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.
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.
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 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.
Abstract—We study the secret-key capacity in a joint source-channel coding setup—the terminals are connected over a discrete memoryless channel and have access to side information, modelled as a pair of discrete memoryless source sequences. As our main result, we establish the upper and lower bounds on the secret-key capacity. In the lower bound expression, the equivocation terms of the source and channel components are functionally additive even though the coding scheme generates a single secret-key by jointly taking into account the source and channel equivocations. Our bounds coincide, thus establishing the capacity, when the underlying wiretap channel can be decomposed into a set of independent, parallel, and reversely degraded channels. For the case of parallel Gaussian channels and jointly Gaussian sources we show that Gaussian codebooks achieve the secret-key capacity. In addition, when the eavesdropper also observes a correlated side information sequence, we establish the secret-key capacity when both the source and channel of the eavesdropper are a degraded version of the legitimate receiver. We finally also treat the case when a public discussion channel is available, propose a separation based coding scheme, and establish its optimality when the channel output symbols of the legitimate receiver and eavesdropper are conditionally independent given the input. Index Terms—Information theoretic security, joint sourcechannel coding, public discussion, secret-key agreement, wiretap channel. I.
Physical layer security (PLS) can be used to pro-vide keyless and innately secure communications by exploiting the propagation characteristics of the wireless channel at the physical layer (PHY) layer to co-generate cipher keys for symmetric encryption. While existing methods use channel state information as input for secret key generation, we consider a novel approach that derives features from frequency-time domain representation of in-phase and quadrature (IQ) samples to derive initial keys with high agreement rate. A recurrent neural network (RNN) with a quadruplet loss function is trained based on spectrograms collected from bi-directional time-division duplex channel probing between the two parties and on spectrograms collected from a passive eavesdropper. Information reconciliation is achieved using Reed Solomon codes. At the last step of the protocol, a 512-bit cryptographic key is generated by feeding the reconciled bit sequence to the Secure Hash Algorithm 3. Our experiments with software-defined radios in both indoor and outdoor environments evaluate the proposed key generation system under different channel propagation environments and hardware inaccuracies. We demonstrate that the proposed RNN-assisted channel feature extractor trained on indoor channel probe data operates successfully in two outdoor setups and produces up to 70 amplified keys out of 100 probes exchanged between two trusted parties i.e., Alice and Bob, while the passive eavesdropper fails to directly predict any of the generated keys.
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.
In this paper, we consider a situation such that legitimate parties, Alice and Bob, share an identical source to generate a secret key, and an eavesdropper, Eve, can access a correlated data that is stored in a storage with bounded size. Then, Alice and Bob want to extract a secret as long as possible. We show a privacy amplification theorem for this problem, i.e., we clarify the rate of key generation for given rate of Eve's storage. The problem can be regarded as a dual randomness generation problem of the Wyner-Ahlswede-Körner type source coding system, and the techniques used in the proof are exchanged, i.e., the so-called Markov lemma is used in the converse part, and the so-called image size characterization is used in the direct part.