Physical layer secret key generation using discrete wavelet packet transform

Abstract

Physical layer secret key generation leveraging reciprocity principle of the wireless channel is a promising substitute for traditional cryptography. However, in certain scenarios, the channel measurements extracted by the wireless transceivers are of high correlation but not similar. Therefore, preprocessing channel measurements prior to quantization is highly essential to facilitate successful generation of shared secret keys at the transceivers. In this paper, we put forth the idea of employing discrete wavelet packet transform (DWPT) for dynamic secret key generation in indoor environments. We propose two schemes which are employed at both the transceivers. Proposed method 1 (Prop. method-1) involves fixing the wavelet packet coefficients of selected terminal nodes in the wavelet packet tree to zero and proposed method 2 (Prop. method-2) involves compression of wavelet packet coefficients of selected terminal nodes. The performance of the proposed methods are evaluated using Pearson correlation coefficient, bit disagreement rate (BDR) and NIST randomness tests. Simulation results demonstrate that, Prop. method-1 performs well in terms of cross-correlation, especially when the measurement error variance is high. In contrast to Prop. method-1, Prop. method-2 renders better randomness at the expense of slightly reduced cross-correlation whilst both methods pass all eight NIST randomness tests. The tradeoff between cross-correlation and randomness can be improved owing to the richer signal analysis offered by DWPT. The simulation results are compared against existing works for validating performance of the proposed methods. Simulation results demonstrate that, DWPT based preprocessing is a highly promising solution for successful physical layer secret key generation.

Introduction

With the progress of wireless networking, huge amount of data exchange take place over the wireless medium. However, because of the inherent broadcast nature of the wireless medium, the intruder can eavesdrop or jam the legitimate channel with ease, if the intruder is present within the communication range of the legitimate transceivers. This concern for wireless security can be resolved by the algorithms developed for ensuring security of the physical layer. Unlike the traditional cryptographic techniques which the intruder can easily decrypt with the help of adequate computational power, physical layer security (PLS) [1], [2], [3], [4], [5] schemes cannot be exploited with ease even with the backup of enormous computational power, as PLS schemes leverage temporal variation and reciprocity property of the wireless channel to generate shared secret keys. To generate shared secret keys, channel probing, quantization, encoding, information reconciliation and privacy amplification stages are carried out separately at both the transmitter and receiver.

Wireless channel is probed by the involved transceivers during coherence time so that the channel measurements collected by Alice and Bob are correlated. Even though the channel measurements of Alice and Bob are correlated, the measurements are not identical in certain scenarios, because of the presence of high measurement error variances. Channel measurements of Alice and Bob holding high measurement error variance on direct quantization yields distinct secret keys at the transmitter and receiver leading to failure of the secret key generation system. Therefore, preprocessing the channel measurements before quantization is highly essential for the successful generation of shared secret keys. Currently, several signal denoising and compression techniques are available. However, wavelet transform has emerged as one of the most widely employed preprocessing technique, as it performs time–frequency localization in contrast to the Fourier transform. Similarly, wavelet packet transform [6], [7], [8], [9] is also employed for improving the correlation between signals. However, most of the analysis involving wavelet packet transform is performed on biomedical signals. Due to the richer signal analysis offered by DWPT, the technique could be a promising tool to enhance cross correlation of the measurement sequences of Alice and Bob for generating shared secret keys. This served as the motivation for investigating the feasibility of DWPT in the generation of shared secret keys. We have proposed two schemes based on DWPT to study the effect of DWPT preprocessing for secret key generation. Besides the wideband communication application, the proposed scheme has a potential application in narrowband scenarios, e.g., IEEE802.15.4 [10], [11] and Lora [12], [13].

To the best of our knowledge, this work is the first attempt in literature to employ DWPT for generating shared secret keys. Different wavelets have different impact on preprocessing a signal. Therefore, finding out a wavelet family which renders optimal performance is essential. Among the different wavelets available, we have chosen Daubechies, Symlet and Coiflet wavelets of order 4, denoted as $Db4$, $Sym4$ and $Coif4$, for DWPT preprocessing.

Our contributions are as follows,

• For the first time in literature, a DWPT based preprocessing scheme is developed for physical layer secret key generation, owing to the rich signal analysis offered by DWPT.

• To perform DWPT preprocessing, two methods are proposed and validated using Monte Carlo simulations to explore the potential of DWPT in rendering higher correlation than discrete wavelet transform (DWT). An extensive analysis of $Coif4$, $Sym4$ and $Db4$ wavelets in DWPT preprocessing is carried out and evaluated in terms of correlation, BDR, randomness and complexity.

• Through extensive analysis, the ability of DWPT preprocessing to render reduced BDR compared to DWT is discussed. Moreover, a discussion on improving the DWPT preprocessing further, so as to render optimum preprocessing and randomness is also provided.

In literature, several schemes are proposed to generate dynamic secret keys for enhancing PLS and preprocessing of channel measurements has gained much importance as it facilitates successful generation of secret keys. The channel measurements collected by the transceivers contain too many discrepancies and the measurements will be highly correlated but not similar. This is reflected in the secret keys generated thereby leading to failure of the SKG system. To address this issue, in [14], a DWT based compressor is applied to the channel measurements of Alice and Bob before quantization. The proposed scheme is evaluated in terms of bit mismatch rate (BMR), secret bit rate, randomness and complexity. In [15], preprocessing is performed using principal component analysis (PCA). Here, a thorough analysis of PCA, DWT and discrete cosine transform (DCT) is carried out by deriving the signal processing model mathematically to evaluate its suitability for SKG. Moreover, PCA common eigenvector (PCA CEVD) scheme is developed which preprocess the channel measurements very effectively. Results demonstrate that PCA renders better preprocessing than DWT and DCT. In [16] and [17], DCT is employed for preprocessing the channel measurements, but the SKG scheme, SKYGlow, is designed only for IoT devices such as bluetooth low energy transceivers and IEEE 802.15.4.

In [18], authors employ wavelet transform to develop a shared symmetric cryptographic key for wireless body area networks for securing transmission of confidential medical information. Further, a fuzzy vault based key distribution protocol is also developed. In this scheme, apart from enhancing PLS, the implementation and computational complexity is also greatly reduced. Similarly, in [19], key generation for wireless sensor network and IEEE 802.15.4 is explored wherein the major concern of key revocation and recovery is addressed. The technique proposed in [19] is energy efficient and a near 100% key reconciliation rate is achieved. In [20], for efficient generation of secret keys, the randomness from both time and frequency domains are fully exploited. The cross correlation of channel measurements are further improved using a low pass filter. Similarly, in [21], authors prove that, fine grained channel information and high rate of bit generation can be achieved when channel responses of OFDM subcarriers are considered for SKG from both static and mobile environments. Also, unlike other techniques mentioned above, a novel technique named, channel gain complement (CGC) assisted secret key extraction scheme is developed for coping the non reciprocity issues of the wireless medium. Again, in [22], authors have utilized phase information of estimated channel state information (CSI) for SKG in TDD–OFDM systems, considering multipath fading channel. Here, a guard band scheme which achieves an improved SKG rate, by compromising a small channel phase information loss is proposed. In [23], the authors perform wavelet preprocessing and propose an adaptive equal probability quantization scheme to enhance generation of secret keys by reducing the BMR. The issues of low entropy secret keys due to scalar quantization is addressed in [24] by developing a vector quantization based SKG scheme. The proposed scheme aims at eliminating the cell boundary problem in quantization. Further, a clustered key mapping scheme is also proposed to maintain the high conditional entropy by inducing extra randomness at the adversary.

In [25], authors propose to employ singular value decomposition based quantization scheme to increase the length of the generated secret keys in MIMO systems by exploiting the phase and amplitude of the estimated channel coefficients. In [26], authors propose a scheme to generate shared secret keys by exploiting channel phase response in which, only a single node probes the channel and implements quantization. The key thus generated is distributed before equalizing, after mapping. Further, an authentication scheme using the generated secret key is also proposed. There is no preprocessing of channel measurements performed in this work. SKG in static environments is highly challenging, therefore, in [27], authors generate an efficient scheme based on induced randomness for generating shared secret keys from static channels. In this scheme, the legitimate transceivers induce randomness locally. The proposed scheme is of low complexity and hence will be beneficial for IoT networks as well. To prove the efficiency of the scheme, authors have evaluated the performance of the scheme for a realistic 5G mm wave testbed. Similarly, in [28], authors generate shared secret keys by exploiting channel phase of the received signals in MIMO systems. The proposed scheme renders good key generation rate (KGR) performance, for example, the KGR obtained in MIMO systems is 9 times greater than SISO systems, as MIMO systems provide more random variables in contrast to SISO systems. In [29], authors perform wavelet preprocessing to enhance correlation between the legitimate channels by exploiting RSSI measurements collected at the transceivers. To apply wavelet denoising, rigursure thresholding scheme is chosen. To reduce the high bit mismatch rate, an adaptive quantization scheme is employed to quantize the channel measurements. In [30], authors propose a secure group key agreement protocol to secure mobile ad hoc networks. Apart from rendering the general security requirement, the proposed protocol ensures secure dynamic operation within the group as well. The scheme is highly efficient as it reduces the computational and communication costs involved.

The manuscript is organized as follows. Section 2 describes the system and adversary model. Then, in Section 3, we elaborate the methodology followed. Section 4 describes the basic steps in SKG. Section 5 provides the performance evaluation metrics. Section 6 elaborates the simulation results and finally, Section 7 concludes the paper. We use the following notations throughout the manuscript, unless otherwise specified, upper bold face letters denote matrices and lower bold face letters denote column vectors.