  We present a new technique for proving the security of quantum key
distribution (QKD) protocols. It is based on direct information-theoretic
arguments and thus also applies if no equivalent entanglement purification
scheme can be found. Using this technique, we investigate a general class of
QKD protocols with one-way classical post-processing. We show that, in order to
analyze the full security of these protocols, it suffices to consider
collective attacks. Indeed, we give new lower and upper bounds on the
secret-key rate which only involve entropies of two-qubit density operators and
which are thus easy to compute. As an illustration of our results, we analyze
the BB84, the six-state, and the B92 protocol with one-way error correction and
privacy amplification. Surprisingly, the performance of these protocols is
increased if one of the parties adds noise to the measurement data before the
error correction. In particular, this additional noise makes the protocols more
robust against noise in the quantum channel.
