Variational Secret Common Randomness Extraction

TL;DR

This work addresses secure secret-key extraction from correlated observations in the presence of an eavesdropper by proposing a practical two-stage framework that combines variational probabilistic quantization (VPQ) with adversarial leakage control and a secure sketch for reconciliation. The VPQ stage uses probabilistic neural encoders to produce nearly uniform, highly correlated symbols while minimizing leakage to Eve, with variational lower and upper bounds on leakage guiding adversarial training. A code-offset secure sketch reconciles the VPQ outputs into identical keys without requiring additional privacy amplification, ensuring secrecy under the VPQ objectives. The framework is validated on fading wireless channels and further extended to sensing-based physical layer key generation in ISAC systems, where range-angle maps serve as correlated sources; extensive simulations and real SDR measurements demonstrate robust performance, even when Eve has partial knowledge of Bob’s position, and transfer learning enables generalization across environments.

Abstract

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.

Figures (7)

• Figure 1: cr with public discussion.
• Figure 2: Overview of the proposed two-stage cr extraction framework.
• Figure 3: Test results of the extracted sequence in vpq stage for plk generation from fading channels example. The x-axis is $|\mathcal{W}|$.
• Figure 4: Test results of the reconciled secret keys in the second stage for the fading channel example: key mismatch rate $\Pr\{K \neq L\}$ vs. key rate $\frac{1}{n}H(K)$ in bits.
• Figure 5: Examples of synthesized and measured ra maps of Alice (above) and Bob (bottom).

Theorems & Definitions (4)

• Definition 1
• Remark 1
• Remark 2
• Remark 3