Finite Key Security of the Extended B92 Protocol

In this paper, we derive a new proof of security for the Extended B92 QKD protocol. We derive a general entropic uncertainty relation for QKD protocols with data filtering and rejection. Our bound requires one to determine the size of a particular set derived from a classical sampling strategy. Finally, we show how our methods can be used to readily prove security of the Extended B92 protocol, providing, to our knowledge, the first finite key proof of security for this protocol against general, coherent, attacks.