Vector quantization schemes are proposed to extract secret keys from correlated wireless fading channels. By assuming that the channel between two terminals are reciprocal, its estimates can be used as the common randomness for generating secret keys at the two terminals. Most schemes in the literature assume that channels are independent over time and utilize scalar quantization on each element of the estimated channel vector to generate secret key bits. These schemes are simple to implement but yield high key disagreement probability (KDP) at low SNR and low key entropy when channels are highly correlated. In this work, two vector quantization schemes, namely, the minimum key disagreement probability (MKDP) and the minimum quadratic distortion (MQD) secret key generation schemes, are proposed to effectively extract secret keys from correlated channel estimates. The vector quantizers are derived using KDP and QD as the respective distortion measures. To further reduce KDP, each channel vector is first pre-multiplied by an appropriately chosen unitary matrix to rotate the vector away from quantization cell boundaries. The MKDP scheme achieves the lowest KDP but requires high complexity whereas the MQD scheme yields lower complexity but at the cost of slightly increased KDP. Computer simulations are provided to demonstrate the effectiveness of the proposed vector quantization schemes.
Vector quantization schemes are proposed to extract secret keys from correlated wireless fading channels. By assuming that the channel between two terminals are reciprocal, its estimates can be used as the common randomness for generating secret keys at the two terminals. Most schemes in the literature assume that channels are independent over time and utilize scalar quantization on each element of the estimated channel vector to generate secret key bits. These schemes are simple to implement but yield high key disagreement probability (KDP) at low SNR and low key entropy when channels are highly correlated. In this work, two vector quantization schemes, namely, the minimum key disagreement probability (MKDP) and the minimum quadratic distortion (MQD) secret key generation schemes, are proposed to effectively extract secret keys from correlated channel estimates. The vector quantizers are derived using KDP and QD as the respective distortion measures. To further reduce KDP, each channel vector is first pre-multiplied by an appropriately chosen unitary matrix to rotate the vector away from quantization cell boundaries. The MKDP scheme achieves the lowest KDP but requires high complexity whereas the MQD scheme yields lower complexity but at the cost of slightly increased KDP. Computer simulations are provided to demonstrate the effectiveness of the proposed vector quantization schemes.
This paper proposes a vector-quantization-based secret key generation (SKG) procedure to efficiently extract shared secret keys from correlated channel observations at two communicating terminals, Alice and Bob. Most existing SKG schemes utilize scalar quantization to extract secret key bits separately from each individual channel observation. This approach is simple to implement but yields higher key disagreement probability (or lower key entropy) compared with vector-quantization-based approaches. However, regardless of the quantizer design, quantization for SKG often suffers from the so-called cell-boundary problem, which occurs when the channel observations at Alice and Bob lie close to the quantization cell boundaries, resulting in high probability of key disagreement. In this paper, a general SKG procedure that utilizes sample and quantizer selection techniques to avoid this problem is first proposed. The vector quantizer adopted in the above procedure is designed by minimizing the quadratic distortion between the true channel vector and the noisy observation at Alice (or Bob). Then, by considering the case where the eavesdropper (Eve) may observe a channel vector that is correlated with that observed by Alice and Bob, a clustered key mapping scheme that assigns each secret key to multiple quantization cells in different clusters is also proposed to induce additional randomness at Eve and, thus, maintain high conditional key entropy. The effectiveness of the proposed schemes is demonstrated through computer simulations.
By exploiting multipath fading channels as a source of common randomness, physical layer (PHY) based key generation protocols allow two terminals with correlated observations to generate secret keys with information-theoretical security. The state of the art, however, still suffers from major limitations,e.g., low key generation rate, lower entropy of key bits and a high reliance on node mobility. In this paper, a novel cooperative key generation protocol is developed to facilitate high-rate key generation in narrowband fading channels, where two keying nodes extract the phase randomness of the fading channel with the aid of relay node(s). For the first time, we explicitly consider the effect of estimation methods on the extraction of secret key bits from the underlying fading channels and focus on a popular statistical method - maximum likelihood estimation (MLE). The performance of the cooperative key generation scheme is extensively evaluated theoretically. We successfully establish both a theoretical upper bound on the maximum secret key rate from mutual information of correlated random sources and a more practical upper bound from Cramer-Rao bound (CRB) in estimation theory. Numerical examples and simulation studies are also presented to demonstrate the performance of the cooperative key generation system. The results show that the key rate can be improved by a couple of orders of magnitude compared to the existing approaches.
Fundamental limits of secret-key agreement over reciprocal wireless channels are investigated. We consider a two-way block-fading channel where the channel gains in the forward and reverse links between the legitimate terminals are correlated. The channel gains between the legitimate terminals are not revealed to any terminal, whereas the channel gains of the eavesdropper are revealed to the eavesdropper. We propose a two-phase transmission scheme, that reserves a certain portion of each coherence block for channel estimation, and the remainder of the coherence block for correlated source generation. The resulting secret-key involves contributions of both channel sequences and source sequences, with the contribution of the latter becoming dominant as the coherence period increases. We also establish an upper bound on the secret-key capacity, which has a form structurally similar to the lower bound. Our upper and lower bounds coincide in the limit of high signal-to-noise-ratio (SNR) and large coherence period, thus establishing the secret-key agreement capacity in this asymptotic regime. Numerical results indicate that the proposed scheme achieves significant gains over training-only schemes, even for moderate SNR and small coherence periods, thus implying the necessity of randomness-sharing in practical secret-key generation systems.
In order to find an effective secret key generation scheme in wireless networks, many based on received signal strength methods have been proposed.However, the secret bit rates of existing schemes are relatively low.To resolve the problem of low generation rate, a vector quantization scheme is proposed in this paper where channel measurements are reused and every measurement can be quantified into two bits without increasing mismatching rate.Performance simulation results show that our proposed scheme improves the key generation rate almost twice at high entropy in comparison to the traditional schemes.At the same time, our scheme passes the randomness tests of the NIST test suite.
Secret keys can be generated from reciprocal channels to be used for shared secret key encryption. However, challenges arise in practical scenarios from non-reciprocal measurements of reciprocal channels due to changing channel conditions, hardware inaccuracies and estimation errors resulting in low key generation rate (KGR) and high key disagreement rates (KDR). To combat these practical issues, we propose KNEW Key Generation using NEural Networks from Wireless Channels, which extracts the implicit features of channel in a compressed form to derive keys with high agreement rate. Two Neural Networks (NNs) are trained simultaneously to map each other's channel estimates to a different domain, the latent space, which remains inaccessible to adversaries. The model also minimizes the distance between the latent spaces generated by two trusted pair of nodes, thus improving the KDR. Our simulated results demonstrate that the latent vectors of the legitimate parties are highly correlated yielding high KGR (≈ 64 bits per measurement) and low KDR (<0.05 in most cases). Our experiments with over-the-air signals show that the model can adapt to realistic channels and hardware inaccuracies, yielding over 32 bits of key per channel estimation without any mismatch.
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.