  The lists of bits processed in quantum key distribution are necessarily of
finite length. The need for finite-key unconditional security bounds has been
recognized long ago, but the theoretical tools have become available only very
recently. We provide finite-key unconditional security bounds for two practical
implementations of the Bennett-Brassard 1984 coding: prepare-and-measure
implementations without decoy states, and entanglement-based implementations. A
finite-key bound for prepare-and-measure implementations with decoy states is
also derived under a simplified treatment of the statistical fluctuations. The
presentation is tailored to allow direct application of the bounds in
experiments. Finally, the bounds are also evaluated on a priori reasonable
expected values of the observed parameters.
