Effects of Quantization on the Multiple-Round Secret-Key Capacity

TL;DR

This paper analyzes how one-bit uniform quantization affects the strong secret key capacity in satellite communication channels with Gaussian noise, showing a quadratic decrease as channel quality improves.

Contribution

It demonstrates that applying a one-bit uniform quantizer to noisy observations significantly reduces the secret key capacity, especially as channel quality improves.

Findings

SK capacity decreases at least quadratically with channel quality ratio Q when using one-bit quantization.

Quantization impacts the SK capacity in satellite communication settings with Gaussian noise.

The analysis provides insights into the trade-offs between quantization simplicity and key capacity loss.

Abstract

We consider the strong secret key (SK) agreement problem for the satellite communication setting, where a satellite chooses a common binary phase shift keying modulated input for three statistically independent additive white Gaussian noise measurement channels whose outputs are observed by two legitimate transceivers (Alice and Bob) and an eavesdropper (Eve), respectively. Legitimate transceivers have access to an authenticated, noiseless, two-way, and public communication link, so they can exchange multiple rounds of public messages to agree on a SK hidden from Eve. Without loss of essential generality, the noise variances for Alice's and Bob's measurement channels are both fixed to a value $Q>1$, whereas the noise over Eve's measurement channel has a unit variance, so $Q$ represents a channel quality ratio. We show that when both legitimate transceivers apply a one-bit uniform quantizer to their noisy observations before SK agreement, the SK capacity decreases at least quadratically in $Q$.