback-based encoding often yields larger rate-equivocation regions and achievable secrecy rates. More importantly, by exploiting the channel randomness inherent in the feedback channels, our scheme achieves a strictly positive secrecy rate even when the eavesdropper’s channel is less noisy than the legitimate receiver’s channel. In Chapter 5 we study the problem of active eavesdropping in fast fading channels. The active eavesdropper is a more powerful adversary than the classical eavesdropper. It can choose between two functional modes: eavesdropping the transmission between the legitimate parties (Ex mode), and jamming it (Jx mode) – the active eavesdropper cannot function in full duplex mode. We consider two scenarios: the best-case scenario, when the transmitter knows the eavesdropper’s strategy in advance – and hence can adaptively choose an encoding strategy – and the worst-case scenario, when the active eavesdropper can choose its strategy based on the legitimate transmitter-receiver pair’s strategy. For the second scenario, we introduce a novel encoding scheme, based on very limited and unprotected feedback – the Block-Markov Wyner (BMW) encoding scheme – which outperforms any schemes currently available.
Physical layer security (PLS) is a new paradigm aiming at securing communications between legitimate parties at the physical layer. Conventionally, achieving confidentiality in communication networks relies on cryptographic techniques such as public-key cryptography, secret-key distribution and symmetric encryption. Such techniques are deemed secure based on the assumption of limited computational abilities of a wiretapper. Given the relentless progress in computational capacities and the dynamic topology and proliferation of modern wireless networks, the relevance of the previous techniques in securing communications is more and more questionable and less and less reliable. In contrast to this paradigm, PLS does not assume a specific computational power at any eavesdropper, its premise to guarantee provable security via employing channel coding techniques at the physical layer exploiting the inherent randomness in most communication systems. In this dissertation, we investigate a particular aspect of PLS, which is secret-key agreement, also known as secret-sharing. In this setup, two legitimate parties try to distill a secret-key via the observation of correlated signals through a noisy wireless channel, in the presence of an eavesdropper who must be kept ignorant of the secret-key. Additionally, a noiseless public channel is made available to the legitimate parties to exchange public messages that are also accessible to the eavesdropper. Recall that key agreement is an important aspect toward realizing secure communications in the sense that the key can be used in a one-time pad scheme to send the confidential message. In the first part, our focus is on secret-sharing over Rayleigh fading quasi-static channels. We study the fundamental relationship relating the probability of error and a given target secret-key rate in the high power regime. This is characterized through the diversity multiplexing tradeoff (DMT) concept, that we define for our model and then characterize it. We show that the impact of the secrecy constraint is to reduce the effective number of transmit antennas by the number of antennas at the eavesdropper. Toward this characterization, we provide several schemes achieving the DMT and we highlight disparities between coding for the wiretap channel and coding for secret-key agreement. In the second part of the present work, we consider a fast-fading setting in which the wireless channels change during each channel use. We consider a correlated environment where transmit, legitimate receiver and eavesdropper antennas are correlated. We characterize the optimal strategy achieving the highest secret-key rate. We also identify the impact of correlation matrices and illustrate our analysis with various numerical results. Finally, we study the system from an energy-efficiency point of view and evaluate relevant metrics as the minimum energy required for sharing a secret-key bit and the wideband slope.