# Secure PHY Layer Key Generation in the Asymmetric Power Line Communication Channel

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Channel-Based Security Approaches in Symmetric Channels

- Channel sensing: Alice, Bob, and Eve get the observations of length n of the CSI ${X}^{n}=[{X}_{1},\cdots ,{X}_{n}]$, ${Y}^{n}=[{Y}_{1},\cdots ,{Y}_{n}]$, and ${Z}^{n}=[{Z}_{1},\cdots ,{Z}_{n}]$, respectively, where the observations can be performed in the time, frequency, or space domain or a combination of them.
- Key reconciliation via public discussion: In order to agree on a secret key, Alice and Bob can communicate through the PB channel and send to each other a deterministic communication sequence as follows. They generate the random variables ${U}_{A}$ and ${U}_{B}$, respectively, for initialization. Then, they alternatively send to each other the two sequences ${S}_{A}^{k}=[{S}_{{A}_{1}},\cdots ,{S}_{{A}_{k}}]$ and ${S}_{B}^{k}=[{S}_{{B}_{1}},\cdots ,{S}_{{B}_{k}}]$, respectively, where for each step i, we have ${S}_{{A}_{i}}={f}_{{A}_{i}}\left({U}_{A},{X}^{n},{S}_{{B}_{i-1}}\right)$ and ${S}_{{B}_{i}}={f}_{{B}_{i}}\left({U}_{B},{Y}^{n},{S}_{{A}_{i-1}}\right)$. At the end of the communication step, Alice and Bob determine the respective keys as ${K}_{A}={f}_{{A}_{k+1}}({U}_{A},{X}^{n},{S}_{B}^{k})$ and ${K}_{B}={f}_{{B}_{k+1}}({U}_{B},{Y}^{n},{S}_{A}^{k})$. Different protocols have been proposed to implement both the reconciliation procedure, implemented either with cascade or error correcting codes, and the privacy amplification. An extended series of references about this can be found in [16].

## 3. Symmetries of the Power Line Channel

- When the current ${I}_{g}$ is applied to any of the two ports, the open circuit voltage measured at the other port is the same. Referring to Figure 3a, this means that the ratios:$${Z}_{21}={V}_{2}/{I}_{1g}\phantom{\rule{1.em}{0ex}}\mathrm{and}\phantom{\rule{1.em}{0ex}}{Z}_{12}={V}_{1}/{I}_{2g},$$
- When the voltage ${V}_{g}$ is applied to any of the two ports, the short circuit current measured at the other port is the same. Referring to Figure 3b, this means that the ratio:$${Y}_{21}={I}_{2}/{V}_{1g}\phantom{\rule{1.em}{0ex}}\mathrm{and}\phantom{\rule{1.em}{0ex}}{Y}_{12}={I}_{1}/{V}_{2g}$$

## 4. Key Generation in Half-Duplex PLC

#### 4.1. Time Domain Symmetry Technique

#### 4.2. Transmission Matrix Technique

- Binary: The quantized data are converted to binary sequences with Gray encoding to minimize the distance between symbols that are close to each other. Each binary symbol is used as a symbol of the key.
- Coded: The key is defined over an ${2}^{nbits}$-ary alphabet, and each symbol is made by the quantized value of the CSI at one frequency bin. One symbol at the end of the key sequence accounts for the actual value of the least significant bit. The actual key is generated by multiplying the values of all the symbols by the last one. This method is used to avoid data with a similar shape, but different amplitudes to produce similar keys.

#### 4.3. Computational Complexity

## 5. Practical Results

#### 5.1. Channel Correlation

#### 5.2. Time Domain Symmetry Technique Results

#### 5.3. Transmission Matrix Technique Results

#### 5.4. Quantization Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Wide-Sense Symmetry of Topology-Invariant Channels

## References

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**Figure 1.**Essential sketch of a power line network, where we highlight the presence of the transmitting user (Alice), the intended receiver (Bob), and the eavesdropper (Eve).

**Figure 3.**Trans-resistance (

**a**) and trans-conductance (

**b**) communication schemes in a power line network (PLN), with the generator either on Port 1 or on Port 2.

**Figure 5.**Example of a power line communication (PLC) channel transfer function in the two directions, in the frequency (

**a**) and time (

**b**) domain.

**Figure 7.**Correlation coefficients $\left|{\rho}^{H}\right|$ (

**left**) and ${\rho}_{abs}^{H}$ (

**right**) of the channel transfer functions for 200 channel realizations.

**Figure 8.**Correlation coefficients $|{\rho}^{Z}|$ (

**left**) and ${\rho}_{abs}^{Z}$ (

**right**) of the input impedances of 24 outlets in the same household.

**Figure 9.**Correlation R of the sequence of peaks computed by Alice, Bob, and Eve (

**a**) and their ratios (

**b**), considering the first M peaks.

**Figure 11.**$E\left[d\right]$ for different values M of selected peaks (

**a**) and N of the key length (

**b**). Solid and dashed lines refer to the Alice-Eveand Alice-Bob links, respectively.

**Figure 12.**$E\left[d\right]$ of the keys computed by Alice, Bob, and Eve (

**a**) and their ratios (

**b**), for different code lengths N and quantization methods. The ADC resolution is fixed to eight bits.

**Figure 13.**$E\left[d\right]$ of the keys computed by Alice, Bob, and Eve for different quantization bits and arranging methods, with $N=340$. Solid and dashed lines refer to the Alice-Eve and Alice-Bob links, respectively.

**Table 1.**$E\left[\rho \right]$ of the channel transfer function in different cases. CTF, channel transfer function.

Alice↔Bob | Alice↔Eve | |
---|---|---|

CTF (Equation (20)) | 0.4452 | 0.1668 |

CTF absolute values | 0.6298 | 0.4798 |

Impulse response | 0.4285 | 0.1147 |

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Passerini, F.; Tonello, A.M.
Secure PHY Layer Key Generation in the Asymmetric Power Line Communication Channel. *Electronics* **2020**, *9*, 605.
https://doi.org/10.3390/electronics9040605

**AMA Style**

Passerini F, Tonello AM.
Secure PHY Layer Key Generation in the Asymmetric Power Line Communication Channel. *Electronics*. 2020; 9(4):605.
https://doi.org/10.3390/electronics9040605

**Chicago/Turabian Style**

Passerini, Federico, and Andrea M. Tonello.
2020. "Secure PHY Layer Key Generation in the Asymmetric Power Line Communication Channel" *Electronics* 9, no. 4: 605.
https://doi.org/10.3390/electronics9040605