Variational Probabilistic Quantization for Secret Key Generation
Abstract
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.
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BibTeX
@misc{li2026variational,
title = {{Variational Probabilistic Quantization for Secret Key Generation}},
author = {Xinyang Li and Vlad C. Andrei and Peter J. Gu and Yiqi Chen and Ullrich J. Mönich and Holger Boche},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03205},
eprint = {2609.03205},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03205},
}
RIS
TY - UNPB
TI - Variational Probabilistic Quantization for Secret Key Generation
AU - Xinyang Li
AU - Vlad C. Andrei
AU - Peter J. Gu
AU - Yiqi Chen
AU - Ullrich J. Mönich
AU - Holger Boche
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03205
UR - https://arxiv.org/abs/2609.03205
AB - 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.
ER -