ARQ-Based Symmetric-Key Generation Over Correlated Erasure Channels

This paper focuses on the problem of sharing secret keys using Automatic Repeat reQuest (ARQ) protocol. We consider cases where forward and feedback channels are erasure channels for a legitimate receiver (Bob) and an eavesdropper (Eve). In prior works, the wiretap channel is modeled as statistically independent packet erasure channels for Bob and Eve. In this paper, we go beyond the state-of-the-art by addressing correlated erasure events across the wiretap channel. The created randomness is shared between two legitimate parties through ARQ transmissions that is mapped into a destination set using a first-order digital filter with feedback. Then, we characterize Eve´s information loss about this shared destination set, due to inevitable transmission errors. This set is then transformed into a highly secure key using privacy amplification in order to intensify and exploit Eve´s lack of knowledge. We adopt two criteria for analysis and design of the system: secrecy outage probability as a measure of the secrecy quality, and secret key rate as a metric for efficiency. The resulting secrecy improvement is presented as a function of the correlation coefficients and the erasure probabilities for both channels. It is shown that secrecy improvement is achievable even when Eve has a better channel than legitimate receivers, and her channel conditions are unknown to legitimate users.