Secret Key Distillation over Satellite-to-satellite Free-space Optics Channel with Eavesdropper Dynamic Positioning

TL;DR

This paper analyzes secret key distillation over satellite-to-satellite free-space optical channels considering a dynamic eavesdropper whose position can change, providing bounds on achievable key rates under realistic constraints.

Contribution

It introduces a model where the eavesdropper's position varies, deriving bounds on key rates and optimal eavesdropping strategies for satellite quantum communication.

Findings

Optimal eavesdropping on the beam axis in long-distance cases

Key rate bounds involve Bessel function integrals

Eavesdropper's position significantly impacts achievable key rates

Abstract

The conventional omnipotent eavesdropper assumption in quantum cryptography study can be too strict for some realistic scenarios. In this paper, we study the secret key distillation over a satellite-to-satellite free space optics channel in which we assume that the eavesdropper (Eve) is restricted in her ability of power collection due to the limited size of her aperture but can change the position of her aperture to gain advantages over the communication parties (Alice and Bob) and we determine the achievable key rate lower and upper bounds with respect to different scenarios. We first study the case where Eve is behind Bob and we prove that the optimal eavesdropping strategy for her in long-distance transmission case is to place her aperture on the beam transmission axis and set Bob-to-Eve distance equal to Alice-to-Bob distance. We also show that the achievable key rate would be characterized by a Bessel function integral related to Eve's position in a short-distance transmission case. We then investigate the case where Eve is before Bob and show similar results with Eve's and Bob's roles exchanged.