  Quantum key distribution is the most well-known application of quantum
cryptography. Previous proposed proofs of security of quantum key distribution
contain various technical subtleties. Here, a conceptually simpler proof of
security of quantum key distribution is presented. The new insight is the
invariance of the error rate of a teleportation channel: We show that the error
rate of a teleportation channel is independent of the signals being
transmitted. This is because the non-trivial error patterns are permuted under
teleportation. This new insight is combined with the recently proposed quantum
to classical reduction theorem. Our result shows that assuming that Alice and
Bob have fault-tolerant quantum computers, quantum key distribution can be made
unconditionally secure over arbitrarily long distances even against the most
general type of eavesdropping attacks and in the presence of all types of
noises.
