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.
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.
Secret key generation from correlated observations at Alice and Bob, in the presence of an eavesdropper Eve, underpins physical-layer security. Classical pipelines quantize by hand, amplify privacy afterwards, and optimize no objective tied to a key rate. We propose Variational Probabilistic Quantization (VPQ): neural encoders that map the correlated sources directly into a discrete key alphabet, trained by a variational adversarial objective whose entropy, mismatch, and leakage terms match the three terms of the one-way secret key rate. A linear code-offset secure sketch then reconciles the encoder outputs into an identical key without a separate privacy amplification step. We prove that the VPQ losses lower-bound the one-way secret key capacity of the induced source, and derive in closed form the optimal worst-case key rate over the source class of a given alphabet size and mismatch probability, attained by finite-field linear sketches. On Gaussian fading channels, VPQ leaks less to a correlated eavesdropper than one classical and two recent learning-based baselines, and Reed--Solomon reconciliation operates within the predicted finite-blocklength gap.
Two legitimate parties, referred to as Alice and Bob, wish to generate secret keys from the wireless channel in the presence of an eavesdropper, referred to as Eve, in order to use such keys for encryption and decryption. In general, the secret key rate highly depends on the coherence time of the channel. In particular, a straightforward method of generating secret keys in static environments results in ultra-low rates. In order to resolve this problem, we introduce a low-complexity method called induced randomness. In this method, Alice and Bob independently generate local randomness to be used together with the uniqueness of the wireless channel coefficients in order to enable high-rate secret key generation. In this work, two scenarios are considered: first, when Alice and Bob share a direct communication channel, and second, when Alice and Bob do not have a direct link and communicate through an untrusted relay. After exchanging the induced randomness, post-processing is done by Alice and Bob to generate highly-correlated samples that are used for the key generation. Such samples are then converted into bits, disparities between the sequences generated by Alice and Bob are mitigated, and the resulting sequences are then hashed to compensate for the information leakage to the eavesdropper and to allow consistency checking of the generated key bit sequences. We utilize semantic security measures and information-theoretic inequalities to upper bound the probability of successful eavesdropping attack in terms of the mutual information measures that can be numerically computed. Given certain reasonable system parameters this bound is numerically evaluated to be 2-31and 2-10.57in the first and the second scenario, respectively.
Secret key agreement in distributed low-power networks, such as Internet of Things (IoT) networks, is a major requirement for deploying cryptographic protocols to protect the security of sensitive data. However, due to the distributed nature of such networks, the devices need to be able to generate secret keys locally from some common source of randomness. The randomness in the characteristics of the physical layer channel provides such sources, however, this can be quite limited if the devices operate in a static environment and experience static or very slow fading channel. Therefore, fast secret key generation in such environments while keeping a low complexity architecture for the network nodes, such as IoT devices, remains a challenging task. We design a low-complexity protocol for fast secret key generation in static environments. To this end, we propose to use a limited number of random bits independently generated by the legitimate parties, referred to as Alice and Bob, in combination with the fading parameter to create a common source of randomness. In the proposed protocol, Alice and Bob share their random bits over the public channel, assumed to be a fading channel, and then construct a common random sequence. Then they perform several steps for recovery from errors in the shared sequence, privacy amplification to limit the chances of a successful attack, and consistency checking by exploiting universal hash functions. We characterize the reliability of the proposed protocol and provide an upper bound on the probability of accepting a mismatched key by Alice and Bob. The eavesdropper Eve is assumed to be passive and a successful attack by her is the event of guessing the key right based on her observations. We provide an analytical upper bound, that can be numerically evaluated, on the probability of a successful attack by Eve using the cryptographic notion of semantic security. In the simulations, the proposed protocol achieves a bit generation rate of 64-96 bits/packet, bit mismatch rate of 11-24%, bit error rate of 0.005%, 50% randomness efficiency, the probability of successful attack of at most 2-31, and the probability of consistency checking failure of at most 2-16.
Establishing secret common randomness between two or multiple devices in a network resides at the root of communication security. In its most frequent form of key establishment, the problem is traditionally decomposed into a randomness generation stage (randomness purity is subject to employing often costly true random number generators) and an information-exchange agreement stage, which relies either on public-key infrastructure or on symmetric encryption (key wrapping).\nThis dissertation has been divided into two main parts. In the first part, an algorithm called KERMAN is proposed to establish secret-common-randomness for ad-hoc networks, which works by harvesting randomness directly from the network routing metadata, thus achieving both pure randomness generation and (implicitly) secret-key agreement. This algorithm relies on the route discovery phase of an ad-hoc network employing the Dynamic Source Routing protocol, is lightweight, and requires relatively little communication overhead. The algorithm is evaluated for various network parameters, and different levels of complexity, in OPNET network simulator. The results show that, in just ten minutes, thousands of secret random bits can be generated network-wide, between different pairs in a network of fifty users.\nThe proposed algorithm described in this first part of this research study has inspired study of the problem of generating a secret key\nbased on a more practical model to be explored in the second part of this dissertation. Indeed, secret key establishment from common randomness has been traditionally investigated under certain limiting assumptions, of which the most ubiquitous appears to be that the information available to all parties comes in the form of independent and identically distributed (i.i.d.) samples of some correlated andom variables. Unfortunately, models employing the i.i.d assumption are often not accurate representations of real scenarios. A more capable model would represent the available information as correlated hidden Markov models (HMMs), based on the same underlying Markov chain. Such a model accurately reflects the scenario where all parties have access to imperfect observations of the same source random process, exhibiting a certain time dependency. In the second part of the dissertation , a computationally-efficient asymptotic bounds for the secret key capacity of the correlated-HMM scenario has been derived. The main obstacle, not only for this model, but also for other non-i.i.d cases, is the computational complexity. This problem has been addressed by converting the initial bound to a product of Markov random matrices, and using recent results regarding its convergence to a Lyapunov exponent.
Physical layer secret key generation exploits the reciprocal channel randomness for key generation and has proven to be an effective addition security layer in wireless communications. However, static or scarcely random channels require artificially induced dynamics to improve the secrecy performance, e.g., using intelligent reflecting surface (IRS). One key challenge is that the induced random phase from IRS is also reflected in the direction to eavesdroppers (Eve). This leakage enables Eve nodes to estimate the legitimate channels and secret key via a globally known pilot sequence. To mitigate the secret key leakage issue, we propose to exploit random matrix theory to inform the design of a new physical layer secret key generation (PL-SKG) algorithm. We prove that, when sending appropriate random Gaussian matrices, the singular values of Alice's and Bob's received signals follow a similar probability distribution. Leveraging these common singular values, we propose a random Gaussian matrix based PL-SKG (RGM PL-SKG), which avoids the usages of the globally known pilot and thereby prevents the aforementioned leakage issue. Our results show the following: (i) high noise resistance which leads to superior secret key rate (SKR) improvement (up to 300%) in low SNR regime, and (ii) general improved SKR performance against multiple colluded Eves. We believe our combination of random matrix theory and PL-SKG shows a new paradigm to secure the wireless communication channels.
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.