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IEEE Virtual Conference on Communications (VCC)

Power-Line Physical-Layer Key Generation Study Based on Low Complexity 3-Wire 4-Port Modeling

Werner Henkel, Tai Him Yim, Aditya Ojha, Sumit Giri, Ehsan Olyaei Torshizi

Published Nov 4, 2025• 0 citations
Publisher

Abstract

We first present a simplified full ABCD or Smatrix model for a 3-wire powerline grid connection to support our simulations of physical-layer security to finally be able to obtain statically significant results. Typical in-house power-line cables consist of three wires labeled L (Line), N (Neutral), and PE (Protective Earth). $4 \times 4$ ABCD or S-parameter matrices are derived from the well-known $2 \times 2$ ABCD matrix known for 2-conductor transmission lines including a FEXT (Far-End CrossTalk) model for 8 of the 16 ABCD matrix elements. For a point-to-point ABCD matrix, bridge taps with loads over L and N are represented by their corresponding $\Delta$ circuit and its ABCD matrix to finally allow for simple matrix multiplication of the cascade of such line and bridge taps elements between two end points. As a first application that promises secret key generation we study transfer functions when introducing randomly changing reactive loads at the legitimate terminals. We observe that the phase response at a certain frequency is very suitable to be mapped to key elements. The resulting key distribution is close to uniform and the key disagreement rates for legitimate and eavesdropping channels are almost ideal, i.e., close to zero for the first and close to 0.5 for the latter.

DOI
10.1109/vcc67261.2025.11351151

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We first present a simplified full ABCD or Smatrix model for a 3-wire powerline grid connection to support our simulations of physical-layer security to finally be able to obtain statically significant results. Typical in-house power-line cables consist of three wires labeled L (Line), N (Neutral), and PE (Protective Earth). 4×44 \times 44×4 ABCD or S-parameter matrices are derived from the well-known 2×22 \times 22×2 ABCD matrix known for 2-conductor transmission lines including a FEXT (Far-End CrossTalk) model for 8 of the 16 ABCD matrix elements. For a point-to-point ABCD matrix, bridge taps with loads over L and N are represented by their corresponding Δ\DeltaΔ circuit and its ABCD matrix to finally allow for simple matrix multiplication of the cascade of such line and bridge taps elements between two end points. As a first application that promises secret key generation we study transfer functions when introducing randomly changing reactive loads at the legitimate terminals. We observe that the phase response at a certain frequency is very suitable to be mapped to key elements. The resulting key distribution is close to uniform and the key disagreement rates for legitimate and eavesdropping channels are almost ideal, i.e., close to zero for the first and close to 0.5 for the latter.
The transfer function of a power-line connection can be modified by terminations at the end terminals between L-N or also L-PE in common three-wire home wiring, likewise at other end points. Using random terminations with, e.g., reactive loads and varying appliance connections can provide the common randomness required for physical-layer key generation. The amplitude and phase of the transfer function are noticeably modified by these variations. Hence, both can potentially be quantized for key generation. For convenient use of a linear quantizer, we opted for the phase. Dependent on the network situation and the location of the varying loads, the transfer function can be made largely independent between legitimate and eavesdropping connections. In here, we investigate the use of random capacitive or inductive loads at the L-N endpoints that are also commonly used for power-line transmission. We use a simulation program that is also modeling all transfer functions in a 3 -wire system, although the results reported here would not be influenced much by crosstalk contributions. The simulation models the connection between two end-points as a back-bone with bridge taps. We determine the transfer factors S12S_{12}S12​ and S21S_{21}S21​ (ideally identical) instead of the transfer functions for legitimate and critical eavesdropper placements. We include a key reconciliation option and investigate the key disagreement rates for legitimate and eavesdropping connections and provide NIST test results.
Physical layer key generation is based on reciprocal channels providing common randomness, which was so far known from TDD wireless channels. This paper opens the door to wireline physical-layer security, especially focusing on power-line connections. Additionally to the known reciprocity, we now also provide randomization by terminating idle branching connections (e.g., empty sockets) with random (reactive) loads. Alternatively, unused pairs at the power-line modem's end may be terminated by random (reactive) loads. Simulation and measurement results are shown. We also indicate, how the actual key generation can be realized by quantizing a frequency range and using the position of notches of the transfer function or of transmission coefficients selecting a quantization interval and with it a binary label as a key segment. Key reconciliation can simply be realized by a publicly announced shift of the quantization grid. Applications are seen for in-home and industrial devices required to exchange data over the power-line network securely.
We have already shown in earlier publications that reciprocity of power-line channels, expressed by, e.g., S12= S21using scattering parameters, can provide the desired common randomness for physical layer key generation. We had used minima or maxima of those transfer S-parameters to select possible keys. The tree-like power-line topology with bridge taps that are imperfectly terminated, possibly just left open, provide the means to create deep notches and, of course, local maxima in between. Using those positions, however, does not work well under noise conditions and power-line channels are known for their stationary and non-stationary disturbances. Minima will just be filled by noise, maxima that are wider than the minima experience a ripple thereby making it difficult to obtain identical positions under uncorrelated noise at the legitimate users’ ends. To solve this issue, in here, we propose to instead use the amplitude values at maxima positions. Disturbances there are directly related to the noise amplitudes. High maxima and corresponding key sequences resulting from amplitude quantization of the transfer characteristic are then less error-prone. Further improvements to reduce noise effects are obvious, just like averaging measurements, smoothing over frequency, or just only accepting measurements above certain thresholds. Quantization of amplitudes is carried out in log domain and mapping to bit patterns is realized in a cyclic fashion together with Gray coding. Key reconciliation is realized by shifting measurements into the middle of quantization intervals.
Due to the inherent broadcast nature, power line communication (PLC) is vulnerable to eavesdropping. Traditionally, the secret keys are generated/distributed by pre-shared keys, adaptive tone mapping, or asymmetric encryption algorithm. All of these methods face problems such as high computational complexity, high cost, or less security. To solve the problem, a physical layer security (PLS)-based secret key generation (SKG) scheme aiming at the typical in-home broadband PLC network is proposed in this paper. However, the slowly time-varying characteristic and the serious noise interference in PLC channels will degrade the performance of the PLS-based SKG scheme. To break through the limitation of the randomness of PLC channels, two-way random signals are introduced. To make the SKG system more resistant to noise, the channel frequency response-based adaptive quantization (CFR-AQ) algorithm is designed, in which the amplitude threshold and the quantization level are adaptive to the noise power and the target key disagreement rate (KDR) to maximize the key generation rate (KGR). The performance is analyzed in two scenarios: single eavesdropper and multiple eavesdroppers. The simulation results demonstrate that the proposed scheme has a good overall performance in terms of KDR, KGR, and security with a lower complexity in the presence of single or multiple non-collusive eavesdroppers, and it can be regarded as an alternative solution to generate secret keys in PLC networks.
Physical-layer secret key generation (PSKG) stands as a promising privacy protection technique, establishing shared encryption keys through the analysis of highly correlated wireless channel measurements. This approach relies on exploiting reciprocal channel characteristics between uplink and downlink transmissions. Nonetheless, the distinct carrier frequencies employed for uplink and downlink in frequency-division duplexing (FDD) systems pose a challenge in identifying common features. This paper presents a novel approach that exploits the inherent reciprocity between scattering parameters of passive two-port networks within same frequency ranges to overcome this obstacle. By capitalizing this reciprocity and considering closely situated FDD bands, a seamless continuity is anticipated in phase differences extracted form the corresponding S-parameters, between neighboring antennas of an antenna array from both uplink and downlink directions. This continuity, thereby ensures consistency in the generated keys from both transmission ends. Furthermore, a two-stage pre-processing method is proposed to enhance performance effectively. Additionally, the paper suggests the utilization of polynomial curve-fitting through measurement data to improve reciprocity and proposes a non-linear framework for quantizing the merging points of the two FDD bands. A statistical analysis employing multiple linear regression is provided to determine the error probability associated with the generated keys. Empirical results validate the feasibility and effectiveness of the proposed key generation scheme, affirming its attributes in terms of randomness, efficiency, key distribution uniformity, and key disagreement ratio (KDR).
Leakage of information in power line communication (PLC) networks is a threat to privacy and security. A way to enhance security is to encode the transmitted information with the use of a secret key. If the communication channel exhibits common characteristics at both ends and these are unknown to a potential eavesdropper, then it is possible to locally generate a common secret key at the two communication ends without the need for sharing it through the broadcast channel. This is known as physical layer key generation. To this aim, known techniques have been developed exploiting the transfer function of symmetric channels. However, the PLC channel is in general not symmetric, but just reciprocal. Therefore, in this paper, we first analyze the characteristics of the channel to verify whether physical layer key generation can be implemented. Then, we propose two novel methods that exploit the reciprocity of the PLC channel to generate common information by the two intended users. This information is processed through different quantization techniques to generate secret keys locally. To assess the security of the generated keys, we analyze the spatial correlation of PLC channels. This allows verifying whether the eavesdropper’s channels are weakly correlated with the intended users’ channel. Consequently, it is found that the information leaked to a possible eavesdropper has very low correlation to the locally generated key. The analysis and proposed methods are validated on a measurement dataset.