A Note on the Information-Theoretic-(in)Security of Fading Generated Secret Keys

TL;DR

This work calculates the reduction in the conditional mutual information between transmitter and receiver that can occur when an adversary with unlimited computational and communication resources places directional antenna interceptors at chosen locations and shows how the key rate can be driven to zero.

Abstract

In this work we explore the security of secret keys generated via the electromagnetic reciprocity of the wireless fading channel. Identifying a new sophisticated colluding attack, we explore the information-theoretic-security for such keys in the presence of an all-powerful adversary constrained only by the laws of quantum mechanics. Specifically, we calculate the reduction in the conditional mutual information between transmitter and receiver that can occur when an adversary with unlimited computational and communication resources places directional antenna interceptors at chosen locations. Such locations, in principal, can be arbitrarily far from the intended receiver yet still influence the secret key rate.

Figures (2)

• Figure 1: Probability density functions (pdf) for different path settings. The inset graph shows the pdf at Bob for an infinite number of paths (dashed), 6 paths (dot-dashed), and a colluding Eve who has perfectly intercepted (see text) 5 paths (solid). The sketch on left illustrates the nature of the colluding attack where the solid (black) lines indicate some of the potentially many rays towards Bob that Eve intercepts, and the (red) dashed line indicates one of the potentially many 'interference' paths to a directional antenna held by Eve.
• Figure 2: Change in the conditional mutual information between Alice and Bob as function of the diameter of Eve's directional antenna (a circular aperture) for different path conditions. Six paths (top figure) and 20 paths (middle figure) are used to construct the approximate Rayleigh distribution. One calculation (bottom figure) on the 20 path scenario assumes zero receiver noise at Eve and zero location error on Bob. Results shown are for 1 million Monte Carlo runs.