Secret-Key-Agreement Advantage Distillation With Quantization Correction

TL;DR

This work addresses secret-key agreement (SKA) in a physical-layer setting with correlated Eve by introducing an advantage distillation method with quantization correction (adqc). Alice quantizes her channel observation and publicly shares the quantization index for the error, allowing Bob to apply a partial-information correction before quantizing his observation, thereby aligning their key bits while limiting information leakage to Eve. The approach is formalized via a lower bound on the secret-key capacity $C_\mathrm{sk}^\mathrm{low}$ and an iterative quantizer-design procedure that accounts for Eve's best response. Numerical results show that optimally designed quantizers and quantization-error correction substantially improve $C_\mathrm{sk}^\mathrm{low}$ (up to ~60% on average) compared to benchmarks, with efficient use of a limited-rate public channel; this holds even when Eve also adapts her quantizers. The findings highlight the practical value of coordinated quantization and controlled public-channel leakage for robust physical-layer secrecy in realistic, correlated scenarios.

Abstract

We propose a novel advantage distillation strategy for physical layer-based secret-key-agreement (SKA). We consider a scenario where Alice and Bob aim at extracting a common bit sequence, which should remain secret to Eve, by quantizing a random number obtained from measurements at their communication channel. We propose an asymmetric advantage distillation protocol with two novel features: i) Alice quantizes her measurement and sends partial information on it over an authenticated public side channel, and ii) Bob quantizes his measurement by exploiting the partial information. The partial information on the position of the measurement in the quantization interval and its sharing allows Bob to obtain a quantized value closer to that of Alice. Both strategies increase the lower bound of the secret key rate.

Figures (3)

• Figure 1: Scheme of a channel probing procedure.
• Figure 2: Lower-bound of the secret-key capacity for $b = 3\bit$, $\rho_\mathrm{AB}\in[0.8,1]$ and $\rho_\mathrm{AE} =\rho_\mathrm{BE} = 0.8$, achieved when Alice, Bob, Eve use uniform quantizers, the GB method, and the ADQC with no quantization error correction transmission, $B = 2$ and $3\bit$.
• Figure 3: Cost $\gamma$ vs correlation $\rho_\mathrm{AB}$ with $\rho_\mathrm{AE} =\rho_\mathrm{BE} = 0.8$, for scenarios $B = 1\bit$ (dashed lines) and $B = 2\bit$ (solid lines), with $b =2$, $3$ and 4.