Bob has a detection *andhis count has occurred in the same basis that Alice used. An *error  event is a sift event in which Bob decodes the incorrect bit value. Alice and Bob employ a prescribed set of operations to identify errors in their sifted bits, correct these errors, and apply sufficient privacy amplification to deny useful key information to any potential eavesdropper (Eve). At the end of the full QKD procedure, Alice and Bob have a shared one-time pad with which they can communicate in complete security.***

In long-distance QKD systems, most of Alice’s photons will go undetected, owing to propagation loss and detector inefficiencies. Dark counts and, for atmospheric QKD systems, background counts can cause error events in these systems, as can intrusion by Eve. Employing an attenuated laser source, in lieu of a true single-photon source, further reduces QKD performance as such sources are typically run at less than one photon on average per bit interval, and the occurrence of multi-photon events, although rare at low average photon number, opens up additional vulnerability. Security proofs have been published for ideal BB84 [@security1], as have security analyses that incorporate a variety of non-idealities [@security2]. Our attention, however, will 