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arXiv:2110.12785

Random Matrix based Physical Layer Secret Key Generation in Static Channels

Zhuangkun Wei, Weisi Guo

Published Oct 25, 2021• 3 citations
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Abstract

Physical layer secret key generation exploits the reciprocal channel randomness for key generation and has proven to be an effective addition security layer in wireless communications. However, static or scarcely random channels require artificially induced dynamics to improve the secrecy performance, e.g., using intelligent reflecting surface (IRS). One key challenge is that the induced random phase from IRS is also reflected in the direction to eavesdroppers (Eve). This leakage enables Eve nodes to estimate the legitimate channels and secret key via a globally known pilot sequence. To mitigate the secret key leakage issue, we propose to exploit random matrix theory to inform the design of a new physical layer secret key generation (PL-SKG) algorithm. We prove that, when sending appropriate random Gaussian matrices, the singular values of Alice's and Bob's received signals follow a similar probability distribution. Leveraging these common singular values, we propose a random Gaussian matrix based PL-SKG (RGM PL-SKG), which avoids the usages of the globally known pilot and thereby prevents the aforementioned leakage issue. Our results show the following: (i) high noise resistance which leads to superior secret key rate (SKR) improvement (up to 300%) in low SNR regime, and (ii) general improved SKR performance against multiple colluded Eves. We believe our combination of random matrix theory and PL-SKG shows a new paradigm to secure the wireless communication channels.

DOI
10.48550/arxiv.2110.12785

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Physical layer secret key generation exploits the reciprocal channel randomness for key generation and has proven to be an effective addition security layer in wireless communications. However, static or scarcely random channels require artificially induced dynamics to improve the secrecy performance, e.g., using intelligent reflecting surface (IRS). One key challenge is that the induced random phase from IRS is also reflected in the direction to eavesdroppers (Eve). This leakage enables Eve nodes to estimate the legitimate channels and secret key via a globally known pilot sequence. To mitigate the secret key leakage issue, we propose to exploit random matrix theory to inform the design of a new physical layer secret key generation (PL-SKG) algorithm. We prove that, when sending appropriate random Gaussian matrices, the singular values of Alice's and Bob's received signals follow a similar probability distribution. Leveraging these common singular values, we propose a random Gaussian matrix based PL-SKG (RGM PL-SKG), which avoids the usages of the globally known pilot and thereby prevents the aforementioned leakage issue. Our results show the following: (i) high noise resistance which leads to superior secret key rate (SKR) improvement (up to 300%) in low SNR regime, and (ii) general improved SKR performance against multiple colluded Eves. We believe our combination of random matrix theory and PL-SKG shows a new paradigm to secure the wireless communication channels.
Physical-layer security (PLS) is superior to classical cryptography techniques due to its notion of perfect secrecy and independence to an eavesdropper's computational power. One form of PLS arises when Alice and Bob (the legitimate users) exchange signals to extract a common key from the random common channels. The drawback of extracting keys from wireless channels is the ample dependence on the dynamicity and fluctuations of the radio channel. However, some radio channels are constant such as line-of-sight (LoS) and can be estimated by Eve (an illegitimate user), or can be quite static in behavior due to the presence low-mobility users thus restricting the amount of randomness. This in turn lowers the secret key rate (SKR) defined as the number of bits of key generated per channel use. In this work, we aim to address this challenge by using a reconfigurable intelligent surface (RIS) to produce random phases at certain carefully curated intervals such that it disrupts the channel in low-entropy environments. We propose an RIS assisted key generation method, study its performance, and compare with benchmarks to observe the benefit of using an RIS while considering various important metrics such as key mismatch rate and average secret key throughput. Simulations are made to validate our theoretical findings showing an improvement in performance when an RIS is deployed.
Physical layer secret key generation (SKG) is a promising supplement for high-level encryption, which leverages the channel reciprocity and the natural randomness of wireless channel. However, practical implementations often exhibit static environment. To solve this problem, this paper proposes a novel secret key generation scheme assisted by an intelligent reflecting surface (IRS) which can smartly reconfigure the radio signal propagation to improve the secret key rate of SKG. Specially, we formulate the minimum achievable secret key capacity in the IRS-assisted multiple-input single-output (MISO) system with multiple eavesdroppers. Then, an optimization framework for designing IRS reflecting coefficients based on the secret key capacity lower bound is proposed. Numerical results show that our optimal IRS-assisted SKG scheme can achieve much higher achievable secret key capacity when compared with two benchmark schemes.
Physical layer key generation (PLKG) can significantly enhance the security of classic encryption schemes by enabling them to change their secret keys significantly faster and more efficient. However, due to the reliance of PLKG techniques on channel medium, reaching a high secret key rate is challenging in static environments. Recently, exploiting intelligent reflecting surface (IRS) as a means to induce randomness in static wireless channels has received significant research interest. However, the impact of spatial correlation between the IRS elements is rarely studied. To be specific, for the first time, in this contribution, we take into account a spatially correlated IRS which intends to enhance the secret key generation (SKG) rate in a static medium. Closed form analytical expressions for SKG rate are derived for the two cases of random phase shift and equal random phase shift for all the IRS elements. We also analyze the temporal correlation between the channel samples to ensure the randomness of the generated secret key sequence. We further formulate an optimization problem in which we determine the optimal portion of time within a coherence interval dedicated for the direct and indirect channel estimation. We show the accuracy and the fast convergence of our proposed sequential convex programming (SCP) based algorithm and discuss the various parameters affecting spatially correlated IRS assisted PLKG.
Two legitimate parties, referred to as Alice and Bob, wish to generate secret keys from the wireless channel in the presence of an eavesdropper, referred to as Eve, in order to use such keys for encryption and decryption. In general, the secret key rate highly depends on the coherence time of the channel. In particular, a straightforward method of generating secret keys in static environments results in ultra-low rates. In order to resolve this problem, we introduce a low-complexity method called induced randomness. In this method, Alice and Bob independently generate local randomness to be used together with the uniqueness of the wireless channel coefficients in order to enable high-rate secret key generation. In this work, two scenarios are considered: first, when Alice and Bob share a direct communication channel, and second, when Alice and Bob do not have a direct link and communicate through an untrusted relay. After exchanging the induced randomness, post-processing is done by Alice and Bob to generate highly-correlated samples that are used for the key generation. Such samples are then converted into bits, disparities between the sequences generated by Alice and Bob are mitigated, and the resulting sequences are then hashed to compensate for the information leakage to the eavesdropper and to allow consistency checking of the generated key bit sequences. We utilize semantic security measures and information-theoretic inequalities to upper bound the probability of successful eavesdropping attack in terms of the mutual information measures that can be numerically computed. Given certain reasonable system parameters this bound is numerically evaluated to be 2-31and 2-10.57in the first and the second scenario, respectively.
The development of reconfigurable intelligent surfaces (RIS) has recently advanced the research of physical layer security (PLS). Beneficial impacts of RIS include but are not limited to offering a new degree-of-freedom (DoF) for key-less PLS optimization, and increasing channel randomness for physical layer secret key generation (PL-SKG). However, there is a lack of research studying how adversarial RIS can be used to attack and obtain legitimate secret keys generated by PL-SKG. In this work, we show an Eve-controlled adversarial RIS (Eve-RIS), by inserting into the legitimate channel a random and reciprocal channel, can partially reconstruct the secret keys from the legitimate PL-SKG process. To operationalize this concept, we design Eve-RIS schemes against two PL-SKG techniques used: (i) the CSI-based PL-SKG, and (ii) the two-way cross multiplication based PL-SKG. The channel probing at Eve-RIS is realized by compressed sensing designs with a small number of radio-frequency (RF) chains. Then, the optimal RIS phase is obtained by maximizing the Eve-RIS inserted deceiving channel. Our analysis and results show that even with a passive RIS, our proposed Eve-RIS can achieve a high key match rate with legitimate users, and is resistant to most of the current defensive approaches. This means the novel Eve-RIS provides a new eavesdropping threat on PL-SKG, which can spur new research areas to counter adversarial RIS attacks.
This paper presents a random pilot full-duplex (FD) secret key generation scheme designed to enhance security in static wireless environments. In these environments, where inherent channel randomness is limited, efficiently extracting secret keys poses a significant challenge. The proposed scheme leverages the benefits of both FD operation and random pilot transmission to overcome this limitation and enhance the physical layer security. In this scheme, one of the FD nodes transmits random pilot signals, unknown to the eavesdropper, during the channel probing phase to artificially increase the shared randomness between the legitimate communicating nodes. By considering correlated eavesdropping, we derive the lower and upper bounds for the achievable secret key rate (SKR). The results reveal that the proposed FD scheme outperforms the HD scheme even in the presence of residual SI. Furthermore, the secret key rate can be improved by better SIC channel estimation and lower eavesdropper channel correlation.