  It has been widely claimed and believed that many protocols in quantum key
distribution, especially the single-photon BB84 protocol, have been proved
unconditionally secure at least in principle, for both asymptotic and finite
protocols with realistic bit lengths. In this paper it is pointed out that the
only known quantitative justification for such claims is based on incorrect
assertions. The precise security requirements are described in terms of the
attacker's sequence and bit error probabilities in estimating the key. The
extent to which such requirements can be met from a proper trace distance
criterion is established. The results show that the quantitative security
levels obtainable in concrete protocols with ideal devices do not rule out
drastic breach of security unless privacy amplification is more properly
applied.
