Finite Key Rates for QKD Protocols with Data Filtering

In this paper, we derive a new proof of security for a general class of quantum cryptographic protocol involving filtering and discarded data. We derive a novel bound on the quantum min entropy of such a system, based in large part on properties of a certain classical sampling strategy. Finally, we show how our methods can be used to readily prove security of the Extended B92 protocol, providing the first finite key proof of security for this protocol against general, coherent, attacks.