Random and high-agreement secret key generation from noisy wideband channels is challenging due to the autocorrelation inside the channel samples and compromised cross correlation between channel measurements of two keying parties. This paper studies the signal preprocessing algorithms to establish high-agreement uncorrelated secret key in the presence of channel independent eavesdroppers. We first propose a general mathematical model for various preprocessing schemes, including principal component analysis (PCA), discrete cosine transform (DCT) and wavelet transform (WT). Among preprocessing schemes, PCA is proved to achieve the optimal secret key rate. Next, PCA with common eigenvector has been found to outperform PCA with private eigenvector in terms of an overall consideration of key agreement, information leakage, and computational expense. Then, we propose a system level design of key generation, including quantization, information reconciliation, and privacy amplification. Numerical results verify that the key generation enhanced by PCA with common eigenvector can achieve secret key with high key generation rate, low key error rate, and good randomness.
Random and high-agreement secret key generation from noisy wideband channels is challenging due to the autocorrelation inside the channel samples and compromised cross correlation between channel measurements of two keying parties. This paper studies the signal preprocessing algorithms to establish high-agreement uncorrelated secret key in the presence of channel independent eavesdroppers. We first propose a general mathematical model for various preprocessing schemes, including principal component analysis (PCA), discrete cosine transform (DCT) and wavelet transform (WT). Among preprocessing schemes, PCA is proved to achieve the optimal secret key rate. Next, PCA with common eigenvector has been found to outperform PCA with private eigenvector in terms of an overall consideration of key agreement, information leakage, and computational expense. Then, we propose a system level design of key generation, including quantization, information reconciliation, and privacy amplification. Numerical results verify that the key generation enhanced by PCA with common eigenvector can achieve secret key with high key generation rate, low key error rate, and good randomness.
Physical layer secret key generation techniques have spurred much recent research interest. In general, the secret key establishment contains four main procedures: channel sounding, quantization, information reconciliation and privacy amplification. However, to overcome the non- reciprocity and correlation problems in key generation from orthogonal frequency division multiplexing (OFDM) channels, a preprocessing procedure is added to prepare inputs for quantization. This paper demonstrates the optimal preprocessing approach in secret key generation and addresses its practical problems in realization. More specifically, we first build the mathematical model of a preprocessing procedure. Then, we identify that principle component analysis (PCA) can achieve the optimal performance in this model from the perspective of secret key capacity. Next, we discuss the realization steps of PCA algorithm and the corresponding procedures to cooperate with it. The parameter design in matrix partitioning and covariance matrix calculation are also analyzed. Numerical results verify that the proposed PCA preprocessing outperforms other tall unitary transforms and thus, it can be used to generate secret key with high key generation rate (KGR), low key error rate (KER) and good randomness.
Due to the new channel characteristics, previous preprocessing methods for physical layer key generation cannot be directly applied in mmWave massive MIMO systems. Actually, due to the intolerable high computation complexity and time consumption caused by large dimension of massive MIMO channel, even the previous optimal preprocessing method principal component analysis (PCA) is not suitable. To address the problem, in this paper, we propose a lightweight preprocessing approach called beamspace refinement, which is suitable for mmWave massive MIMO channel by exploiting its channel characteristics namely sparsity. The proposed scheme brings the following advantages. 1) It is lightweight. The computational complexity is quiet low. Unlike the PCA scheme, the proposed scheme does not involve the exponential calculation of the number of antennas, which makes it very suitable for mmWave massive MIMO channel. 2) It is robust against noise. Thus, it can be used to generate secret key with quiet high-entropy and high bit agreement ratio even in low SNR regimes. Numerical results show that the proposed approach outperforms the previous method DCT, WT and PCA in terms of bit agreement ratio, and is on par with PCA in terms of key capacity. Besides, the increase of the antennas number can improve key agreement ratio in our scheme, which is beneficial for massive MIMO system.
ABSTRACT With the rise of Industry 5.0, smart cities, and the ever‐expanding use of general wireless networks, ensuring seamless communication and robust data security has become a critical challenge. Generating secure secret keys (SKG) through wireless channels is particularly complex in environments where noise and wideband conditions introduce discrepancies and autocorrelation in channel measurements. These issues compromise cross‐correlation and randomness, leading to substantial bit disagreements, distinct keys at the transceivers, and unsuccessful SKG. This research begins by outlining the mathematical model of the signal preprocessing technique called multiscale principal component analysis (MSPCA). Subsequently, it explores the performance of key generation when employing the proposed scheme. A holistic system‐level framework for creating initial shared keys is presented, encompassing quantization methods such as uniform multilevel quantization (UMQ) and encoding methods such as 3‐bit Gray encoding. Monte Carlo‐based simulations in an indoor scenario evaluate system efficacy using metrics like Pearson correlation coefficient, bit disagreement rate (BDR), randomness, and complexity. The proposed scheme achieves a BDR lower than 0.01, a correlation coefficient greater than 0.95, and passes all National Institute of Standards and Technology (NIST) randomness tests, establishing it as a viable solution for securing wireless systems. In the context of Industry 5.0 and smart city infrastructures, where seamless communication and robust data security are paramount, the proposed SKG framework offers significant potential. With its ability to ensure secure and reliable communication, this scheme can underpin the development of advanced wireless systems that cater to the high demands of interconnected ecosystems, enhancing resilience and trust in critical applications.
The inherent randomness of wireless radio channels can be employed to extract secrets, whenever the channel reciprocity holds. Privacy amplification is an ingredient step for removing the redundancy of key, of which, the mount of information leaked to potential eavesdroppers, is often difficult to determine. In this paper, we propose a secret-key generation scheme without privacy amplification, of which the disagreement of key is coordinated through the reconciliation of sample positions as did in the level-crossing scheme. Compared to the level-crossing scheme, the proposed approach accumulates the reliable samples and further employs multi-bit quantization for improving the rate of secret-key generation. The accumulated samples should be decorrelated for generating random keys. Through extensive simulations, we find that the Karhunen-Loève transform for decorrelation is very sensitive in implementation.
Secret keys can be generated and shared between two wireless nodes by measuring and encoding radio channel characteristics without ever revealing the secret key to an eavesdropper at a third location. This paper addresses bit extraction, i.e., the extraction of secret key bits from noisy radio channel measurements at two nodes such that the two secret keys reliably agree. Problems include 1) nonsimultaneous directional measurements, 2) correlated bit streams, and 3) low bit rate of secret key generation. This paper introduces high-rate uncorrelated bit extraction (HRUBE), a framework for interpolating, transforming for decorrelation, and encoding channel measurements using a multibit adaptive quantization scheme which allows multiple bits per component. We present an analysis of the probability of bit disagreement in generated secret keys, and we use experimental data to demonstrate the HRUBE scheme and to quantify its experimental performance. As two examples, the implemented HRUBE system can achieve 22 bits per second at a bit disagreement rate of 2.2 percent, or 10 bits per second at a bit disagreement rate of 0.54 percent.
Key generation is essential for protecting wireless networks. Based on wireless channel reciprocity, transceivers can generate shared secret keys by measuring their communicating channels. However, due to non-simultaneous measurements, asymmetric noises and other interferences, channel measurements collected by different transceivers are highly correlated but not identical and thus might have some discrepancies. Further, these discrepancies might lead to mismatches of bit sequences after quantization. The referred mismatches significantly affect the efficiency of key generation. In this paper, an efficient key generation scheme leveraging wireless channel reciprocity is proposed. To reduce the bit mismatch rate and enhance the efficiency of key generation, the involved transceivers separately apply discrete cosine transform (DCT) and inverse discrete cosine transform (IDCT) to pre-process their measurements. Then, the outputs of IDCT are quantified and encoded to establish the bit sequence. With the implementations of information reconciliation and privacy amplification, the shared secret key can be generated. Several experiments in real environments are conducted to evaluate the proposed scheme. During each experiment, the shared key is established from the received signal strength (RSS) of heterogeneous devices. The results of experiments demonstrate that the proposed scheme can efficiently generate shared secret keys between transceivers.