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arXiv:1902.10998 · IEEE Vehicular Technology Conference

Shared Secret Key Generation via Carrier Frequency Offsets

Waqas Aman, Aneeqa Ijaz, Muhammad Mahboob Ur Rahman, Dushantha Nalin K. Jayakody, Haris Pervaiz

Published Apr 1, 2019• 12 citations
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Abstract

This work presents a novel method to generate secret keys shared between a legitimate node pair (Alice and Bob) to safeguard the communication between them from an unauthorized node (Eve). To this end, we exploit the reciprocal carrier frequency offset (CFO) between the legitimate node pair to extract common randomness out of it to generate shared secret keys. The proposed key generation algorithm involves standard steps: the legitimate nodes exchange binary phase-shift keying (BPSK) signals to perform blind CFO estimation on the received signals, and do equi-probable quantization of the noisy CFO estimates followed by information reconciliation-to distil a shared secret key. Furthermore, guided by the Allan deviation curve, we distinguish between the two frequency-stability regimes-when the randomly time-varying CFO process i) has memory, ii) is memoryless; thereafter, we compute the key generation rate for both regimes. Simulation results show that the key disagreement rate decreases exponentially with increase in the signal to noise ratio of the link between Alice and Bob. Additionally, the decipher probability of Eve decreases as soon as either of the two links observed by the Eve becomes more degraded compared to the link between Alice and Bob.

DOI
10.1109/vtcspring.2019.8746406

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This work presents a novel method to generate secret keys shared between a legitimate node pair (Alice and Bob) to safeguard the communication between them from an unauthorized node (Eve). To this end, we exploit the reciprocal carrier frequency offset (CFO) between the legitimate node pair to extract common randomness out of it to generate shared secret keys. The proposed key generation algorithm involves standard steps: the legitimate nodes exchange binary phase-shift keying (BPSK) signals to perform blind CFO estimation on the received signals, and do equi-probable quantization of the noisy CFO estimates followed by information reconciliation-to distil a shared secret key. Furthermore, guided by the Allan deviation curve, we distinguish between the two frequency-stability regimes-when the randomly time-varying CFO process i) has memory, ii) is memoryless; thereafter, we compute the key generation rate for both regimes. Simulation results show that the key disagreement rate decreases exponentially with increase in the signal to noise ratio of the link between Alice and Bob. Additionally, the decipher probability of Eve decreases as soon as either of the two links observed by the Eve becomes more degraded compared to the link between Alice and Bob.
Common Randomness (CR) provides sequences of random variables at two physically separated locations. Ideally, the random variables at the two locations should be identical, i.e., have low probability of discrepancy, and should have high entropy. Previous CR research has focused on CR for physical layer security (mainly physical layer secret key generation), where a low CR generation rate, i.e., a low rate of CR bits per second is sufficient. However, emerging semantic communication paradigms, e.g., identification via channels, require high CR rates. We develop and evaluate a Carrier Frequency Offset (CFO) based methodology for high-rate CR generation from reciprocal observations of a common wireless channel between two distinct wireless terminals. The proposed CFO-CR methodology proceeds in several stages, including channel probing, random parameter extraction, noise reduction, quantization, information reconciliation, and randomization. Our evaluations with single-carrier software-defined radios, for which we make measurement traces publicly available, indicate that high-rate CR generation should observe (probe) the CFO and employ a Savitzky Golay low-pass filter with a low cut-off frequency for noise reduction in conjunction with multi-bit quantization, Gray code encoding, and a shuffling based randomization. We provide insights into the tradeoffs between the reconciliation cost for correcting bit discrepancies and the CR generation parameters. Our proposed CFO-CR methodology can generate 2048 bits of CR at a comparatively low reconciliation cost of 72 bytes while only making 256 channel observations and passing all common randomness tests. For generating 2048 bits of CR, other state-of-the-art approaches either require more channel observations (≥2048\ge 2048≥2048) or incur a higher reconciliation cost (≥450\ge 450≥450bytes).
Symmetric cryptography is the de-facto approach to information security for ad-hoc underwater acoustic networks. The requirement is that all network nodes possess the same cryptographic keys and key distribution that happens offline. Thus, it is hardly possible to include a new keyless node during network operation. In addition, online key replenishment is an open problem. In this article, we tackle key distribution/replenishment by formulating a new protocol that generates a key between two trusted underwater acoustic nodes (Alice and Bob) without the need to exchange the key itself. The proposed protocol initially extracts common acoustic channel features between Alice and Bob after some signal exchanges. Then, each party uses these features to generate his/her own secret bits via a random sequence generator. To correct any differences in their secret bits, we propose two reconciliation methods that employ Reed–Solomon codes. At the last step of the protocol, a 256-bit cryptographic key is generated by feeding the reconciled secret bit string to the Secure Hash Algorithm 3. We evaluate the key generation rate of the proposed protocol with real acoustic data recorded from a littoral environment, in which Alice and Bob exchanged 915 channel probes over different link geometries. To assess security performance, we invent a passive eavesdropper, Eve, who is able to simulate the acoustic link between Alice and Bob. She uses her simulated channels and the same protocol to generate her keys. Our analysis demonstrates a tradeoff between the key generation rate of Alice and Bob and Eve's ability to extract the same key. Our best result shows that Alice and Bob can independently generate 567 keys out of 915 attempts while Eve does not have access to any of the keys.
This paper studies the problem of extracting common randomness (CR) or secret keys from correlated random sources observed by two legitimate parties, Alice and Bob, through public discussion in the presence of an eavesdropper, Eve. We propose a practical two-stage CR extraction framework. In the first stage, the variational probabilistic quantization (VPQ) step is introduced, where Alice and Bob employ probabilistic neural network (NN) encoders to map their observations into discrete, nearly uniform random variables (RVs) with high agreement probability while minimizing information leakage to Eve. This is realized through a variational learning objective combined with adversarial training. In the second stage, a secure sketch using code-offset construction reconciles the encoder outputs into identical secret keys, whose secrecy is guaranteed by the VPQ objective. As a representative application, we study physical layer key (PLK) generation. Beyond the traditional methods, which rely on the channel reciprocity principle and require two-way channel probing, thus suffering from large protocol overhead and being unsuitable in high mobility scenarios, we propose a sensing-based PLK generation method for integrated sensing and communications (ISAC) systems, where paired range-angle (RA) maps measured at Alice and Bob serve as correlated sources. The idea is verified through both end-to-end simulations and real-world software-defined radio (SDR) measurements, including scenarios where Eve has partial knowledge about Bob's position. The results demonstrate the feasibility and convincing performance of both the proposed CR extraction framework and sensing-based PLK generation method.
Abstract The vast majority of existing secret key generation protocols exploit the inherent randomness of the wireless channel as a common source of randomness. However, independent noise added at the receivers of the legitimate nodes affects the reciprocity of the channel. In this paper, we propose a new simple technique to generate the secret key that mitigates the effect of noise. Specifically, we exploit the estimated channel to generate a secondary random process (SRP) that is common between the two legitimate nodes. We compare the estimated channel gain and phase to a preset threshold. The moving differences between the locations at which the estimated channel gain and phase exceed the threshold are the realization of our SRP. We study the properties of our generated SRP and derive a closed form expression for the probability mass function of the realizations of our SRP. We simulate an orthogonal frequency division multiplexing system and show that our proposed technique provides a drastic improvement in the key bit mismatch rate between the legitimate nodes when compared with the techniques that exploit the estimated channel gain or phase directly. In addition to that, the secret key generated through our technique is longer than that generated by conventional techniques. Moreover, we compute the conditional probabilities used to estimate the secret key capacity. Copyright © 2016 John Wiley & Sons, Ltd.
Power domain non-orthogonal multiple access (NOMA) enhances spectral efficiency by superposing multiple users in the same time-frequency resource block at the expense of exposing the users' data. However, current approaches to improve the secrecy levels of users are limited to rate reduction. This paper proposes a secure NOMA system based on the shared randomness extracted from the reciprocal carrier frequency offsets (CFOs) between the transmitter-receiver pairs for M-ary phase-shift keying. As multiple users will have physically separated oscillators, it will result in independent CFOs among users. This randomness is used to introduce a constellation rotation in the transmitted symbols. We show that under ideal CFO estimates, the proposed approach achieves perfect secrecy among all NOMA users without introducing any rate reduction. We also demonstrate the practical applicability of the proposed approach by using a software-defined radio-based test bed.
The broadcast nature of wireless communications imposes the risk of information leakage to adversarial users or unauthorized receivers. Therefore, information security between intended users remains a challenging issue. Most of the current physical layer security techniques exploit channel randomness as a common source between two legitimate nodes to extract a secret key. In this paper, we propose a new simple technique to generate the secret key. Specifically, we exploit the estimated channel to generate a secondary random process (SRP) that is common between the two legitimate nodes. We compare the estimated channel gain and phase to a preset threshold. The moving differences between the locations at which the estimated channel gain and phase exceed the threshold are the realization of our SRP. We simulate an orthogonal frequency division multiplexing (OFDM) system and show that our proposed technique provides a drastic improvement in the key bit mismatch rate (BMR) between the legitimate nodes when compared to the techniques that exploit the estimated channel gain or phase directly. In addition to that, the secret key generated through our technique is longer than that generated by conventional techniques.