  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.
